IPMU Interview with David Eisenbud Interviewer: Toshitake Kohno

Kohno: Professor Eisenbud, on the collaborations of it is a great pleasure for me to mathematicians with physicists, have this opportunity to talk astronomers, and scientists with you about the Institute for in other areas? What roles the Physics and Mathematics can mathematicians play in of the Universe. collaboration? As you might have seen on our web page, one of Mathematics and physics the main issues for us at our provide each other with institute is to create new sustenance research fields that go beyond Eisenbud: It’s an interesting traditional boundaries between question. It’s not so easy disciplines; especially between to organize collaborations, mathematics and physics. as I’m sure you know. The It is therefore essential that history is very interesting in mathematicians and physicists mathematics and physics, and get together for discussion in the other sciences, too. Very and work together. Could many of the great problems of you tell us your viewpoints mathematics have come from applications. Mathematics is deeply enriched by its contact with the applications. Many other very important ideas David Eisenbud is a professor of mathematics at the University in mathematics come from of California Berkeley and was , , pure imagination. Somehow, Director of the Mathematical Sciences Research Institute they’re just thought up by (MSRI) from 1997 to 2007. mathematicians because they He was President of the American Mathematical Society are curious about mathematical (AMS) from 2003 to 2005 . things. The surprising thing, I Eisenbud’s research interests include commutative algebra, think, is that both of these turn algebraic geometry, topology, out to be equally applicable and computational methods in these fields. He established the afterwards. So while there AMS Leonard Eisenbud Prize are these two very different for Mathematics and Physics in 2006 in memory of his father, sources, the way they look in Leonard Eisenbud (1913-2004) , applications is the same. an eminent mathematical physicist. The first prize was Riemannian geometry was awarded to Hirosi Ooguri, in some way an applied and Andrew Strominger, and Cumrun Vafa in January 2008. in some way a pure interest

22 IPMU News No. 1 March 2008 of Gauss and Riemann, and develop. Physicists are became the basis for relativity. extraordinary and voracious The noncommutative algebra consumers of these ideas. As of infinite dimensional matrices soon as they hear anything, became somehow the basis they quickly apply it, and of quantum mechanics. These it becomes high fashion in were completely unanticipated physics and very exciting. developments. I think that is In return, the mathematicians a pattern which will continue get problems which they in the future. The best guide cannot solve because we have to the future in this physicists are liable to do regard is the past. One can things with their mathematics learn some lessons from this. that mathematicians would One is that it is very never dream of doing. And the important for mathematics physicists are much better than to be exposed to and interact we are in computing things. with experimental and They make computations, theoretical science. I think and if the computations this kind of exposure is a are successful they know wonderful thing the new that what they did must be Institute can bring about. fundamentally correct. In That’s where some of many cases this is enough for the problems that enrich them, whereas for us it’s not mathematics will emerge. enough and we need to go on It’s also very important and develop the mathematics to maintain the strongest behind this. So I think it’s a possible purely disciplinary very fruitful time of interaction capability so that it can there. feed the interdisciplinary capability. You cannot have How to decipher mountains interdisciplinary science if you of data don’t have disciplinary science. That’s of course only one side And I think that this university of the interaction with physics has such a strong tradition in today. There’s another side to mathematics, that it is well it, and the situation is common placed for that. to the other sciences, as well. The current development Biology has led the way here, of mathematics and physics but it’s very much across is really very striking, because the board. That is, we are I think theoretical physics now capable, with electronic and mathematics are closer instruments and computers, together today than they of producing much more data have been for 100 years. The than we can handle. development of string theory and the very intense work in Interview quantum mechanics in our day Toshitake Kohno is a professor is highly dependent on the of mathematics at the University of Tokyo, and he is a principal tools that the mathematicians investigator of IPMU.

23 I remember the physicist Chance favors only the discussions. Then one of the working on physics circa 1950. Robert H. Dicke coming to prepared institute groups will have no chance We have really understood speak once at a colloquium Kohno: Research in statistics of getting into the ideas of the mathematics of the kind many, many years ago. He and experimental physics is the other group. I think it is of quantum mechanics that talked about measurements also an important aspect of very important to have an people were doing before of the oblateness of the sun. our institute. organized forum in which 1950, but the kind of quantum The sun is not perfectly round, You mentioned each group is supposed to talk mechanics that was done in and exactly how much it fails interdisciplinary research. to the other group. It’s quite the second half of the 20th to be round is important if you Let’s talk about this. As a hard for them to do, so unless century is still very hard for think about the verifications former director of MSRI, you you push hard they don’t do mathematicians to understand, of general relativity by the have organized a number it. But if they do it, then they and I think for physicists to bending of light around of activities in various fields are quite pleased afterwards, I understand, too. the sun. So he was very of mathematics. I was very think. So it’s worthwhile. The most accurate interested in this question of impressed by a program of There are various ways that predictions in all of physics, the oblateness of the sun. He MSRI in the mid-eighties. Two one can do social engineering. in some way, are those in collected data－at that time, very different programs, one Of course it’s important simply quantum electrodynamics. in those early days, it was still in topology and the other in that they meet each other, They are made by summing only a tiny, tiny fraction of operator algebras, started talk to each other, and know the first few terms of a what we do today－but the in parallel and then were each other’s names. This is series which is known to be data sat in his laboratory. Each unified to create a new field difficult enough. I think it’s divergent. This is not a happy day there would be a pile of of mathematics, the discovery also important to have series situation. Despite lots of work printouts. Who could read all of the Jones polynomial. In of elementary lectures by one I think this remains a difficult these things? your opinion, what makes group for the other group to problem. People in physics This is widely recognized interdisciplinary research make it possible for people to integrate over nonexistent as one of the fundamental possible at the Institute level? learn things they didn’t know spaces all the time perfectly problems of experimental Eisenbud: I have to say luck about already. Then there are happily, and I think the science today: our ability to plays a big role. Since you new ideas, and it’s exciting, absorption and understanding produce interesting data is can’t control luck, you have to and people talk to each other. of that material will be very far greater than our ability control the other things around “Oh yes! I have a tool that important for mathematics, to absorb and understand luck. The great biologist Louis might fit your problem.” And and ultimately for the progress it. The mathematicians are Pasteur said:“ Chance favors this then goes forward. of physics, as well. the only ones, I think, who the prepared mind.” In the Approaches to string On the other hand, the have the tools which will same sense, chance favors the theory problems of string theory begin to be effective in prepared institute. involve the deepest parts of this way, mainly through One thing that MSRI does Kohno: Recently there have mathematics. I think physicists statistics and combinatorics regularly is to bring programs been very close relationships, have made very good use and computer science. One together which are in some again, between geometry and of many surprising tools and sees this very much in the way related, in the hope that physics; for example, mirror results from mathematics, study of the genome and the this will make interaction more symmetry. Could you tell us and have often led the way. matching algorithms we have likely. Of course if you have about your prospect for future There’s a great interchange developed there. This bleeds very smart people working on developments in synergy between the two fields. I think over into computer science. related things and one group between mathematics and this is a very happy time for By the way, I think one should has the chance to learn from physics? mathematics and physics in regard computer science, the other, then this makes Eisenbud: I think the that regard. mathematics, and statistics one the luck possible. One way to possibilities are very Kohno: Thank you very much subject for this purpose. These inhibit interaction is only to bright. In some ways, the for your valuable comments. are very important trends. have very technical, specialized mathematicians are still

24 IPMU News No. 1 March 2008