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Closing Round Table  Are pure and applied mathematics drifting apart?
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playing Welcome to the closing round table 1st I would like to introduce panel which consists of fine very distinguished mathematicians my farright amended Collison professor emeritus at the University of observer and a former president of iron you his research interests are in harmonic analysis and dynamical systems that will evolve panelists the recipient of many awards and I decided that it would take far too much time to Mr. Mole but I make an exception in reminding you that lender Collison was awarded this year global choice which we amending congratulations if you would like say so much a new values its collaboration on several fronts with the Norwegian Academy of Sciences and Letters and the Opel thought so next Ronald push areas of mathematics and computer science at Yale University and his research interests or analysis and particular harmonic analysis wavelet an application information vs. Inc a lot each Ochoa right rebounding the best of mathematics at Northwestern University former director of the Max Planck Institute of Mathematics in Bonn and a former chair of the metal and program committees of the ICM and his research interest like in algebraic geometry and number theory differential equation and mathematical physics on Monday Judge left helmet points professor emeritus at the University of Kaiser slot is a founding member and former president the European consortium mathematics in industry and his research interests Lauren kinetic theory and fluid dynamics and finally on the far left Peter Sonic a professor of mathematics at Princeton University and his research interests foreign number theory and analysis just in case of troika some point my own views on the subject of the roundtable at what analysis especially the countless variations and its application to materials by way of introduction perhaps I can show the 2 other I know of which the pure and applied mathematics teacher literature visually but it was the first one is the 1st issue of the journal journals divider From this journal which 1826 and the contents of the 1st issued a
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show that actually see several up papers by Opel and 10 years later the 1st fully with the Journal de maturity of eradicating Duvall still appeared and here you see the paper was a much more plot the authors include Correa will only Jacoby and still bad for 1st issues John D. it killed volumes of these journals incidentally Erector digitized and entry accessible which is where think images the pure applied mathematics explicitly mentioned for nearly 200 years would doubtless recognized thing some way different before that and the topic is whether they are drifting apart each panelists will develop a 10 minute presentation and that the subject will be opened the flawed and hope we will have a lively discussion so most of them comes to begin Red Square Berwick Reser my they may have assisted different phases of the 1st
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chorus earned general education that is of course death important learning to read and it is a very important for all over society and the 2nd to intonation too the year of were in mathematics as the language of sigh and physical with the way in which are going to use the word applied mathematics is the language of science and a 3rd aspect is the course the sub will be sold are the logical system and it did it for most of us are not represented and we must clearly understand that of history of the fall Baron that it is absolutely vital for the continuation of a sign that read out so much 2 they good relations with the other 2 were as they so they acid to the question or if their mathematics and applied mathematics drifting apart I would say that we we should make every effort that it doesn't happen and I would like to get some out of the word Dave stores we are not really get fish but by the region do antibodies ourselves so I should like to concentrate on the U.S. aspect of the EU East you as for closer the teaching of mathematics a really like to talk about mathematics and applied mathematics in these awarded which used to be indicated that applied mathematics some kind of
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code of all of the mathematics and that we are looking for ways of applying and as folk Ortiz Court material from the point of view of all history or through this year's mathematics has still to be being beaten film nature and we have observed the world Frank said that so nature can be coordinated to do and they for those who a these started with a your material course and numbers and then we we will know how difficult it has been make 20 years he said that in the end of something don't get it the look is and it's been around a long before going 200 years you know in the Nordic assisting if we take a subject that Over lifted its but it a show that I told but anyway it has been billed as a mathematical subject in my lifetime and don't think the future can see new area emerging but mathematics is missing and the most spectacular there is probably a computer scientist nevertheless but I have to Eugene mathematics it has always been done in Maynard deducted way that run goes from the general to the special I did it as a logical system or being at 5 and is contrary to traditional ways of seeing should be toward but let me mention to the these as happened in my lifetime when I started studying at the university In 1945 the 1st lecture was devoted to they didn't really tough and redefined continues Frankfurt with alone and that does and we had actually we have definitions and we have no money debated don't know what as the number of students have been released and very interesting the logic of the carries 1 has existed being kept in typical Mathematica the all you have all of us the mathematics teaching and to put it in in starting way I would like to say that it's only applied mathematics that remains saw and we have I guess all of us experience how there has been pressure from Of the From physics of technical subjects biology that they wanted he said mathematics and that we don't you know way and I would like to to stay there I just don't see the point because we have no they don't see the effort 2 were implemented any kind of inductive where your teaching that is going from examples cases and applications to the cones and you would think that the year use of computers would have changed in the weight but that doesn't seem to be the case told we steel fumbling for ways of using computers and so right disease here today would be to say that we should make really concentrated effort to make our teaching into the entire teaching we single Over different ways of Eric accommodating students with different interests so are a major shortly over water warm could possibly do 2 to change here 1 of these central points created the attitude of all over sense the city and also would calling everybody knows that most were most mania mathematicians are really these interested in in things which are not leading the twoyear new Richmond and and the there you just get disease among my In other areas the missing youthful you can count on the contrary to petition and it is my wish that you would do Will we would also try to to work and that his situation so so what could be done is that I have made by MAC . cn of the 1st there there were some of the films a called 3rd review will be between teaching and you've got areas that it is still in Sweden most departments which are ride have separate buildings and we don't this year the year due to the State Line area and you in another area and it would be my wish that April the plight interest would be involved Bolivian indeed cost
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doctrinal there and the teaching of the basic courses and also 1 would lead to a change in the year it killer is unsuitable wary and so I just up the use Over all computers In end he year into teaching and most we should they be accept the fact that most students are not being toasted rap are where the main yours interested in large but some of the most interesting in other areas and wants to do it should accept that and we shouldn't who put our values of people who don't you want them in another wire could compared these people How you know at how do I have no idea how the court right where you can still use it and it's similarly people would learn refractive they only want to be able to read book and understand the formula that they have toward the other courses and I think twice wouldn't kid decide wants these really natural attitude after resurrecting said we know it users Rosa a sophisticated and not the he is also said to be for example something like he is part differential equations everybody should have a word about that they are going to need somewhere else and finally there is a movement in India where they found us to make a make a difference applied different sections so much and I think you think there are a few mathematics there is endorsed in mathematics and that God mathematics and teaching mathematics of Richard different organizations and meeting and leaves a lot and I think that makes sense still beat and they have returning but nevertheless that should be be places where you need and where the people from these areas cab together and can change it opens and you have wove code but I will try to address the issues are drifting your for the 3rd reprimanded for years the they cortical system of different species of hotter attrition parent each pieces like a stink of better than the other day they should know it that the world recommend expanded dramatically our universe is so much bigger that and if