First, I think this is a very welcome, very open interview (several questions/comments are just great, congrats to the interviewers!) and it is extremely interesting to see the opinion of this great mathematician (inter alia, Fields Medalist in 1982) on a wide range of topics. The pros: I completely agree with Connes's view on the distinct (ir)relevance of String Theory for Mathematics and respectively, Physics. I also like his (humorous) detachment from being considered the guru of NCG (of which unfortunately I know currently epsilon, albeit once I was almost sure this is what I wanted to do...) and from the tendency of always looking for / looking up to the one mastermind, in general, in any (sub)discipline. So no more on those, read for yourselves in the transcript of the interview. What I don't quite agree with is summarized below:
- resources (money) in research are not important (Connes's context has to do with the large interest/funding in Bio-Mathematics; he actually says "nothing", which I take as far stronger than "not important":-)): to the extent that it shapes incentives, I think it is actually very important. Intrinsic motivation is (the most) relevant, but it is not everything. The marginal (very able-- let us simplify) scientist can be moved into one direction or another by means of designing proper (or improper; but then again, who is to decide what is proper/improper in the context: I think we ought to take the view that lots of money is being thrown in one direction, because there is a lot of interest in that particular direction) extrinsic rewards. That being said, I personally (also) think there are a lot more interesting things in/to Maths than Biomaths :-).
- the European academic system is better than the US one. Hmmm, this is an endless debate and, as always, the truth is probably somewhere in the middle. Inter alia, it goes back to whether you need/want tenure or not in the academe (see for instance such a debate I've earlier linked to, especially within Economics) and to what goals you expect researchers to meet. And this also goes beyond one or another discipline, although it is perhaps interesting to discuss it indeed in the light of fundamental Mathematics, given its very abstract nature. Now, Connes believes that a system such as the French CNRS (which possibly is in the process of changing since 2005, when this interview took place) is perfect for mathematicians working on extremely complicated issues, that take years and years and years, since they are insulated from being subjected to those "n publications" requirement per year and in general from the eternal harassment of frequently showing how you compare to your peers, something specific to the top US institutions (Connes dismisses that the US places are ultimately inherently better in producing top scientists, because they get all the top European people-- not (entirely) true and to a great extent working eventually against his thesis, e.g. need to justify preferences of those very high European achievers for the US places, but let us not get also into that). The potential problem (sacrifice), as acknowledged by Connes, is the cost of such a practice, given that a lot of people might end up not producing anything and that the vast majority of them will be very far from getting Fields Medals or similar recognition among their peers... I say that the main problem is who bears that cost, namely the taxpayers here; and the public (not all of them having the same goals as Connes or as the specific, minority, group of the scientists, in general) is justified in knowing and assessing (whenever it so pleases) where its money is going and what precisely it pays for (if the funding is private, all this discussion has a completely different flavour-- remark that the US top academic places are privately funded, while all European examples Connes mentiones are public institutions; in my view, this again tips the balance towards the US academia). Related, but extremely surprising, Connes seems to be nostalgic after the Soviet Union academic system, but I think he deeply confuses things-- anyway, let us just say for the sake of this brief post that, fortunately, France was never quite like the Soviet Union, despite its tendency to lean extreme left, particularly within its academe... As for the claim that the Soviets would have been far ahead US and everybody else, if their system remained in place, I guess we'll never know (though I have opposite priors). And I think it is better we don't... So I am rather dissapointed that one of my idols in Mathematics has/had (this was '05) such, hmm: uninformed, views. But then again, I've always thought Economics (Not Politics. Politics is just a surface, not relevant in the long run, ultimately all boils down to Economics-- really!) is far less intuitive than Mathematics or Theoretical Physics :-).
I am sure one can go on and on, but I trust the main ideas are all outlined above (read also between the lines).