5th HLF – Interviews with mathematics and computer science laureates: Sir Michael Francis Atiyah
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00:00
Elektronisches ForumComputerMathematikAtiyah, Michael FrancisABEL <Programmiersprache>DatenfeldFormation <Mathematik>Wort <Informatik>Familie <Mathematik>TelekommunikationBitApp <Programm>DifferenteComputerspielMathematikerRechter WinkelBildverstehenTreiber <Programm>Numerische MathematikInteraktives FernsehenDatensatzNeuroinformatikVertauschungsrelationInformatikMathematikMixed RealityFeuchteleitungWellenlehreMetropolitan area networkQuick-SortAuswahlaxiomt-TestParametersystemKernmodell <Mengenlehre>TermCoxeter-GruppeExogene VariableFunktionalGenerator <Informatik>EinsWeg <Topologie>EnergiedichteGroße VereinheitlichungWeb-SeiteMultiplikationsoperatorDateiformatComputerunterstützte ÜbersetzungProzess <Informatik>Spannweite <Stochastik>MereologiePinchingVollständigkeitVollständiger VerbandMAPMessage-PassingComputeranimationXMLUMLBesprechung/Interview
09:35
Elektronisches ForumABEL <Programmiersprache>Atiyah, Michael FrancisDatenfeldTopologieWellenlehreNeuroinformatikGeometrieVirtuelle MaschineCASE <Informatik>AnalysisFundamentalsatz der AlgebraProgrammbibliothekMathematikInternetworkingTheoremUniformer RaumMereologieFrequenzFließgleichgewichtZahlentheorieSoftwareentwicklerPolstelleBlackboard <Expertensystem>Fortsetzung <Mathematik>Ordnung <Mathematik>Tablet PCOptimierungBillard <Mathematik>Maschinenschreibent-TestInformatikYouTubeComputerspielBildschirmmaskeDimensionsanalyseDatensatzGenerator <Informatik>Formation <Mathematik>Lokales MinimumIndexberechnungMagnetbandlaufwerkBitQuick-SortMessage-PassingEnergiedichteMultiplikationsoperatorGrundraumMAPGüte der AnpassungEvoluteTrennschärfe <Statistik>Prozess <Informatik>RuhmasseEndliche ModelltheorieVektorpotenzialRotationsflächeAlgebraisches ModellNewton, IsaacKomplex <Algebra>Turing-TestMaßerweiterungWhiteboardBesprechung/Interview
18:48
Elektronisches ForumAtiyah, Michael FrancisDatenfeldABEL <Programmiersprache>MaßerweiterungDifferenteInformatikDimensionsanalyseFokalpunktMultiplikationsoperatorSoftwareentwicklerFormation <Mathematik>MereologieArithmetische FolgeArchimedesGüte der AnpassungSchaltnetzGefangenendilemmaFigurierte ZahlMAPEinsQuantencomputerMathematikerVarietät <Mathematik>Generator <Informatik>QuaderReelle ZahlNeuroinformatikQuick-SortMathematikMetropolitan area networkFields-MedailleSoundverarbeitungKonzentrizitätPhysikalische TheorieGauss <Rechenmaschine>ABEL <Programmiersprache>Inverser LimesWechselsprungMittelwertFrequenzFließgleichgewichtGamecontrollerFächer <Mathematik>Data MiningBildverstehenFamilie <Mathematik>TabelleGrundsätze ordnungsmäßiger DatenverarbeitungPhysikalismusDivergente ReiheDatenkompressionKlasse <Mathematik>BildschirmsymbolWellenpaketSpieltheorieMehrrechnersystemZweiKartesische KoordinatenQuantenkanalRechter WinkelBitMomentenproblemBesprechung/Interview
26:34
ABEL <Programmiersprache>Atiyah, Michael FrancisDatenfeldQuantencomputerNeuroinformatikSatellitensystemInformatikPhysikalische TheorieKartesische KoordinatenFlächeninhaltSoftwareentwicklerBefehl <Informatik>PhysikalismusGravitationQuantenmechanikPhysikerArithmetische FolgeMomentenproblemSystemprogrammMathematikProzess <Informatik>MultiplikationsoperatorWechselsprungAnalytische FortsetzungQuantengravitationBesprechung/Interview
28:53
Atiyah, Michael FrancisDatenfeldABEL <Programmiersprache>Elektronisches ForumMathematikComputerMultiplikationsoperatorNeuroinformatikFamilie <Mathematik>MomentenproblemLokales MinimumEinfache GenauigkeitMetropolitan area networkMathematikerMereologieVorhersagbarkeitFlash-SpeicherBildschirmmaskeDifferenteInformationMinkowski-MetrikFundamentalsatz der AlgebraGeradeArithmetische FolgeEingebettetes SystemTopologieCoxeter-GruppePunktVirtuelle MaschineFlächeninhaltSchaltnetzKollaboration <Informatik>FrequenzAuswahlaxiomAlgorithmusMathematikOptimierungDeskriptive StatistikAbstraktionsebeneFields-MedailleHierarchische StrukturFormation <Mathematik>Hausdorff-RaumElektronisches ForumInformatikRichtungFramework <Informatik>Besprechung/Interview
35:11
Elektronisches ForumComputeranimationJSON
Transkript: Englisch(automatisch erzeugt)
00:22
I'm very glad you're here, partly because you're one of the more popular laureates. Actually, let's start with that. I assume it's because you interact well with the young researchers. Well, I always like talking to people. I'm very extroverted. I talk with my students. I talk with my teachers. And surrounded by young people, I like to talk with them.