everybody is drifting apart from everybody else but in reality we which are life substantially what seen I would say over the last 2 decades is making insertion half the computer line with the digital age now that that insertion is occurring in a variety of levels on this sort of every ability to collect numbers and collect their path to the ability for the petition drive long experiments in the end I would say that you've got we're here he would probably run experiments like crazy like magnets To End everybody of knowledge and it will if you ask the question of the pure applied who just laugh for In a way the we think this is mostly social and not necessarily electron this Congress and many many people and many of the talks on related to outside scientific fields or inspired by outside scientific fields and the way I see it now is that in fact indeed from the imitation fuel efficiency not necessarily in the areas of applications is actually much greater than lost is sort of the a pre Newtonian time In way and we don't have the managed to do the simplest of old saying we don't have descriptive language tried various things and leave we don't even the ability to define the geometry need to be defined in the real world so I think there is a serious opportunity here from the petition that opportunity to realize we need to follow line Leonard said of revamped on teaching style and say not that they saying I'm not advocating changing what we teach and just the way that we do it in a way that makes it more transparent from people who don't want to invest in their friends that somebody was born mathematics in his blood the opportunity is really that could be the same occurred in they sort of physical scientific revolution and that kind of Newton lively which is that there is indeed a quantitative and describe specifically criticized all kind of phenomena that surround a number of phenomena as is and their complexity is really growing exponentially just because we can and so did she they can generate a few overwhelming quantities all over the place where this is where data that document they that sent said they found a best back so for months let me give you an example of the can maybe you have the results of some medical tests of blood tests to or some number that you get you'll want to evaluate the functions which is how I'll see you are held that we're dealing with a very simple object which depends on 10 and 20 permit here we don't have the tools the approximate them with read heard around the board today telling us something of what about about some potential tools but this is the most elementary object of dramatic function except unfortunately the function and make many more parameters then tree used to duly for computers from number of that baby print in reality you may have sent thousands of millions of them the 2 of them out there what is needed in this context is for somebody think deeply and come up With his potential solution tho mathematician pure there were loads of solid necessary computer scientists are not trained for the job and I know a lot to the example that having to do with his acoustic calculations for medical applications from Leicester completely revamped for the matter reorganized everything you need to do we build the language for describing the object you can't go anywhere it doesn't do us any good to just throw a big matrix of some problems still in your problem and matrix of that that doing so the the obstacles confronting us actually much more until the everywhere and they require these ability to build the language to organize a very complex ought to organize the mint in a variety of geometry so I just described miniature goes very acoustic into full room that's a problem that 20 years ago nobody could and even now I doubt that is more than maybe 10 people in the world who can actually accomplish anything because the object which is you
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hear the echoes of everything Christa here is so complex that the less you build a language you cannot use formal because followers will not deal with but unless you build a new language to describe it know that's 1 opportunity similarly but only if you go to the social sciences would do face just documents or a machine learning on the field of that sort of language and the geometry to describe the object that you want to manipulate their internal relations between them and all of that is yet should the the timing people of the kind we had at the beginning of a few of them we had last century like chain load the wrote here recognized geometries of people consistently ignored all of those are opportunities for mathematics and that mathematics is pure although the opportunities and the challenges that come in from the outside world In the past it has always been that the outside world was probably the most inspirational pushing to let his governing structure and it's very nice to be 4 much of it by internal ideas but that may don't should be that arrogant and thinking that we know Everything that needs to be done and we should let the world tell us and and I said convention is really what's needed and that the crafting and the people who crafted mathematical to a list of people who are interested but tool the application that test if you wish effective but the people who told the should called the community may be working like challenge as an engineer but he built mathematics and it was it is purely a matter of what we know what we said effect is being used consistently every his probability applied field of course is what so I think basically we see a by various communities machine communities bioinformatics computer science community we see emerging a variety of methods which are serious somewhat odd extraordinary successful and the question is what are the underlying structure that enable us said that it will work on not work and what they think achieving what are they real Oh trip through from the wounded were superb job Pugh pollution frigid Yuri burning but but like too good I Europe the magician and what I would like to discuss Europe is uh we need impressive person position that lies in the base Our distinction between the white commodity later that Maddox can tell us something about these external world as that mathematics can be cognitive tools all those doesn't like come to tool it doesn't see products anything specific in view of the surrounding world so In order to understand How long mathematics is flights of the state of the convenient for me to do some divided into the forwarding authorities the functioning model Fiore metaphor and medical model describes because of the range phenomena quantitatively or quantitatively but are lazy pretending to be something war a forward 1 of these Our more successful polluted models is but it is model the by cyclists describing door emotions about 150 around and 1 of the latest models which does model of the tiny guard model describing interruption of the amendatory articles it's wrong 100 260 190 want source 1960 and Jr. earlier quantitative models lead the V observable reality by ingesting a numerical values of sometimes dozens of free parameter list went to some dark model and such models can be remarkably and there of course the quantitative models all foreign inside the stability instability attract critical phenomena as an example I hold a recent report which is dedicated to predicting of surge well my sides in Los Angeles is a myth of Lord is it uses them recognition frequently result we have found out what to learn of the homicide rate is preceded within 11 months by a specific veteran of the crime statistics bought burglaries around the simultaneously escalating Wyo wrong door is homicides declined what changes deletion and the decline our of the dawning profit of or sporadic each lasting up to 6 months now the age of computer is seen the proliferation of models now produced on an industrial scale sold numerically and very often used as wood boxes he the computerized procedures and oracular Out of prescribing behavioral human use for example financial from search what distinguishes mathematically formulated fury from the model it is primarily higher of irradiation Fiore suitors and aristocratic model or if you reach model is a democratic the model physical fury of also physical figures generally for the described the world with absolute precision will only be feed the world consisted of some restricted the rights of stuff massive point articles of being only the law of gravity a recovery riding for the June reading here is From Sept the reality beyond the back to world reality which may be dressed only by Of article tools from episodes to the bill's language of nature to Quantum's of strings and the article metaphor when this virus is a cognitive tool postulates that some problems range of phenomena might become the article construction probably the most known the my article for now it is artificial we know very complex systems which are persisting formation because of constructive and there try trying to compare them with human race each region of the world but still almost as all so at the moment it is a very interesting with a modicum of and what it allows us to do mostly is Chu so cut out to wrong assumption is the theory them With some there will no reality out
