IC16: Communicating Modern Mathematics To A Wide Audience: Snapshots Of Modern Mathematics From Oberwolfach

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IC16: Communicating Modern Mathematics To A Wide Audience: Snapshots Of Modern Mathematics From Oberwolfach
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Communicating modern mathematics and mathematical research in writing to a wide audience is a challenging yet important endeavor. Snapshots of modern mathematics from Oberwolfach take on this challenge. These are short texts on modern mathematics aimed at mathematics teachers, science journalists, undergraduate and advanced high school students as well as the interested general public worldwide. But how to present intricate mathematical concepts to an audience without much mathematical training? For example, how do you explain what a “group” is to somebody who never took algebra? We discuss examples from our editing work and present how we try to make mathematics more accessible. One focus will be on common pitfalls that occur when professional mathematician write texts for a broader audience.
Area Ocean current Mathematics Mathematics Projective plane Mathematician
Point (geometry) Standard deviation Group action Process (computing) Multiplication sign Projective plane 1 (number) Translation (relic) Student's t-test Mereology Mathematics Mathematics Modulform Summierbarkeit Right angle Mathematician Imaginary number Physical system
Point (geometry) Polynomial Process (computing) Natural number Generating set of a group Mereology Theory Set theory
Point (geometry) Well-formed formula Order (biology) Ideal (ethics) Circle Figurate number Mass Algebra Flow separation Set theory Social class
Point (geometry) Cross-correlation Term (mathematics) Thermal radiation Algebraic structure Mereology
Point (geometry) Cross-correlation Atomic number Physicist Figurate number
Degree (graph theory) Group action Mathematics Multiplication sign Prisoner's dilemma Sheaf (mathematics) Energy level Nichtlineares Gleichungssystem Student's t-test
Standard deviation Binary tree Dot product Graph (mathematics) Stress (mechanics) Algebraic structure
Proof theory
Ocean current Mathematics Process (computing) Logic Different (Kate Ryan album) Kinematics p-adische Zahl Solid geometry Analytic continuation Numerical analysis
Ocean current Population density Different (Kate Ryan album) Student's t-test Körper <Algebra> Mathematician
Mathematics Goodness of fit Moment (mathematics) Student's t-test
Point (geometry) Entropy Functional (mathematics) Multiplication sign Projective plane Moment (mathematics) Sheaf (mathematics) Lemma (mathematics) Parameter (computer programming) Mereology Graph coloring Wave packet Degree (graph theory) Goodness of fit Mathematics Arithmetic mean Many-sorted logic Order (biology) Energy level Right angle Object (grammar) Imaginary number Physical system
Mathematics Fields Medal State of matter Model theory Nichtlineares Gleichungssystem Imaginary number Set theory Connected space
so who do hold the area of the I and and as I'm more words and today we will talk about and the project snapshots from all of us and and we add to the editors in this and project and you try to tell you what the project is all about and then dive into all editorial work what actually do to give you some examples things yeah so and this has been presented many and imaginary rents already and so this is what going to quickly look talk tell you what the snapshots actually are the snapshots are and texts written about current mathematical research and by mathematicians who was that all of us mathematical research institute there and the
special thing about these texts is that they're not mates of 4 specialist what form a wider audience art target audience allow my high school students for students a math teachers method journalist only 30 people who are already interested in math and and perhaps even have some from method ication already so we are not trying to convince people that are not in some of em but you already read speech of people that already looked somehow so and an this is part of the META-NET project 3 distributed via their website you can print them during sum to distribute but apparently the notes that money and all of them because they have an and because we and all of them and print them and so and says nuclear ones coming out all the time this start in 2014
Soviet have and more than you can read in regard going to be it's already and I would say and this is what they look like from this is the front pages of 2 of them they usually 8 or 12 pages long so um uh did pretation afternoon to reason and address them and so the goal here is also that there still readable in 10 years and many effects and and this is why he chooses classical formant and the language system mostly English but if you German ones and there's also translation it's going on in the back and forth and no French 1 so far so and that's the euphemism editing process today and In the mathematicians that by these articles on formal us and it's about them beforehand and that and out for the what the audience and you get a standard they usually use to rights to high specialists audience audience and that come on you think you technical language and and that not trying trying to communicate the idea to a wide audience so this is quite different from most of them and and this is well on the very common and we helped office to communicate their ideas to a wide audience and only point the pieces in the text that might be difficult to understand for high school students and trying to change it to work and and additional information across all stuff that is too difficult and and so on and you want to know for you a few examples
of that I actually from the use of from past natural theory that August so let me walk you if you want through some of the examples and for the rest of the talk you will always
see these maps chart as the authors submitted a task on the top of the page and then below that you will see what it looks like after the editing process so this pricks example is about improving accessibility here and also send us a snapshot that was otherwise wonderful but and this 1 spot he wrote that the the the set of all points where all polynomials from my vanish it suffices to check this just for the generators of so when I read this I thought wall can