00:42
Of course, the young people here are so clever. They're very bright, even selectively because they're bright. And that comes across at the speed of their reaction, their responses. So when I come here, I think that's one of my functions. The main function is to talk to the next generation, inspire them.
01:02
And that is really the main purpose of this HLF, is to bring the young and the old together. And we'll pass on the wisdom that we've learnt over the years, inspire them to do great things in the future. So we hand the torch on from one generation, jumping a few.
01:23
So they're the age of my grandchildren here, most of them. How many HLFs have you been to? I've been to every one. Really? Have you noticed any differences since the first one? Yes. Right at the beginning, there was a very marked distinction between the computer scientists and the mathematicians.
01:41
First of all, the computer scientists hadn't had a similar... They all turned up. Mathematicians have similar meetings there, and they were rather blasé. So the number of mathematicians turned up was quite small. We probably outnumbered five to one. Really? And there was not much interaction.
02:01
We didn't really cohere together. But by the second or third time, first of all, more mathematicians started to turn up. And secondly, the mathematicians and the computer scientists did start to talk. And I found that the computer scientists were quite clever chaps. And I found that talking with them, we had a lot in common.
02:23
Nearly all of them started mathematicians first and drifted into computer science. So they were educated in the background. And I got interested in what they were doing, and I started, well, this is common ground. So then from there onwards, I felt the diffusion of the computer scientists. By the third or fourth, I find it very hard to tell whether somebody was a mathematician or a computer scientist.
02:45
I wouldn't know. You know, they were trained in mathematics, and then they knew computer science or the mathematicians. So they really merged. And particularly, I suppose, the people who came here, mathematicians, well, they would be those in the mathematical world who had some sympathy with computer science, probably.
03:04
It was slightly self-selecting, not entirely. And anyway, I found that from then onwards, the mix was excellent. And you couldn't really distinguish one from the other, and the talks were already very good. People made big efforts to bridge the barriers.
03:22
And my only complaint, like for example today, is the computer scientists are so skilled at pressing buttons and having 25 pictures jump out at once. We mathematicians are rather primitive. You know, we have one picture. Look, there's Einstein or something. And so we're a bit left behind in terms of presentation.
03:40
Well, presentation in the technical sense, you know, doesn't mean it's a good lecture if you give 2,500 pictures. So there's little differences. But we learn from each other, and the students, the young people, then they're totally mixed. Whatever the subject they're studying, you can't tell. They're interested and very clever.
04:01
And they come from absolutely all over the world. Obscure parts that you haven't heard of. Guatemala, Kazakhstan, you know, you wouldn't think. And yet there are some very clever ones come out of there. Some very bright ones. Why, why, why? Out of Siberia or Mongolia, you know. Or some very obscure Central American republic, you know.
04:23
Or now increasingly from China and places. Or China is no longer, it's backwards. So it is very, very cosmopolitan. And that's very good. And these people, quite often you find they're not clear which country they come from.