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they would not why nearly it is the mathematical amid the worst more often than not some models and fear is also are used Monaco amid the force that is largely them contribute to changing reduces the world in themselves and I am a little bit concerned to about a proliferation of both Michael models which are hidden in sight a computer's hardware and software concerns about moral issues that are not fulfilled address children in discussing the application and in discussing VUT of marks in just chill very briefly showed you what I am concerned about by all of the recent sentence sentences as Chile from a recent bill the markets and war by seeing the center was originally victory method addicts also and it is indispensable true that's what I mean these effect of fragmentation bombs on Hulu borders we tasted back humanitarian breaking tasting we see them articles tuition most to please think of Africa a which that but now you get a little bit of contrast program after amid a series of applied mathematics that we go back down to earth maybe that is the difference between the purity of the plight of the petition now life but I must say we are not 50 apart With respect to his last sentence I totally agree with them but from the point of view I would like to change a little bit of a point of human now when I have spoken with people opulent applied medics drifting apart some settle these these old question we had some say yes I believe it is really a question of the department of the people the pure and applied like each other then it's fine if they don't you have a trip to a point they didn't but at the I would really like to change we always do what if mathematics would be the mathematics do we academic mathematician bewildered mathematics are we really there is 2nd World in my opinion there's a 2nd gold medal at least not trying taste working not my yes there it is there's 2nd work the mathematics and in the 2nd World War mathematics almost all our labor those people we sir they are not in general entering our local both backup mathematics they go somewhere else and they go into the industry they going in Barrington insurance is they going R&D departments that he has set the goal of mathematics out what side I what was outside of academia industry and this is what I would call mathematics as the technology and we should all be very happy that mathematics has become a technology that's wrong with 1 that already described it is really for IS also even if when with a pure mother but it helps us a lot that would come point so these mathematics and the technology 2nd will of mother Maddox pure or is it applied found let me described a little bit the result Altschuler although I had together with the psychologist and a story of its nice for for a mathematician to work with other people and that it was footslog Foundation project and we were trying to find out what happened to all the credibility of Germany's mathematics in 1998 8 years ago said and you know this psychologists unbelievable they have really asking question if these people on the players that would have never dared to ask I played in the ghetto children who are were based new profession and you have friendly and so on but she did and people answered that the people aren't said then and the person what what can be done in the next 8 years what happened today did did treaty if wishes come true or not misunderstand had a 3 thousand regulates Germany in 1998 that's quite a lot I think the number 2 days even higher and now demand is very attractive in Germany you may ask why and on these 3 1400 went into high schools so they normally become high school teachers and the other ones 1600 made a people fool or knowledge Master and and we aren't they people and seized hundreds of these where willing to answer that question is a very good sample and be aware that 600 of 1600 altogether is a rather good assembled and we people again In the following years 2001 . 3 in 2006 I want what what happened what came out 1st of all of these deceased of these 1600 if you take this as a sample all we can and became academic people I mean they entered universities for research centers so he always about 10 per cent and we pulled back the Theada 1 80 per cent I'm mean percentages of feuds somehow 80 per cent of work areas solved scientists in R in banks insurance system consulting and so on the basis of mathematics that they don't do much pure mathematics I must say I have lost 20 years formal peace of mind will work now and in the street and that will laughing and saying you really are you kidding me if you ask us to pure about replied Of course we do do not make tough force models and and Icarus if we do mathematics and or not although they do revealed that thinks so if I solid correctly from the scene 25 per cent credibility are doing mathematics industry duress change they do management data they don't do they do something which is not really but 25 send out quality and 25 of the 10 per cent which goalie academia I played in the 2nd will of mathematics is a little bit larger than the 1st world and we should keep that in mind there was a citation and the chairman of values of society of a mother of 2 who works at IBM he
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said madam and we should not overdue overestimated the value of mathematics this is the life of the mother of innovation but maybe there it's good be devise very active midwives which so so many boats is it would the self just what it is the man then there is found 2nd at least bears many people do mathematics at the 1st world but of course they do mainly applied mathematics now on these people drifting 2 of the money what would you say I need they will set the world on the 1st floor pure mathematics I don't think that they know whether they drifting about they don't see each other so far away How only these 2nd World War and Peace Conference if I am very optimistic that would save 10 Of house so you see is an earnings yield big difference between applied mathematics industry and the pure mathematics happening here and these of course is very very bad I think it would be easy he said damage verbose wills it's a damage for the sake of world but a world of mother Majesty history of course there were some arguments are ready we heard by 1 another's of course we need more mathematics to enter it is not at all it in medicine for example we are totally meeting good models which really tried a complex system of body sold we would personally need good Madam mathematics which deals really live debt problem but our mathematicians really dealing with the problems yet they feed their own way if not by adopting and for for the 1st full of course 4 0 the daily Globe dead where the headaches as a technology offers a look at these people 1st I would new challenges that will said many many with problems come from east Outer will certainly public prestige they be 2nd World ends money if we have contact with them and attract students but it's not such a minor thing so I think really polls will need each other very urgently need each other but we have to do something we in the 1st will have to have open minds we have the goal the industry and feed their problems to speak with them to get in contact with them that they know we care of them and they would be interested in what we are doing a commitment a a a Peters OK eyes because a pure mathematicians very keen interest in mathematics broadly tried to follow mathematical topics another applied to much more difficult and the main credit based on actual double major method of blood at a group difficult choice choosing between pure my views going to be of little extreme from the pure math side but I think that's a good proportion of the people in the audience to Somerdale try From that angle and also says I think 1 views of highly influenced by once a local interaction that whatever your department the discussions you have your colleagues impact to and you will see my views on the by of this work but went off thank you that support and so firstly drifting apart will serve earlier we have to take Inter campus inflationary process of everything drifting apart but even given that it is my feeling that they are drifting apart have been in mathematics for 30 years and mother of the very short period my own experience is that it's not exactly what it used to be 30 years ago and I think 1 of the big In fact the computer changing abuser many things is it a problem I think it is a problem but not 1 that's that's serious think that these kind of matters should evolve naturally it with good science surviving and lots of good science going away and the think that's what will happen to about they all along with the suggestions or which of which sounds very good I will mention some alarms sounded by some of my younger colleagues who I think we should therefore they take a very may be controversial way of dealing with this question of whether they do it and drifting apart but trying to see what is good about what's good applied math is anything in common in fight between these 2 activities erotic giver a formal definition of what pure Mathias I would be very dangerous to show that I would get out of the hole and but I think there's 1 thing that was pure mathematicians evoking the Parramatta petitions We will also recognize that when we see a block of Foxwoods use rap you can see something that's really good exciting and cuts to the bottom of the problem I think the key ingredients America without me once the use guess there's a lot yet crap sir the key is sort of cycle ingredients In mathematics of firstly inside medical inside of them become conjectures a series language is a crucial but To me the underground mathematics of something never give up is that of proof to me once broke much mathematics at least that much I the difference between mathematics and of the Son and given the exciting week we have here let me give those preservation conjecture as the epitome of the sort of conjecture the conjecture which when put forward immediately clarified what 1 is looking forward as Albright conjectures if they showed a grant of was the founder before much less interesting but it appears to be true it's a unifying conjecture it clarifies the shape of threedimensional topological spaces is nothing in its something that was obvious and was something that was built up with many examples of theories that developed in order to come to that conjecture so conjecture is of course a major part in our subject but 1st the thinking about the really have never spoke recently but I think you could say this was entirely problem rather than by application and it's them good even as driven in many fields have such powerful conjecture that unified theories and I'm not talking just about these great conjectures and I'm not talking about mathematics that sort of it comes once in a very very in a blue moon it said so there's that border the saga which is conjecture and then goes out for an hour without proved but without proof it's not about subjects that we really need that is