somebody has never heard about the vanishing set off many maybe never taken a class in algebra understand this concept at this point and as you probably know so let's try to make
this more accessible then how did we do this them several entrance points as in the previous talk 1st we added a formula for some people already have some experience with mass but not the VAD around this might be that the way to go um and then we had examples so apart from making the text a little bit longer and maybe a little bit more wordy in order to make it easier to read we also added these examples um and he wrote 2 examples are displayed in Figure 4 the vanishing set of the ideal and so on is a circle and then a 3rd example and we also added this figure them which has 2 purposes 1st it helps understanding what a vanishing centers and 2nd it makes the snapshot appear more digestible and more accessible we believe as a whole so it in in this example we added
several things to the snapshot hoping that it would become more accessible then
In other examples we also delete parts that might overwhelm the readers so here them in this snapshot that was very good also in the also offer wrote them something about patterns of radiation record such as X-rays and then it mainly measures 2 point correlations in a structure and then these 2 point correlations are not mentioned anymore and the rest of the snapshot so here we thought and is it really necessary to have this technical term 2
point correlations in here that's not mention any more from the rest of the snapshot and we decided to remove it and
instead of that the elaborated little bit more on X rays so we change the text known it now reads to study the atomic warden crystals physicists and invented x-ray crystallography then be explained it a bit about this and then figure 3 a shows a point like pattern in Figure 3 b shows that a device for X-ray crystallography so these are the 2 figures that we created an and added to the snapshot began with the idea being that figures makes the whole thing more accessible it looks more attractive and it also helps readers to digest the the explanations and in the text then and the next example lesson and the 3rd point still so here the snapshot was very good very accessible that contained nice figures already in the version that the author send us but the author didn't really say something about the ongoing mathematical research he gave a nice introduction off the Navier-Stokes
equations that was wonderful to read but he didn't say anything about himself so I wrote a note to him displayed in blue here and I read your of very welcome to insert
a paragraph where explained on much more advanced mathematical level what the main steps of your own work and the also known fortunately agreed with me that he could do that and he inserted an 9 times section a short discussion of subcritical transition for advanced readers which is on a more difficult mathematical level than the rest of the snapshot but before that for for high school students maybe they can skip this section but 1 people already have a bachelor's degree in mathematics for example the but are not specialized in PD might well understand this section so it's more interesting for them they might already know all the rest of of the snapshot and he wrote this entire page explaining his own published research and 1 last example that I'm going to show you this bird where we just try to improve the visual quality of the snapshot so this method was also very good but it contained these pictures which are certainly not optimal so I wrote to the author is it may be possible to just recreate these photographs and he happily agreed and put prepared these new photographs that are much clearer and nice no more it's the prison more
examples this and in the you see is that this some was stress among them in on the bottom page again there's a
moving robots and their standard to other so I know what you see in this picture and and staying with adding pictures um here the author and described a graph structure along the ethnic progressions and and I mean Donetta picture and to it's a very nice picture here to to just the Preston within the graph that he's describing although the if the graph you can kind of and start at the top and then put some dots in the bottom and and receive the binary trees and could continues
on this is 1 more example and then we also have all the offices and melodic problems
also easy is sorry for the latter problems here's another of the thing that often occurs often and the all ideas to saying it is easy to check is this true to see him and you can check yourself and so on and then sometimes for the readers is probably not so easy to check and and we don't wanna assigned to many exercises and this is why I'm we often elaborate and then on the proof that are easy to check them In this case the the the blue thing is the elaboration of the black sentence of of longer and is only 1
implication of communication that need to be shown at implication then is the left to the reader after you've seen you yes he's seen the 1 implication into the other 1 also OK and then
the last thing on logic problems here and there a lot of it signed explain how what and p-adic numbers solid kinetic numbers in this case and you want to and say that the numbers gets smaller to the left and he used 3 different font sizes and then to me that make them look nicer stand the continuous font sizes to make them with a smaller and and there's also a job to fix them make topography well thanks the so so what and 1 reason why it's important to us that some B and communicate current research is because off never never never nutrition people say to me 1 you do math and usually everything is already known that was a new discoveries going on and and this is shows interested readers that I