04:40
They're originally from country A. They were educated in country B. They were educated in country C. They are now studying in country D. So where do they come from? They are citizens of the world. And if they represent four or five cultural backgrounds, there are two under them here. Well, we have the entire globe. But many of them do seem to connect with you in particular.
05:02
Why do you think that is? Well, I'm receptive, I'm talkative. I'm always too talkative. My wife used to complain. And I like young people because I feel, also I like, for a long time, I like to explain my ideas in, not monosyllables,
05:26
but I try to explain my ideas in non-technical formats. I can talk about anything, whatever it is, how difficult, in words which the average man in the street, people used to say if you can't explain it to the average man in the street or woman,
05:43
you haven't understood it. So I try to explain whatever level it is, if it's a taxi driver or the shopkeeper or the clever girl in the front row, I try to talk to them in the words which are meaningful. Don't try to impress them with greater knowledge.
06:03
That's stupid. Try to approach them in a way where they understand, give good ideas and then you get rapid communication and then they all fire back. So it's a bit of a, I've been doing that all my life. As you get older you need more.
06:21
You don't like to sit down and work. You get a bit lazy. You like to sit back and think and talk and let the young guys work. Well, there's a side of the exaggeration. I've just got a paper that I've just written and it's, I think, almost the best paper I've ever written but I have problems persuading people that an old man can write.
06:40
You can't possibly write. You're an old man. How can you have a good idea? So my job is to try to show it. Well, this is something about mathematicians. They say that, you know, what is it, at 30 if you haven't made it and so on and a lot of these people are in the sort of mid-20s range. Yes, yes. I'd like to ask you, for somebody at that age now,
07:03
what should they be looking to do for the next five years? What's the most important things to develop? The most important things, first of all, listen to what your elders and teachers say but don't do what you're told.
07:20
Listen but don't make your own choices. Follow your own guidelines. Take your own guts and do what you enjoy doing and within the parameters you hear their advice so you know you're not going to waste your time completely. But you want to go off track. You want to do something new. If you just follow, do what you're told,
07:42
you'll just be reproducing what they did before. You will never do anything new. So to do something new you've got to be fresh, young and bold and have a crazy idea. Paul used to say, you know, that idea wasn't crazy enough.
08:00
You have to be really brave and have a really good hunch and then you pursue it. Of course if it doesn't work out you come back and try again but you must be brave, you must be enterprising, you must follow your guts, your instincts. Of course you've got to work, that's the routine but that doesn't by itself, if you're just a drudge
08:22
you don't do anything, you just get more and more learned but not more and more imaginative. So the most important thing is to keep your imagination and your enthusiasm and your ability to talk to other people because you don't want to pinch people's ideas but you want to be stimulated by other ideas.
08:42
And two people coming together spark and those sparks produce new things. So mix around, spark each other off and when you're young, you know, the world's your oyster, they say, you can... And, you know, I used to meet people and they were students
09:02
in 2025, five years later they would be 30, they would be professors. Five years, in that page, is like a lifetime. You go from being, finding your way around to being, if you made it, very successful, fully fledged in the prime of life
09:22
in five years, between the ages exactly. Well, let's say 25 or 30, roughly speaking, you should be aiming to move from being an apprentice to being a real creative artist. And that's when you make your course,
09:42
then you can go on for the rest of your life and developing and improving your skills and your art but you must start young until you take the advantage of enthusiasm of youth, energy of youth, bravery of youth. Yes, so this is very good.
10:02
We have these young people who are very young. Last time I met somebody who was 16, this time I brought a young person with me who was 19 and then there are old people who are 23, you know, occasionally one or two old. It is that cohort, very young but very clever,
10:22
they go through quite a selection activity process here. Of course, they're not all equally good because you have to have a diversity of backgrounds and culture, but there are, amongst them all, these half or more potential whiz kids. Now these are some traits that I think probably go from generation to generation,
10:44
the need for imagination and such, but the landscape, I'm sure, has changed since when you were 22. Well, the landscape changes, I mean, not the landscape, the technology changes. There were no computers when I was a student. They hadn't been invented.
11:01
Now everybody has five computers in their pocket and they talk always about, the talk is about big data. That wasn't the case, of course, but that's the superficial side, that's the fundamental side. People have been studying mathematics for thousands of years and Archimedean was as clever as anybody now and they did things which are still pertinent
11:22
and so although it changes, it doesn't change as much as you think it's changed. The fundamentals, I think, remain the same. There's the superficial gloss on the top that is different. People dressed in fancy clothes, they wear fancy uniforms, fancy hats.