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seems clear now aroma proved this conjecture that sort of this is good as it gets may have been other successes of this magnitude as us said we can't judge or mathematics such great success but this is what we strive for and I think many people young people very strong people going to methods with sort of remind me of course we'll get disappointed users but I do believe is driving central conjectures what right so we have cycle of conjecture theories both from the conjecture solution and then good solutions problems always develop further conjectures and further theory and the cycle seems to just go around and books for was someone from outside might look like a recipe for disaster this is completely internally driven it looks like the recipe for rock thereof subject infected even within mathematics subjects that are introspective that interact with no other subjects that I just 3 experts in the world talk to each other midnight of paper to the animals and you get the 2nd expert opinion and of course the best thing ever written but you can't get a 3rd opinion that's a problem and such subjects eventually shrink I think revolution is used the best way to let these things right now but I don't believe that mathematics is purely drove and I strongly believe that we all want to argue that fewer needs other sciences this my point as badly as they need us everybody there would that we need to develop more serious for more applications of the beautiful applications them there is a very important to make mathematics as this real living in gold Arab pure mathematics abilities because of the success as we've seen in recent years and it is not the case that this could have been internal if their initial conditions we are at the stage and because of the Giants we have around I don't think so I think that we impact From the outside limit continue this With this 1 example to repeat what Hamilton said in store here last week so no one's work depends heavily on how things work which in turn is based on rigid and as Hamilton explained Richard flow was motivated him by Einstein's equations in fact the process the very process and went through in writing down gravitational equations in equating the unease invariant sensors that are around so when it was forming his reaches equation 25 years ago and yet to everything was very experimental he relied on us thing that knew about Einstein's equation is getting a lot of confidence that is on the right track so the indirect about means of Sciences example impacting this particular program which on the face of it seems very subtle but it does give you the confidence that you the right direction and I could give you many many examples of some of the things where beat out import comes from often from physics but much from computer science of course the more complex the applied Massimo engineering the effect of the order to see but we do live in a world where we expect each other and I don't really we're closed cycle and we do need applied math just on social logical level it is a story that always find someone comes into my office and I wanted decide with kind that with a mathematical physicist decide whether somebody a mathematician physicist and this tell the difference between these 2 cultures and 1 that I think shows out weakness in a bit of a rich a mathematician always them until they knew how complicated what he's doing might prove thousand pages long and estranged discipline where you have to come but when you have the right of doesn't it probably means you don't really understand what today doing because of some of the white on just simple what is doing is always lying because it is hiding 50 60 300 pages of that just straight would cover budget this of culture is 1 that I think expires With the difference between man and theoretical physics that something has to be good at best be complicated is something that evolved orders of mathematics amount it seems strange unfortunate merely we always looking for the simple things the real truth is somewhere in between that's a social of to good applied math about which are really very little right thoughts I lost a few people but many 1st I complete extreme view that you'll find I always remember this article by article of course he made that part of of the article by what's called applied mathematics and mathematics didn't bother to read at them for was asked of them but I wonder what he's got to say so in red and it is very entertaining is a good writer but that think it's entirely got in bad points in the article even if it isn't that some interesting points but I think the 1 bed is very relevant to what I'm saying he argues that mathematics exist without application applications generally necessarily applied for asylum cases of course mathematics exist will exist but the Commerce you would argue it is as for the I don't agree with them at I think mathematics cannot exist without application even the most pure math would not be reduced today if it weren't for the application of course if you look far enough that everything is you talk about life in New Salem philosophers mathematicians applied mathematicians simultaneous but today with everything requiring people to be very specialized it's much harder to be universal but even so I strongly believe the impact of applied petitions is crucial to the development now lost a colleague of mine when a year younger and younger but opinionated applied mathematician which His opinion value as to what just to give me a definition what's good applied mathematics and responded as as follows it has to be relevant application areas whether the application areas in science Imagineering Technology industry that's 1 thing you demands the 2nd thing and this is a founding to help putting the relevant application area on a solid sound scientific foundation Mr. Picchi requires lighting up the mathematical foundation emphasizing the foundational aspect of a mathematician is posted in another sign and then he added and that's what worries me personally I'm very worried that mathematics and applied mathematics gradually drifting apart and he says this is particularly worried In the areas in which he works it works from professional scientific computation eliminate India but saying is obviously a common ground was always the common ground for mathematics and anything else and that is what really what we always feel is the crucial thing on new breakthrough ideas and applied to when I was young I was absolutely no difference however I'm beginning to feel may be adjusted so that it's not really is differences so that it us said in June that I can't imagine pure mathematics without proof not that I can imagine without proof that with who is not important with people say Well I don't even care about approach that would bother me applied methods clearly the big issues or inside an explanation of some phenomena so it is not clear to me that it proof His value or if indeed this has been so the past that it will be that it is at evaluating applications often go to a lecture and the person in especially for someone who's got a code of something my covered so why do I need a proof that it well I want to work with something that works that requires approval by presumably in an ideal world the proof will give the inside all inside will to
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approve and that was always become a world for 25 years ago was what it was all about but I think drifting apart is occurring in a think you see this the scientists involved and I'm just so early and budget saying Well I think the Goals and the requirements of an apartment all about coaching taking into account inflation I think myself that evolution will take care of things but I'm quite confident by the comments of where in and the comments of analysts who seemed to be quite a I'm a big toe so thank you is interesting presentation was virtually will work a livelier calls goodnatured discussion so I invite contributions from the these they either the comments all questions to the panel when you speak could you please use 1 of the a roving microprobe Burrows what problems and say safe most of you off is River might provoke fraud a sudden but yes Monday John on all of a subject centuries of teaching and research consultant all the years of durum brought by more fortunate article suggestions for beginning but that was working reputations of badly needed industry that normal said industry to cover all of but there's a brick begin fodder working with sessions to begin to connect with industry or they can find out that they know what students are placed in With the touched on but they were covered in books their teaching of if they know that if it's us on the radical playing a bottle of industry its or make a formal decision most not radical much in industries are priced terms you and if someone would be much influence they need to they need to understand about computing song now generally tribute to get started this is what you were talking about several weeks to begin 2 days of competence in computing it's not that hard several weeks is nothing her mother corrupt