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Fourier and Legendre

[T]he comparison between Mochizuki and Grothendieck is a poor one. Yes, the Grothendieck revolution upended mathematics during the 1960’s…. But the ideas coming out of IHES immediately spread around the world, to the seminars of Paris, Princeton, Moscow, Harvard/MIT, Bonn, the Netherlands, etc. Ultimately, the success of the Grothendieck school is not measured in … theorems … but in how the ideas completely changed how everyone ELSE thought about algebraic geometry. This is not a complaint about idiosyncrasy or about failing to play by the rules of the “system.” Perelman … repudiated the conventions of academia by … posting … to … arXiv [instead of submitting to journals]. Perelman did go on an extensive lecture tour and made himself available to other experts…. … Usually when there is a breakthrough in mathematics, … other mathematicians are able to exploit the new ideas … usually in directions not anticipated by the original discoverer(s). …

Frank Calegari

Shortly after Faltings announced his proof of Tate’s isogeny conjecture and the Mordell conjecture, he lectured on it at the Arbeitstagung, explaining the new tools he had introduced. Everyone in the audience who had thought about the problem was immediately convinced. Instead of producing 300+ pages of manuscript, Mochizuki needs to give one or two lectures ([not in Japan:] in Bonn, or Paris, or Boston, or..) clearly explaining the new ideas in his argument and showing how they lead to a proof of ABC. This shouldn’t be difficult — I have no idea why he refuses to do so.

—Dick Gross

(NB: Calegari’s claim that years of work are never required to understand a decade of someone else’s thoughts, like every time a mathematician invokes the phrase “all of science”, are obviously wrong.

Nevertheless this is a vastly more valuable comment from an insider about the culture of mathematics and number theory than normal people could read in a newspaper. Given the way suppositions about what mathematics is like influence the way children are treated in the real world, it’s worth passing around insider comments that clarify what mathematics is and how it works—it’s quite more informative than the NYT reporting about Yitang Zhang or Terence Tao, or much worse, Stephen Hawking Versus Philosophers: yawn, and wrong. Nothing about us without us. Notice the focus on communication between known individuals: you would see the same stuff in “The Fortuitous Arrival of Heegner Points” (which Dick Gross was part of). And if you wander into a mathematician’s office wanting to talk about stuff, you will probably get the same response personaly: who are you, what have you been working on, what is your style, what have you done before?

I believe it’s a beautiful collaborative community for those who can play—as Jacob Lurie described it, Mathematics is a giant room full of toys, some of which have very long instruction manuals. And when you find someone else you can play toys with, you want to share everything you find with them, enjoy playing together, and so on. Mathematics is rare among intellectual pursuits as well, in that people from a different sub-field can and do fruitfully exploit each other’s findings. Try that with a Lacanian seminar—the excitement may be there at the outset, but quarrels are more likely than collaborations, and talking over listening carefully enough to faithfully replicate the other theorist’s ideas into another profitable pursuit. And that spirit of honest, joyful collaboration, quite different from the chilly competitive machismo one usually hears about of mathematicians, is a human pursuit worth emulating and, perhaps, participating in.

how do you feel about him walking away................

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Romain Koszul - Probing the dynamics of complex microbial communities...

Romain Koszul – Probing the dynamics of complex microbial communities…

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