11:42
Take them off, back to the skin underneath, and we're all the same. My brain is no better than the brain of somebody 2,000 years ago. He may have had the opportunity. He may have been a caveman, but all right. Even within the cave you probably go up and you may find he scribbled something on the board
12:01
and when you understand it, it might be a theorem. Somebody might discover somebody out of Mongolia, somebody discovered, well, I'm sure there's a theorem discovered everywhere. So in many fundamental ways we don't change. The changes are really the superficial part.
12:23
Fundamentals are really universal. Of course you've got to take note of the changes and we still use blackboards. The blackboard has been used since the days of the Greeks because it only required a slate and chalk.
12:42
And that is, despite all the technology, many people still prefer, in the mathematical world, mathematical scientists, still prefer to give a lecture with chalk and blackboard. So that's the same technology as 2,000 years ago. And we have one right behind you actually. We could lower it if you want to start scribbling. No, no, no. I'm just saying that despite the availability of much more fancy,
13:04
sometimes the old technology is perfectly serviceable. There are places in the world for theatre and cinema. People say, oh, when the movies, when television came in, the movies were out, or when films came in, theatres were out.
13:22
That's not true. We still have very active theatres. We still have films again as people go to the cinema, even though it's now all available on YouTube. So somehow the new technology is added. There are now more canals.
13:40
You can see more things. But it hasn't displaced the original one. People still prefer a live performance in a theatre or a live symphony to listening to the most perfect recording there is. There's something about the involvement of other people who create in front of you that sends a signal that is missing when it's translated through technology.
14:01
I listen to music on tape, and of course it's cheaper, easier to get it up and go into a concert hall, but it is not the same. What were some of the interesting problems when you were this age? I'm sort of also trying to look at comparing your time when you were 22 or so to today, and I hear what you're saying about it,
14:21
about the fundamentals being the same. Well, you see, when I was in Cambridge, it was just after the war, and it was flowering of new ideas. So there were things which my supervisor Hodge had done before the war, which saw the foundations of a lot of what had been going on the last hundred years, and there were some great people in the university,
14:42
very, very high level, and that was the university which had Isaac Newton before that and so on. But the new ideas coming in, I think the most important new idea was fundamental topology. Topology had been lurking in the background from the days of Riemann and Poincare and others,
15:02
but it didn't, it really came to fruition just after the war, mainly through the School of France in Paris and Princeton, and then topology spread like wildfire through algebraic geometry
15:21
and complex analysis, and there was a whole new exciting period of about five to ten years, and I was lucky to be there just as that happened. So I would go every week to the local departmental library, I would see what the Cointreau-Newnote said about what people were proving in Paris the week before.
15:41
It wasn't like the internet, but it was pretty fast, and sometimes somebody would travel and say, have you heard of the latest theorems? And we were in touch with people in Princeton. So things moved quite fast even in those days, and the ideas were really exciting new, big developments. In the 1950s, when I was a student,
16:04
there was an exciting development, and I happened to be there at the beginning, and I got to know also all the top young people who came up, Pittsburgh and Bonn, Serre in Paris, Borel in Princeton, and we were all young together, and we learned,
16:21
got friends from them, and that launched, so there was a launch pad, I went on, I had a very good, I was launched in my career early on. And of course each generation comes, and there's some new fashion or new ideas, and maybe some of them come from computer science, the ideas from computer science have had an impact.
16:42
But of course when I was around, we also had people like von Neumann and Turing, and I went to Princeton, which is where von Neumann was, although he was dying when I arrived, and so the beginning of the computer science, although there was no machine, the ideas, Turing was there, von Neumann was there,
17:02
and that was the beginning of the computer revolution, just I was there at the start of it, before it got to the first steps. The age generation will arrive at some stage when something is exciting, and so it was natural that students at that period will say, well, look, this is the exciting period.