question now the brutal consulting arrangements are not so easy to come by and I'm suspicious of a bureaucratic solution product your mouth petitions in particular industry but that's that that's a possibility but each concern and virtual could begin the take some steps With what's over the medium term to be able to make some connections of their own to world to industry think that would help model on the course although some and then began the brought the 2 the 2 together Rove heart from terror scientific problems demand the ability of permit mathematicians and among you have become more wants the ball and but yes might be Jens and I am watching Mr. tested evolutionary I'd been name popular applied Japan With edition of the country for example know what I made up my beauties pure much and robot and a touch of and the other on and this is part of the pure butt arrange school provocative I plus division which includes as outlined by my my my attitude then I can their job different kind of day it up like much much markings industrial much much you can't come soon but I'll be Jules orally pure which hard and maybe fun was called to might or you can have some doesn't have true or something my team this is a picture of you the deep jeweler or or reached U.S. Patent vary with that them yes you is due more to adapt and mean light you would be more outright thank you yes site but is my question is what you're saying we are not what you think about they need to invent a new mathematics to deal with said reference suffer organization as they wait for me now biology or otherwise there would would you see if you look back at available mathematics nowadays sealed we will also put back box metaphor for snake eating its own take metaphor this working there terrific question 5 in terms of dealing with the kind of threat to Merrick said you need to deal with this biology on social scientist the more complex structures every piece of information measure linked to the others I think what seems to be emerging there's something somewhat like emergency physics I'm aware Einstein's decided physics geometry and you described a physical equations as they geometry of spacetime and later on in young males and gage fields series somehow the physicist got to the point to geometry encapsulates the relationship between all object around I think we see this emerging in In do not exist off of actually take of various kinds whether it today on the Web where you actually fast search by making every unit of were glad to each other and doing some global geometry of the lab in order to get to Google blank some others this it's a subtle and profound idea that we we happened and biology and neurology and everywhere else it's sort sort of thing its own web relations between objects which encapsulates their their jobs their internal geometry can't teach that affect my duty to moment I think it just emerging of us 2 does that have a little solitaire besides I actually don't feel it so much that these the sides of mathematics drifting up thought maybe debts because a year so of grew up in a branch which will consider flight and I never considered a Wisconsin basically few Wisconsin basically an area dude mathematics which has good application now want them I'd like to point out Is that but I really can't applied mathematics of applications of mathematics is really a very wide arrange and congress actually a discount program of Congress I can find excellent exam professor Lee told 1 problem London most prices were good
1:09:17
which we did my motivation that died of cancer completely purity mathematical among the nations not motivations and then he became extremely important in in that area light activities like option pricing for stocks on how these another kind Of application is that the mathematician looks at some phenomenal and and and and begins to think about what kind of mathematical phenomenon will be good mainly days what would have standards um is like that aren't enough a prize winner John Klein probably looking at the Internet and how it relates the lead again values of of the Paris funding matrix water China by looking down at China Of the communication came out fundamental ideas of information and and that is also at my command which it broke mindset 2nd were I was talking about but I just came down from here from my which also described some there where you actually have to do was a applicable results now I think that still the ban any of these are the kinds of many of these as and the they would be ready CDs mistake I think it's intellectual content of the that that should matter and not wanted uptick in the form I think all the city and there may be other variations of we relates field I Teddy important and now I just 1 more Is that an international calls mathematics that debts debts other scientists need that is very much and sometimes as simple thing Solana things get quadratic equations would be extremely useful and in other cases of course you really need is a very sophisticated new mathematics but that I don't feel that the thing about not really I think in in in their mathematical areas which I I is always a lot of exciting connections they make mathematically lately made up applications and daggers that come from the at so my name Is that of course from Oscar university in Denmark and the I will actually the author of disease monthend which was voted from the book mathematics and by Judy amending my Chen confident you that his boss man as a sarcastic remark and that kind of calling against the former president the American Mathematical Society cool found at that time lost best making more funds for national Foundation that fall mathematics he arranged for congressional that's coming to said it just seemed the very moment when said efficiency a mathematical technologies of the but it's annoying the 2nd College of mathematics woes transmitted television around the world with pink point to receive the game Iraq and believe me it to the broader questioned the model because I noticed that profits and went for example fund you'll come just we should all be happy that mathematics has become technology which helps Everybody it all in the nation's good innovations and Of call tenuous situation perhaps mathematics that we are confronted the degree that some of Alice series become law opted political broke annoyance anointed correctly pointed there is a 2nd College of mathematics developing that we are also going confronted with problems with that is on medical doctor Chen along with of discussing ethical issues than we have In mathematics that we should perhaps at the moment think of that Head of mathematics should be not to overstate the around mathematics in new different connection 1 of disasters perhaps of these Iran book what they have been Jan believe pulse In United States and in some European countries that deep complicated political problems can be solved like nothing by held model on mathematics base technology and I think if we try as mathematician a little bit to be more modest I love all statements about the value and is Of the Allah mathematical applications not only the ballot what we usually Channel to and where we ask the vendor we would perhaps the the the plot command that the public is that putting too much at the at operations in mathematical Technology Inc I think it is the kind of 2nd Marlowe a she will that we should try to keep jobs to substance and it had tried to be modest in our statements about possible met the medical application Newton times try dance and when I say better medical technology needed mathematics has become a technology is not so that all technologies the money to turn it around I mean it's not so that I think I don't believe that mathematics is now responsible for weapons which are in the world that maybe some other medics used can you guarantee with any mathematics you do that it not used by somebody else for weapons you can never guarantee that we can only have the following moral we use our ability as mother but as good as possible with the full responsibility for what what we we can do so we must have a moral week at would work for for weapons for example that's my decision but we we cannot say that we should stay abroad from from from from of cases of mathematics sit there may be some some s some obligation which we would not life I mean that most his passion in Germany in everywhere but I would guess I would say that we can go what I am still had good mother medics has become a technology and I would nevertheless try drill avoid any better a case of but Brokers Butch beat thank you very much disease and that that had my subject is wanted to gone on commuter as we all know that madam that pot of science and the new turn state if we can't see them it aristide part of science we note that assumed on this side because nite this phenomenon of natural so he I've ever
1:18:43
