2014-12-94

InterviewPictures are very important; although crude and specific,they convey more than a thousand words, as they say.Proofs, when written down, are formal, although ofcourse never adhering to the standards logicians maywant to impose. In that sense, they provide a detourwhen it comes to communication. How do you readproofs, or do you at all?When I encounter a result, my first reaction is: ‘Can Iprove this myself?’ And I try. Usually, I see how it is beingdone but occasionally I get stuck. I look for how thatdifficulty is treated in the proof, so in effect I am successivelybisecting the proof, zooming in on the crucial point(there could of course be several). So I either get it ordiscover that the proof is wrong.This ties up with how to present mathematics to an audience.What do you think of this modern fashion ofPowerPoint, beamers and all? I find them flashy.They certainly are flashy. I prefer the blackboard, ofcourse, but in a situation like here at the congress, youhave no choice. Using a blackboard presentation, you donot really have to prepare, if you see what I mean; also,you can change your presentation in mid-flow; you candraw pictures spontaneously. Also in my published workI try to include as many pictures as is feasible.How do you draw them? Personally, I taught myselfPostScript.I used to program in PostScript myself, or rather I generatedPostScript code writing in C++. Now I have adoptedTikZ, developed by the same guy who invented beamer.It makes the interface with text much more natural; youdo not need to keep separate files.Another disadvantage with this is that the speaker becomesmore and more superfluous; the talk becomes amovie and the speaker can join the audience. In otherwords, there is a lack of presence and presence is whata personal conversation has. But I would like to pickup on a thread we lost some time ago. Time is linearlyordered but structures of ideas are not, which is part ofthe difficulty of conveying mathematics in time. In thepast there was not this pressure to publish. What is betterfor the ordinary mathematical graduate student: tostudy and learn something which is well-known but interestingor to do something new, which even if originalis uninteresting?For the sake of culture, the first is obviously to be preferred.But it is hard to predict what is interesting, just asit is hard to predict what may be applicable.But in many cases a thesis, or more generally a typicalpaper, may just be a pointless technical exercise, thepurpose of which is solely to satisfy bureaucratic demands,not to be read and pondered.As I have already said, this is the way the world worksand there is little we can do about it.In the past, there was the possibility of being a highschool teacher. Most people with PhDs in mathematicsin Sweden in the first half of the previous century endedup as high school teachers. Weierstrass was one for along time. It was a prestigious position.Not anymore. Times have changed. True, I know personallya woman who was very good and ended up as a highschool teacher in Switzerland.Finally, to return to a theme we touched upon earlier,what motivates you to solve problems? Obviously notmoney. There can hardly be any more difficult way ofearning a million dollars than by solving one of theMillenium problems, even for mathematicians. Couldit be fame?Money – certainly not. As I noted we have modest needsand they are usually met. And as to fame, I’ve got my fairshare of that now.So we come back to the love of mathematics, the sweetnessof the challenge and something most people simplycannot understand.Ulf Persson [ulfp@chalmers.se] has beena member of the editorial board of theEMS Newsletter since 2006 and a professorof mathematics at Chalmers Universityof Technology in Gothenburg, Sweden,since 1989, receiving his Ph.D. at Harvardin 1975. He has in the past interviewed recentFields medalists specifically for the EMS Newsletter,as well as other mathematicians for alternate assignments,in a conversational style, some published, others as of yetunpublished. There is a plan to make a selection and collectthem into a forthcoming book.EMS Newsletter December 2014 47