17:21
There's a little temptation for them to think, well, that will always be the exciting period. That's wrong. The excitement is like waves, they move, and they have a peak when they are at their maximum, and then they decay a little bit, and they stay steady state, and another wave comes along. And you have to realise that just because when I was there,
17:42
this was the big explosion, you've got to realise that ten years later, the interest has shifted, or maybe it's shifted backwards. I remember meeting some people in number theory who were older than me, and they said, well, there is this fashion for topology, but it will pass, and then we will revert to good old-fashioned number theory. To some extent that's true, but it turns out
18:02
that the topology is another theory, and you get new ideas. So if the evolution of ideas is very much criss-cross, changing with time, the students are coming to any given stage thinking, we're on the crest of this wave, we're going to go on infinitely, they're on the crest of the wave, and then the wave goes down,
18:20
and they have to learn to adapt, to prepare to move for the next wave. If you don't, you just go in the by-waters. Now you mentioned von Neumann and Turing, particularly von Neumann, so you were together at Princeton at least briefly. Would you consider him a mentor? No, no, I didn't really know him.
18:41
I mean, he was very ill when I arrived. He died shortly after. But he was still there. His machine that he built, the first computer that was still at the Institute of Grounds, and I knew the people who worked with him. It wasn't quite my... Who were your mentors?
19:00
My mentor wasn't... I came to my mentor Hodge, and Hodge theory became a big thing, and then I went to Princeton, I met all these clever young people, people like Sayer, just a year or two older, was a sort of fly flyer, he had a big influence on me.
19:20
Hertzberg was just a year older. So these are my contemporaries, more or less, and they had a big influence on me. Amongst the older people, I was proud of me, I found it wasn't the older people who had the most influence on me, it was the younger ones, my contemporaries, partly because the war had certainly had a kind of compressing effect. Some people had been...
19:40
Their careers had been affected by the war, so immediately, in the subsequent years, we had a lot of compression, people covering a period of about ten years or so, squashed into about three, and so we had more concentration of talent than you would get in an average steady state situation. These were the young people coming back from the war?
20:00
War people, careers had been served at that time in the Navy, or they'd been in prisoner of war camps, you know, a variety of reasons, there would be... So, yes, so there were... and could already be in Japan, so yes, there was a real concentration of talent in those years,
20:21
and also there hadn't been the opportunities to go, to travel and go, so after the war there was these great opportunities and we met in places like Princeton, they could all go there, the Americans had money, and so nowadays it's much more easy to go, there's money everywhere, you can go anywhere you like, but at that time the limit to travel was limited, there was less money,
20:41
but it was a great period for me, and I think every period has its own era of certain development, new ideas, and now, undoubtedly, computer science is the one which has the money, it has the applications, the technology, and it's very fashionable, so obviously a lot of young people now see this as the great thing for them,
21:04
to some extent they're right, and they're right to focus on it, because that is the thing of the moment, you don't take advantage of what's going on, now there'll be opportunities, and the creative young people will create things out of that, but it won't stay the same, it'll change again.
21:20
In a few years time, much of what they do now, and they say it might be automated, out of control, no longer left to the mathematicians. You're speaking a lot about things that are eternal, things that stay the same, would you care to look five years in the future in your own field and say what you think will be interesting,
21:43
what breakthroughs might happen, what developments might come out? Well, I'd like to explain, I did this morning, science, including mathematics and physics, has two kinds of developments, one is incremental,
22:01
you improve on the techniques, you make them better, you carry on doing things in a slightly better way, and occasionally there are breakthroughs, where a totally new idea comes in from the side, opens a new field, and you jump. And so it's a combination of steady progress and quantum jumps.
22:21
And the quantum jumps, they are unpredictable. If they were predictable, they wouldn't be unexpected, they would not be jumps, it would be part of the incremental progress. By definition, you cannot predict the unpredictable. And the big steps forward are the unpredictable ones, and the unpredictable ones tend to come from the younger generation
22:42
working, as you say, outside the box. They come along and say, look, all this work's been going on, all these guys, they've solved all the old problems, I'm using the old techniques, if I'm going to do anything, I've got something new, what can I do that's new? And they say, well, I don't want to stick to the old focus class, I want to go that way or that way,
23:01
and some of them will succeed. And without that, you just keep treading along, you've got your old steam rolling, you crack a nut, you crack a bigger nut, and okay, it makes progress, but it's slow progress, it's tiring work. It is not the big exciting breakthroughs. The big exciting breakthroughs are what you really need.