seen can be concert that I phenomenal stupidity this no and use using far more prosaic of you might think if come see their not cannot at site and I think he'll mind is a plot of up might not matter it's is making their phenomenon the by British and I think you can't do said by versions might be not that Is there point that Van Natta like to generalize Thomas St. From varying a reality problem to meant on problems at that point because that Putin for Renaissance a generalized equation all they need to reality today between Villarreal do they have set as might and a to end glass wine 2 and close Tuesday 2 and 7 other candidate to be solved by might be no immediate application its twoman mat is route that don't that and known phenomenon from this site said it's on up to like not so I don't know why I might add that secretly mathematics especially cannot Chad that actually plot matter From site and as sort of science rather planned Jan arising in that Peeler Chu comes set you tell some long I think I remember in there not as always as long gone see that carriers as part of a Mrs. Mississippi In some places died and from 0 route From the main train songs that analysts it is at fault the demand some plot of cannot be like this saying that a generalization color they may not have immediate application I think this huge share don't subplot saying it would be really that then maybe not they not have any matter not teaching thank you very much looking what wipe or with what the bulk of but you what that's if but Mr. at my name is editor of the magician I think and I want to go year I am a big believer discussion about definitions and understand are 15 From from me is replied with a pure movement it so company News slack applied some additional 38 it a science Maracaibo look populations those formulas I think it is impossible to call Ms. made by isn't possible say plan 81 or even a very successful told Muslim but there's a professor of replied with him in there should be some occasional say a show those people right musicians what ensued what mathematicians nor semantics Mr. methodology I must this question because they are practical and also makes sense for a special thank maybe I try 1 of these things that there was most concerned about let people that he defines as doing applied math be educated mathematically the traditional way he felt this was really important um that's answer when Yemeni city was very concerned theme fired added that 1 of these concerns a must direction of education and students is that some out the applied method community was not attracting the very mathematically talented people so I am just refer firstly answering your question in connection with Woody don't mean a thing am I agree with you I was drifting from that's a good question but I think there is a difference in what applied mathematician doesn't what pure mathematician does a B as he moved with of Irish mentioned heater he and of major impact on the world but he was not motivated in what he was doing my application must pure mathematicians feel they're working on problems purely uh because of trying to understand and number geometry theory equations more deeply but the application we all hope will come and it it wasn't for that would be that important the subject but we do have a different way of going about things applied mathematics mathematics thing game quoting has to have applications in mind and the style is very different if you pick up a journal impure mathematics is a theorem is approved What is an attempt of making a certain kind of discussion mini applied all scientific journals you pick up and they talk about a phenomena members a pictures of his them phenomenology which is all very interesting science but we do things very differently and and I think that with these things says is in your own department so I would like to say that I agree with you that we all the same but I think we way we go about things very different that is what social status others use them so maybe I can offer definitions of a mounting what should have been there I would like to address 1 issue that has been implicit in all talks that psychology and I would like to add psychology of institutions to lead a their camps in different buildings and not Council said well be applied mathematician building that basically corn tributes feeling of them and us and they could be just different people and all of a sudden he is applied or not and many of us have lived different lifestyle pure mathematician for wild and now very applied but a valuable size and I think 1 of the greatest experience of my life as a move to Berlin and they didn't have the Institute of Applied of pure mathematics there altogether and actually is something Bergalis valuable and people the scientists a mathematician and students float between the various areas which are defined a genie positive for both sides and that will help to keep these pieces together and I believe that driving also areas from mathematics applied mathematics for Applied Mathematics the institutions has been really their historical process look at the U.S. situation applied mathematics is basically leadership dealers French
1:28:08
liquidation the optimizer sitting in the best of engineering the discrete mathematicians often in computer science statisticians said new everywhere else but in mathematics away what the reason for this certain periods of time over parlor games that soldiers with the pardon and this since motion process we can and we should try bringing these groups together and I think that what do you an important part on the institutional side that would was solved Mineo the issues we are discussing he and I don't OK I cannot offer definition of pure and applied mathematicians but I believe that this kind of space distribution that contributes a lot of this feeling that there are other parts of mathematicians and mathematics little Photoshop a mother thank the panel for Ray thoughtful discussion they from University of Maryland I hope I have a happened pure have applied so I could try people issues a Big Board raised vary important point is institutionally what can we do I think the issue is not so much richer department that criticism is about as we do have control of this think Obama has to do with the expansion of human knowledge and endeavor and I think all this with some measure are confronted with us and particularly universities but also to should not just academic ad I think 1 mile from the states that a rapid response to this vulcanization that you describe actually is want to look for work too because wears you were talking about a Thai people who call themselves were different matter perhaps together really it's an issue of being aware of the intellectual landscape about us and that means not only talking to statisticians or a computer scientist but also to engineers and former physicists chemists biologists 1 mile but does exist the U.S. I think thriving some institutions is the development of Centers Centers that focused around maybe an application learn idea that brings together people no matter who corn games were an engineering pound whatever to work together learn from each other stimulate each other half I think just for example the mathematics department Maryland this tied with Norbert Wiener Sun earned applied harmonic analysis which involve pure mathematicians and engineers but we have a list of several institutes like that and I think we have we put our minds to we can overcome these certain intellectual barriers ersatz separate artificially alternately I think the picture the whole panel has I played that this is a human doubles it is really the right 1 I look forward to a burger future but something about my parents is applied mathematics I work come out relations but also in its applications to materials papers with electron microscopic no I believe in the value of their and applied mathematics I believe the value of their rooms telling us when computer work to me it seems that the please 3 elements of modeling analysis and computation under the old feed on each other To what is on the line I think an interesting process you start working on on it in a new area news typical some new application every summer getting interested in its menu Buick you see the disarming mathematical and learn bit more about it and at some point you have perhaps uncle but if you could offer something to this field at the same time we've not donor a degree in bias answers materials all or whatever subject it isn't so you have to somehow be humble and had put in a lot of work to to learn to London at least a little bit area so that you could break down the use language Paris really exciting process but just don't you might encounter some resistance from people in the area and 1 bus I have a wish to cut out the middleman talk directly to the person who's doing experiments and try make what's on the intervening years Gross would like to speak after have made clear what last month I did best created about definition I want proposed sale if you really believe that a mathematician applied mathematician is mathematician he or she should have put evocation of mathematician the children all basic things will be mathematical novels basic about base but let's say they face this 5 they 5 there's a people Bob published publishing he and John applied mathematics in but this is 1 thing we have something more specific in mind some other things my answer would definitely be yes but I think a better let some of the other people the panel give their view of what would you say yes with respect to the question he must have a mathematical qualification the modem amateurs that deal to a certain extent not married needs to know certain basic steps of the a meditation these rules do not have a mathematical education I mean I know many physicists who have become very good mathematicians later on would do not trump them thank if we follow Peter Sonic here he would tell you that anybody concludes formerly right Yonny Shiloh what move for Europe's planned said that I know what you mean that I think is that you did not talk about it enough for a plant that imitation would come out with the computational and this year I'm involved in it now is
1:35:32
