Written: Nov. 13, 2009
DZ: In the November 2009 issue of the Notices of the American Mathematical Society I read Mikhail Gelfand's very interesting interview with the eminent human mathematician Yuri Manin. I don't want to take too much from your precious time (I understand that are you working very hard on proving the Riemann Hypothesis and the Goldbach conjecture), so I will only ask your opinion about some of the more outrageous-and to my mind-completely false, statements made by Professor Manin.
SBE: Unfortunately this is still true for most "people". But this is because "people" didn't yet realize the full potential of computers to completely revolutionize mathematics from the stone-age of human mathematics.
SBE: This is human-elitist (and implicitly [and I am sure unintentionally] sexist and racist) nonsense. Mathematics is part of culture, and that's why they were so few women or minorities in the past.
SBE: He knew more mathematics than any human, even more than Manin.
SBE: The Four-Color problem is the best problem of all time. Its amazing proof was a watershed in the history of mathematics, and the harbinger of future mathematical research methodology, that will all be done by computers (for the next one hundred years still assisted by humans, but eventually humans will be superfluous). So it didn't lead to a human "program" in the sense of Bourbaki, but it lead to the most exciting meta-program of our time, using computers to prove deep results that not even smart humans like Manin would ever have a chance to prove by themselves. Speaking of Bourbaki, Manin sounds like a Bourbaki left-over, and it bothers me that even today one can speak like Dieudonné who put "combinatorics" in derogatory quotation marks, claiming that it is without issue (which is just one notch above "stillborn" problems, like odd perfect numbers). All these human "programs" are ipso-facto trivial because they were conceived by humans, and as we all know, humans are trivial creatures.
SBE: Very safe prophecy, Prof. Manin! Why did you pick twenty years? You are probably right that the same-old-way since Euclid will still be the "mainstream" as long as you and other mathematical grand-old-men are mathematically alive, just by inertia, and computers will only be used in trivial ways as "pencil-with-power-stirrings" (as George Andrews quipped). But I am willing to bet that in a hundred years all the dusty volumes of Bourbaki, safely saved in electronic archives for pre-historians of mathematics, will only be of historical interest, and mathematics will be very different than that of Euler, Gauss, Perelman, or Manin.