23:21
You need an Einstein here, an Einstein there, a Newton here, a Gauss, an Archimedes there. And of course, the people here invite all the people to get fields of the world, but they think amongst this lot these are people who have, some of them have made quantum jumps, and they will inspire young people to make quantum jumps,
23:40
and you need those quantum jumps. And that's what keeps things refreshed, otherwise it gets a bit stale. Okay, you can improve the way you cook spaghetti, and you can make spaghetti even better and better, but maybe you need something different from spaghetti. You've only discovered, gosh, when you've discovered if you cook fish, it's much better.
24:01
So you have to vary your diet because you keep eating the same stuff, writing the same books. Look at the literature in art. Every now and then, art that is a breakthrough in art, when it came to Picasso, he'd done all the old painting, and he wanted to say something different. And he entirely knew all the impressionists.
24:23
And the musicians, you go along copying Mozart and Beethoven, but the time comes when you need to do something different. And then that's difficult. People struggle, and then eventually somebody makes a breakthrough and gets away from the old stuff, or not necessarily better than the old stuff,
24:42
but somehow different, a newer aspect, a new dimension to the art, to the music to create. I don't think that any of the mathematics we do now is necessarily better than what Archimedes did. It'd be hard to be better in an abstract sense when you go before God and say, what did you do, and Archimedes said like this. Well, I'm afraid Archimedes wins, you know.
25:04
But, okay, you may not be as good there may be no musician alive today who's as good as Beethoven. I think it's very hard to be as good as Beethoven. But, you know, okay, after Beethoven, we really had to do something else. Franz Schubert wasn't bad, and Brahms was okay.
25:22
So the same is true in mathematics. There are great figures of the past, and there are maybe some in the present century who will be seen in future years as, yes, they weren't bad. They were roughly at the same level as, you know, Abel was an example of whom the Abel prize is, right?
25:43
He was, I think, if he hadn't died young, people would have seen him as the successor of Gauss. And he, and I used to tell people, he would have been like Gauss, except he was much nicer a man than Gauss. Whereas Gauss was a rather grumpy old man,
26:01
and he was, I don't know, Abel was a nice young man, because he didn't, probably you don't get, as you get older, you get nasty. He died young, and I tell people, it's not necessary to die young to become an icon. Everything helps. If you die Galois or Abel, and you've done your age of 21 or 26,
26:21
you've done great things, and you die, of course you become an icon. But you can go on like Gauss or Newton until your 80s, and you're still not quite as, you're still admired. And I hate to take you down from, or to move you away from this very noble statement about a discontinuity, these quantum jumps and such,
26:42
but in the next five years, are there any incremental progresses that you think are especially interesting? Of course, and some of them I'm hoping to do myself. There will be significant progress, I predict. At the moment, the big issue is how do you combine quantum theory and gravity?
27:03
Now that may sound to you like physics, but it's also very mathematical. Quantum mechanics is heavily mathematical. Gravity is very geometrical. So that's an area which is common ground to mathematicians and physicists. And there I predict there will be
27:22
modest breakthroughs which collectively add up to significant, at least mini-jump, and which are predictable, and I think they will happen within the next five years. So that's an area which I know well. I'm involved with it. I may even contribute to it.
27:40
There are, it's quite clear there are, of course, things happening in the computer world in the area between learning, utility, new technologies, making advantage of the opportunity of learning, where we will make significant incremental steps
28:01
which may add up to something more in the next five years, and that's happening here. You can see it on the ground. There are all these people. They will obviously have to produce good work so that you can predict within the next five years that that area will blossom. There's a lot of money going into it. Everybody is supporting it. You have commercial applications
28:21
and all the technology is there, and there are lots of people, clever guys. That will obviously happen. And in the areas of physics and areas we involve taking the data that comes from satellites and all that, there is a similarly vast amount of data going in. But if I had to predict the most exciting developments
28:41
over the next 50 years, I would say it would be in understanding the human brain, which you might say is neuroscience. But neuroscience is not unconnected with some of the things in computer science. And actually, if you look at neuroscience, it's moving much more in the direction of abstraction. I've got a grandson who's just starting to do neuroscience.
29:01
And they're looking for fundamental principles. How does the mind work? What is the hierarchical structure in which the mind manages to use and understand information? That's such a broad question. It covers everything in this conference. The computer scientists, the mathematicians, the philosophers. And that is the big question.