dead he can by then scheme in computers To some procedure matters hang they the ball there it is not binding the Everest and from some conjectures dissenting impression calling the ball is To achieve was more difficult problems to find the tools To do an entreaty title challenge involves which may be qualify as being a good application for a good up but I don't like that Sweeney they intellectual novelty and content I like to think of the people in that as a person and the 2 magician citing channel with an injured knee right but and there's no way you could say that wasn't in the I thought From from from Institute I actually find it very reassuring that there some difficulty in defining separating by mathematicians and German here and I think that something that nobody took the time that was to talk about power of mathematicians pure and applied really rather different in ah mission in our world and power in our inner functioning from well wealthy the other sites pick the most boring thing here is not that we worry about creating separations between journal applied mathematics mathematicians for defining those it's really more about making sure we don't leave the again between mathematics on the 1 hand and other areas of sank Sunday in theories I work in which tend to be mainly closed the physical sciences or finance the mathematicians job is To think about whether the opportunity to think about what the properties of this model to solve a problem for me to look at where terror Our opportunities have been missed by not bringing to bear the right said tools to develop don't work on time recalled the application area and there's nobody else out there and do that if we don't fortunately I an area To a large extent were not drifting apart I of disagree with any panel members and I think that not that the talks at this meeting your the best possible proof of that question metal that same a bidding to Rome newest stroke them that if they discussion is discussed lasts for many years I'd like to be perfume each time a bolt Piedras beaches Carl Pope pulled before pages Bookaloo he will suffer of science cut Pope the more you book at both the short statements but current and which leak current said that he notes about long discussion the city but tedious a your security and leader of Aeneas circles much because says that when he the bolt I want discussion believes that it is a matter of water firms soul several people waited to see of that did show she worked and the plight of the medics I didn't hear a thing you'll suggest that he don't by assist reports but I believe that cities of water the issue reachable proposed a each I it is Daugherty the must get them produce violent because what he connected on a 2nd police station suggested that summit there is also sociological and they think he probably could be divided into sociological potent in fact by try to formulate its you wouldn't let them or suggest a perimeter of each could defiance D and probably you will the leave it to the bottom of the the Duma have some power in such a logical warned that I was pleased to hear that someone you're trying to suggest that military power of the as a rule that need to be joined the plight of medics odd of trade in services he will a case of very close to tour along with Michael Jordan oil leases details of the communities they themselves history so I would like to hear media cities another parameter beach cool idea on how to use it or any other border cities to the Commission's proposals but seems suicide the last time I could use to let me also make it a market value of these patients by remedies and Beijing's somewhat interesting 50 suspected respect of tidal waters the peace of the world argued for life medics suggested told number there for us to continue to buy them each hour I think the detainees of the 2nd World War I believe that this would be the only tool numbers which will be a member of the roses discussed and so I did what a successful copies of each worked to lumbar them what will be members of the instead of statistics suggest that polls the money from the theme of the summit chief almost and that is not to spread of course remember what some that but they deem this is like tool
1:42:54
examples begins there statistics the exempted by What's the matter In my view what support for our applied mathematics makeshift representation much better in bowls from a point of view we moved from point of view of actual 3 so I he that the the portability to them while they were not we're not reaching the analyst added if volume more or comments or quest as 1 of the I am has said was a from moral code and an ingenious scored I am a working on applied mathematics but aII my old Queen uh we should mathematics that he's 1 mathematics Nan Hua and applied mathematics and equation is it he's mathematics do 15 on technology this is the question and deceive the question that she should be uh and might madam magicians and I think that messages showed worked on thinks that that's that's the Arab and good for 4th technology and not only on mathematics that's my point of view thank you always Turkish that 1 then as a physical fund from Russian city was posted was and last year work all what a little fast as a I the 3rd person to do so on from what worked out last year's off said of the time that a must be a new blood and you know things much of that and that's for investigational fidelity and not solely on she will slow statements on him with a buttocks as users and therefore more and more general and global and armed use means that really we are standing before a simulated both socalled global got us global affairs of what it means but I'm psyched explain Lin and new phone traffic period on shares its president local of course if because we are Mr. Gates local better off I want to use a network would want buoyant but and now where is that she moves from such scientific community we have ability create new socalled global culpable when began also of February called Monday for and based on these areas weekend Judith Light yoyo questioned do and blend with went it's very powerful Buffalo be litigation or do we it based on the world will be that I still have no idea what is your medical want more of cited above is disease was my Irish annually and I don't know all icing Samsung will emerge obviously in the next game in years S that will allow us to see new interesting mathematical structure but more than that said on the worst of chore game don't in your might be it is different global analysis it seems to me that the discussion will meeting 3 different levels which I think is that makes the distinction between choosing the revolt from me of the 21 the first one is rated science itself and for me if you speak of sentence I think he can enology mathematics and applied mathematics is not a good 1 as was pointed out by some people a 2nd level as professionals most of us Our really making it living by teaching sweet means from that point of view that he what happens to our students is something which would be of primary importance to us and from that point to you have found that remark by personal into very adequate that he's so many of our have really working in that the world technology EUR for all sorts of technology and think we need to know as professionals what the graduates of do it at this level is assigned to and because he impact of science on society's growing mean bigger and bigger every year we really have also water another which is really providing answers to problems which those at the site in general it then we are asked to Amin into interfere Oh interact with the other scientists but also people from working in the world of technology and seems to me that depending on which level then the drifting s to be measured by different means it's certainly true that should take the 1st I think you know pressure because I think it and is wizardry could prove that we have not ample evidence of beef and dusty impact of new questions coming from technology to mathematics if you take the 2nd point if few things that the growing number graduates who fall in the working in meeting the society and therefore we need using the skills we give them In theory applied something which forces professionally to get a better knowledge of these petitions and the 3rd level even the other 1 which is which way and that's probably the 1 in which request ethical dimension of all professions were important in which way we can contribute to me use the scientific enterprise which is more and more shaping the and shipping the world means good and bad things at the Center for half of the by the blood of the taking a that said he get that is not to New Delhi he played till
1:50:16
With watched to live life the mad Moon mistake would have to made he the fans thank you but only bottle together Will the bath gasses fight signed the deeds of Jean Pugh and applied that I'd seen you like mad site to sign EDT jealous ends the June with the teacher mediation has easy when applying met West Side Finland he says easy ends a situation where he got the SET add I need the letters bikini since she says he is in but the distinction for the phone love between the fuel that and that like that that person indeed Puehler met in the clad the humid and that they say so that find there the litigation inside wake like that that Chen said the EU which should be not to sign but vacation outside only a few weeks ago Blank that demanded that should be deemed leads to answer questions asked by but the sign of the Met imagine ingenious another side to you would sort of sad end maybe what should that person to be said we still on the he said these other peace and killed or can Tarver 1 wall what war quashed at but body missed that just took chill chill bulb well I would not like to talk asked what this summer me me he added and the closing of a CD that too call this saying how about which I learned from Bellard yes he they had seized is hardly sometimes a little bit out distinction from mathematics and mathematics holidays and say distinguished Jan utterly signed the weather it In x tendency face or whether it was in it consulate dating and as I call from what I learned from yes that How will always in value and up ahead up the race for these face up constantly in the physics things that China after the figure was jury of extension with many many new starts that means the end of the 19th century and say always calling that mathematics at that time the means of that in the fifties by the