and indeed new discoveries going on and it turns out that the stepfather not only am that well well-tied always but also by and more advanced mathematicians from different fields and work great break and lead to digest the central also faster at also interested in and thus Nash assignment will eroticism density them printed out already of book and some professors giving them the to the students and so on and the as so we only wanted a few questions and you might have found so and you do not from you if you have at the sniffles what you like about it what you can do better so uh and other accessible enough and what other problems in non-communicating current research to you see this is all going to say the the and 3 have
any answers to these questions or questions and answers yes the was a deal of the public to to test those snapshots when they are uh finished when you do when you
think about finished because you are so you know the mathematics so you can under some old uh before and after and I think it's very good question and it's true we
never officially tested the snapshot of high school students all of the undergraduate students of mathematics so at the moment we don't have any official feedback
system or evaluation system uh that's something we might think about in the future to implement and it would be important to do actually another thing uh on the french uh what side noting that the trial I don't know if it's good but if it's a good done on that but they try to give a call to to say it is more or less difficult uh to say OK we tried to do is that's it's real hot enough so we we we think that is although it was and this is a I think this is a great idea is true that and the difficulty of the sniffles various them and Ed really varies not only between this site's natural but also often within this method often and as the on the given example the sometimes have like a warning section and will be viewed this lemma in the next paragraph is going to be difficult to understand and you can't give over a few free it's not use later in the text we do this with all the color coding but it might be really useful to do this on the web site victory at color code the things on it's hard to the objective the of course right because sometimes and it's also a personal taste question what's that that was not difficult the but I I think 1 point is that we really need to make sure that they aren't too difficult so we once had a snapshot starting with I think we considered as Zito function 2 arguments or something was the 1st sentence of the snapshot so this is something we wouldn't con considered a level that we can work with so this would be the we wouldn't even give a direct color much try to change in making more accessible but with the author and quite often it is then uh they quot very accessible of the 1st few pages so off the signal of an introduction the paragraph rather not on is very understandable so and I think that is the level of difficulty that it varies with an essential is much
more and uh very much greater than and what goes on between snapshots the it and I just want to ask about in the team me how many research matter this is the Aventine how many editorials of experts they haven't disorders on time the thing with 6 so and all of them have and some sort of math degree this that so uh going on and on about publishing experience of this I mean it working I mean not mathematical publishing experience in of journalism well I I can always of I don't have much as were of an experience that I mean I know what the other aging it 3 have tons of over some many images or 1 of them is for example telephone and picture of all for in many years and no answers and I I think also here there's room for improvements of the whole idea of the project is that you need to have a mathematical background in order to edit this if if you haven't the publishing background also that's that's a plus and of course I think we would like to bring more publishing expertise to the team but they're at the moment as mode said there's 1 professional editor on the team and all the others have a mn some experience but no professional training and business next because in both English and German and also mean between the junior just so fired meaning is snapshot never LeCun language question that I feel I cannot answer that American who can as of this and more content any further questions or comments who sort um I love the project has flexible and how do you choose the topics because its implied that Council 100 thousand papers here at the moment so how do you choose which parts and the way it works is that and every week and a wealth of this workshop and at every workshops and which are distributed among the top EU topics of all old math topics and he blast who's willing to write snapshots and sometimes the organizers also signed snapshots to someone so and this is what makes it possible to cover wide areas of basic reviewed do this for the work week the choose a that of from off of them do you perhaps I think also of um and ending material especially for for instance when fused medal winners so it so you have as a journalist and I want to find material on what did they do uh for the price for Abel Prize winners or something like that so cooperate as in the anime thought about this but so as modes and at the moment the snapshots are written by people who come to Obama of workshops and if 1
of the prizewinners happens to come to an above of off of of course we will be very pleased to see that person uh right snapshot but what I saw in several snapshots that appeared already is that the people referred to the big price so for example the 1 on the Navier-Stokes equations of course mentions that this is a Millennium problem and that many people have been working on this for more than a century so you see some connections to these big prizes but so far no Fields medalist has written a snapshot I think yeah the often of the problems that are solved by fuse Miller's of and also discusses snapshot some centering state banking was discussed a model of not in there hasn't got nails if
you've male and it's only in topic that master the scientists and and and the set was also discussed in 1 snapshot and this new uh other questions or comments let's thank because in