29:20
And that is the biggest single question for science in the next 50 years. I can't predict what will happen, but I will predict that it will be. And of course biology, molecular biology and so on, as we heard in one of the lectures, and whether the brain is, of course, part of the biological framework,
29:41
is a very special part of the biological neuroscience. So I think if you look outside as a whole, biology will have fundamental advances in computerized medicine, for example. We've heard about personalized medicine. But it's happening now. There's a vast amount of money going into it. The brain, understanding the brain,
30:01
is also linked, of course, unfortunately, to a lot of other things. Brainwashing, you know. So there are negative aspects to these things as well. That's where all the effort, money, and that's where the big progress will happen. But those are both areas where mathematics has a role to play.
30:20
Not by itself, but in combination with collaboration with these other disciplines. Whenever a young man, and my grandson is a young man, he made his own choice, but I often made his own choice. He made an excellent choice to do neuroscience. He is going in now at the time of maximum opportunity for a clever young man. It doesn't mean he's not going to be fidgeting with brains and stuff.
30:41
He's going to be thinking. But how does this machine work? And the data is there, information is there, but we do need people to think along lines of mathematics and neuroscience. So that's where the big progress will happen. Neuroscience will be... And I predict that, oh, I don't know. Because you see, we know, oh, we don't know. I can't predict.
31:00
But I do know that the brain is the most marvellous machine there is, and we don't understand it. So we have here evidence in front of us of something we did a challenge. Understanding the human brain is the challenge of the 21st century, period. No question. And in the wake of that comes a vast amount of other stuff.
31:20
How is the brain to work? How does it relate to what we do now, the mathematics, the computer science? And the talent. So if you're a young man and my grandson is 18, this is the field to be in. And I predict if you're a clever chap and you go in at 18, by the time you're 28, you'll have made a name for yourself.
31:41
Predictable. That is predictable. What it is you have done, how it will depend on you and depend... And that is not predicting... I'm not contradicting myself. I'm not saying I'm predicting the unpredictable. I'm predicting the predictable here because it is obvious. This is a problem which is with us. Technology is with us. It's just starting to happen. You can see the aeroplane just about to take off.
32:02
It's not imagining something in the future. The aeroplane is already halfway down the runway. And when you're halfway down the runway, and when it goes, it climbs up. That's where neuroscience is right now. If I may... Since we will have to wrap up fairly soon. Is there anything else you'd care to say about the form itself? And I know that's moving very far off of what you were just saying.
32:22
Of the format? Of the Heidelberg Laureate form. Well, I'd say it's excellent. Now it's developed. It's matured. The way it operates, it's been embedded in. I think learnt from experience. Some things work better than others. The workshops, they've always been improvements. The works I was involved in went very well,
32:40
but it can obviously still be improved. The presentations are getting very good presentations. The important thing is to maintain... The thing you have to avoid is to have too much fixed program, not enough time for interchange. That's the most valuable part for you. And sometimes, occasionally, I'm skipping a lecture, because you need some spare time.
33:02
If it's too well organized, too much space, there are people who have too much time listening and less time thinking on their own and talking. So my main recommendation is that the algorithm would be don't pack the program too full. The empty spaces you leave, which you may think of as blank, those are where the real discussions take place.
33:20
It's always very hard. When you improve, you finally pack more in. There's a mistake in all education. People say, teach them more. No, teach them less. Let them learn more. Great line. I thought of it spontaneously at the moment. Bravo. You may not be enough of a mathematician to know this,
33:41
but I coined a phrase once, which I think if I remember for nothing else, I'll remember for this. There's a famous German mathematician called Hausdorff. You may have even heard of him. President Bonn unfortunately died to the Nazis, but he did a topology. He defined something called Hausdorff spaces.
34:01
Hausdorff spaces is a space where there's some topology and the point about it is if you have a point here and a point there, you will draw a little house around this, one little circle around it, which don't overlap. So I told people, a space is Hausdorff. Any two points can be Hausdorff from one another. It came to be on the spread at the moment.
34:21
And it is perfect. It is the exact description. And the man's name is there. He is called Hausdorff. It was one of these things that just came like a flash of inspiration. And now people don't know what it used to mean necessarily, but they've heard it. It's in the books, I think.
34:40
And once you've heard it, you'll never forget the definition of the space again. Before that, there were different kinds of names. If you forget all the other definitions, Hausdorff spaces you'll remember. Two points can be Hausdorff from one another. See, now that's education. Thank you so much.