qualities of last century bill but unfortunately interface but also send Baron said look we need madam the annual face Of Counsel Litigation and would you agree with started not when says we have the she argued Of that year of something like that but the kind of color pure mathematics which then In is a lot the faith Julie consolidation where various fields in pure mathematics shot through intercom and said it could be the goats that too falling also too can't you look make dealers are valuable because he was June other fields line biology which in spite of the great achievements of what Fred 50 years ago still it at most also cities right back others because In these phenomenology and would you share such to that brand at the time the bases overseas but he give us a new world in the LA dude do without some seeing also saw contiguity that clumsily geisha is more phenomenological expanding sign of 1st of all yes I do agree with it or are the last 50 hours a year or so great some intuition and maturing of the year of the Monarchs of the Rangers centuries that on the less short and emotionally lives short coat to characterize such admittedly simplistic terms media development said the development that is connected with his computer 1st computer science and In my Gaurav was named was mentioned here introduces the notion a goal number of complexity Columba of complexity after speaking bar of complexity of the the information is he level of the shortest from around beach show them Hughes nodded Jim the permit and this respect 1 can say that classical rules of these books such as close as Newton loan gravity or Einstein's equations Nordiques geeks are extremely short program descriptions real physical world situation which I am not sure that will not Goris complexities but Decatur that 1 the data that covered by state genetics the idea human genome power or even a modern focused more Bismil due to I'm not at all sure of the model of complexity is sufficiently small that they can be really grass by human line 1 should be aware of that if a certain a large piece of information which has a very large number of complexity and theorem that not To understand To lure rarely each year processing of this thing 2 computers or computer Mets or whatever and I have a very strong suspicions that this is a new situation and and natural sciences beach we really do not yet know how do we put use acknowledge that it might have that this technology is absolutely indispensable to deal with this and since I believe that too a good job he is the best and everything but may propose
1:59:21
you joke weapons good or bad light mites or either of some foreign end of the spectrum expose case and the plight of the magicians Phelps To do well things that should not be done until with that of the draw seems to a close I wouldn't that summarizes discussion of interesting that has being the addressed actually be sure that will be a record of and proceedings to decide
2:00:07
exactly how to do that but contributors may find it was getting emails get out show job what is demand proceedings could I think 1st under not so they organized we granted bold and especially Opel
00:00
Kinetische Gastheorie
TVDVerfahren
Harmonische Analyse
Punkt
Materialisation <Physik>
Mathematik
Fluid
Tabelle
Stoß
Kartesische Koordinaten
Division
Dynamisches System
Elementare Zahlentheorie
Flächeninhalt
Rechter Winkel
Differentialgleichungssystem
Mathematikerin
Ablöseblase
Mathematische Physik
Inhalt <Mathematik>
Optimierung
Geometrie
Auswahlaxiom
Analysis
03:10
Subtraktion
Quadratzahl
Mathematik
Allgemeine Relativitätstheorie
Vorzeichen <Mathematik>
Physikalismus
Physikalisches System
Spezifisches Volumen
Kombinatorische Gruppentheorie
Analytische Fortsetzung
Phasenumwandlung
06:23
Resultante
Stereometrie
Matrizenrechnung
Vektorpotenzial
Einfügungsdämpfung
Subtraktion
Prozess <Physik>
Punkt
Wasserdampftafel
Natürliche Zahl
Physikalismus
Hochdruck
tTest
Zahlenbereich
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EulerWinkel
Mathematische Logik
Übergang
Ausdruck <Logik>
Topologie
Exakter Test
Rotationsfläche
Grundraum
Gerade
Drucksondierung
Parametersystem
Lineares Funktional
Mathematik
Gebäude <Mathematik>
Physikalisches System
Rechnen
Grundrechenart
Objekt <Kategorie>
Modallogik
Verbandstheorie
Flächeninhalt
Last
Sortierte Logik
Rechter Winkel
Differentialgleichungssystem
Mereologie
Mathematikerin
Körper <Physik>
Garbentheorie
Nichtnewtonsche Flüssigkeit
Geometrie
Varietät <Mathematik>
Aggregatzustand
22:11
Resultante
Punkt
Prozess <Physik>
Momentenproblem
Natürliche Zahl
Formale Potenzreihe
Kartesische Koordinaten
Gerichteter Graph
Computeranimation
Eins
Arbeit <Physik>
Exakter Test
Kontrast <Statistik>
Figurierte Zahl
Superstringtheorie
Umwandlungsenthalpie
Parametersystem
Lineares Funktional
Zentrische Streckung
Statistik
Kraft
Reihe
Ruhmasse
Biprodukt
Arithmetisches Mittel
Forcing
Betrag <Mathematik>
Sortierte Logik
Rechter Winkel
Mathematikerin
Körper <Physik>
Projektive Ebene
Ordnung <Mathematik>
Explosion <Stochastik>
Geometrie
Aggregatzustand
Kritisches Phänomen
Varietät <Mathematik>
Subtraktion
Stabilitätstheorie <Logik>
Ortsoperator
Sterbeziffer
Quader
Allgemeine Relativitätstheorie
Verweildauer
Physikalismus
Gruppenoperation
Zahlenbereich
Physikalische Theorie
Spannweite <Stochastik>
Gravitationstheorie
Algebraische Struktur
Stichprobenumfang
Freie Gruppe
Quantisierung <Physik>
Optimierung
Grundraum
Mathematik
Physikalisches System
Kette <Mathematik>
Objekt <Kategorie>
Flächeninhalt
Last
Basisvektor
Numerisches Modell
41:01
Stereometrie
Prozess <Physik>
Punkt
Physiker
tTest
Gruppenkeim
Kartesische Koordinaten
Gleichungssystem
Massestrom
Computeranimation
Übergang
Richtung
Eins
Vorzeichen <Mathematik>
Minimum
Mathematische Physik
Schnitt <Graphentheorie>
Auswahlaxiom
Parametersystem
Winkel
Güte der Anpassung
Reihe
pBlock
Frequenz
Entscheidungstheorie
Arithmetisches Mittel
Topologischer Raum
Sortierte Logik
Rechter Winkel
Beweistheorie
Mathematikerin
Dimension 3
Körper <Physik>
Ordnung <Mathematik>
Subtraktion
Invarianz
Physikalismus
Gruppenoperation
Anfangswertproblem
Eliminationsverfahren
Physikalische Theorie
Weg <Topologie>
Bereichsschätzung
Reelle Zahl
Rotationsfläche
Inverser Limes
Delisches Problem
Optimierung
Mathematik
Flächeninhalt
Dreiecksfreier Graph
Mereologie
Größenordnung
Innerer Punkt
Numerisches Modell
59:52
Resultante
TVDVerfahren
Matrizenrechnung
Prozess <Physik>
Physiker
Punkt
Momentenproblem
Natürliche Zahl
tTest
Kartesische Koordinaten
Gleichungssystem
EulerWinkel
Gesetz <Physik>
Computeranimation
Puls <Technik>
Einheit <Mathematik>
TOE
Vorlesung/Konferenz
Einflussgröße
Nichtlinearer Operator
GrothendieckTopologie
Güte der Anpassung
Reihe
Biprodukt
Kommutator <Quantentheorie>
Entscheidungstheorie
Sortierte Logik
Mathematikerin
Evolute
Körper <Physik>
Ordnung <Mathematik>
Geometrie
Aggregatzustand
Standardabweichung
Subtraktion
Quader
Allgemeine Relativitätstheorie
Quadratische Gleichung
Wasserdampftafel
Kondition <Mathematik>
Physikalismus
Bilinearform
Solitärspiel
Kombinatorische Gruppentheorie
Term
Division
Algebraische Struktur
Spieltheorie
Endogene Variable
Neue Mathematik
Inhalt <Mathematik>
Optimierung
Grundraum
MinkowskiMetrik
Fundamentalsatz der Algebra
Erweiterung
Mathematik
Angewandte Mathematik
Objekt <Kategorie>
Flächeninhalt
Mereologie
Numerisches Modell
1:18:42
Subtraktion
Punkt
Prozess <Physik>
Wellenpaket
Ortsoperator
Besprechung/Interview
tTest
Zahlenbereich
Kartesische Koordinaten
Gleichungssystem
Physikalische Theorie
Ausdruck <Logik>
Richtung
Spieltheorie
Theorem
Gleitendes Mittel
GrothendieckTopologie
Mathematik
Freier Ladungsträger
Angewandte Mathematik
Gebäude <Mathematik>
Flächeninhalt
Rechter Winkel
Sortierte Logik
Tourenplanung
Mathematikerin
Mereologie
Kantenfärbung
Geometrie
1:28:07
Harmonische Analyse
Distributionstheorie
Physiker
Punkt
Prozess <Physik>
Minimierung
Gruppenkeim
Kartesische Koordinaten
Element <Mathematik>
RaumZeit
Minimum
Schnitt <Graphentheorie>
Einflussgröße
Gerade
Parametersystem
Statistik
GrothendieckTopologie
Kategorie <Mathematik>
Strömungsrichtung
Flüssiger Zustand
Frequenz
Verbandstheorie
Rechter Winkel
Beweistheorie
Mathematikerin
Ablöseblase
Körper <Physik>
Explosion <Stochastik>
Aggregatzustand
Allgemeine Relativitätstheorie
Wasserdampftafel
Besprechung/Interview
Zahlenbereich
Physikalische Theorie
Spieltheorie
Endogene Variable
Inhalt <Mathematik>
Grundraum
Analysis
Trennungsaxiom
Erweiterung
Kreisfläche
Materialisation <Physik>
Mathematik
HardyRaum
Schlussregel
Umfang
Flächeninhalt
Mereologie
Wärmeausdehnung
Numerisches Modell
1:42:53
Prozess <Physik>
Punkt
Natürliche Zahl
Wasserdampftafel
HausdorffDimension
Physikalismus
Annulator
tTest
Zahlenbereich
Gleichungssystem
Term
Physikalische Theorie
Übergang
Deskriptive Statistik
Gravitationstheorie
Gruppendarstellung
Vier
Reelle Zahl
Fächer <Mathematik>
Vorzeichen <Mathematik>
Spieltheorie
Theorem
Nichtunterscheidbarkeit
Stützpunkt <Mathematik>
Spezifisches Volumen
Optimierung
Figurierte Zahl
Struktur <Mathematik>
Gerade
Erweiterung
Statistik
GrothendieckTopologie
Mathematik
Güte der Anpassung
Stellenring
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Differentialgeometrie
Frequenz
Arithmetisches Mittel
Druckverlauf
Menge
Flächeninhalt
Sortierte Logik
Körper <Physik>
Kantenfärbung
Aggregatzustand
Numerisches Modell
1:59:18
Prozess <Physik>
Güte der Anpassung
Punktspektrum
Metadaten
Formale Metadaten
Titel  Closing Round Table  Are pure and applied mathematics drifting apart? 
Serientitel  International Congress of Mathematicians, Madrid 2006 
Anzahl der Teile  33 
Autor 
Ball, John et al.

Lizenz 
CCNamensnennung 3.0 Deutschland: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. 
DOI  10.5446/15976 
Herausgeber  Instituto de Ciencias Matemáticas (ICMAT) 
Erscheinungsjahr  2006 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Mathematik 
Abstract  Closing Round Table discussion of ICM 2006. 