Mathematicians have always been willing to accept new ideas

In a recent publication (see here) of a popular internet comic strip that I like, the author poked fun at the supposed notion that mathematicians are intransigent and stubborn, failing to accept new ideas in a timely fashion (this is not merely an outside opinion, there are some insiders who feel the same way… quite strongly in fact. See Doron Zeilberger’s opinion page for instance). However, as someone who is about to get a PHD in mathematics and an amateur mathematics historian, I would like to voice my polite disagreement with Mr. Weinersmith’s premise.

This is the message I posted on the comic’s Facebook page:

“As someone about to get a PHD in mathematics, I can attest that the basic premise of this comic is wrong. Mathematicians have always been much quicker to accept new advances and shifts in paradigm faster than their contemporaries in other fields. The only times when acceptance of new results, even paradigm shifting ones, were slow to be accepted by the mathematical community are those where the result was poorly written or poorly presented (for example, Cantor’s work on cardinality, Brun’s sieve theory, Ramanujan’s work before Hardy, Heegner’s solution of Gauss’s class number one problem, and most recently and still unresolved: Shinichi Mochizuki’s purported proof of the abc conjecture)

Edit: to give a positive example, consider the proofs of Fermat’s Last Theorem and more recently, the Poincare conjecture. These two are considered two of the most difficult mathematical problems in history, and when their solutions were presented, it took only a few years for the mathematical community to verify and accept their correctness. Even more recently, Yitang Zhang’s manuscript containing the proof of the existence of infinitely many primes which are within a bounded distance from each other was accepted in JUST THREE WEEKS by one of mathematics’ top journals, even though Zhang was at the time completely unknown and in particular was not known to have done any work in number theory.”

I would like to elaborate even further on my comments. Not only are mathematicians not intransigent as suggested in the comic, mathematicians are likely to be the group in academia which is the most willing to share their ideas and accept other people’s ideas (this is a broad stroke, there are certainly many people who arbitrarily dismiss people’s work, as anyone who has faced a grouchy referee when submitting a paper can attest) . The lightning fast acceptance of the two big advances on the bounded gap problem should serve as a testament to this. Both of the main players, Yitang Zhang and James Maynard, were at the time more or less completely unknown. Their ‘lowly’ status did not prevent their work from being recognized, almost instantly in fact, by some of the biggest experts in the field (including Andrew Granville and Terence Tao). This seems unlikely in many other areas, especially as one gets further away from pure science.

This is not to say that mathematicians are just more progressive and forward-thinking in general. Social attitudes among mathematicians, while probably better than the general population, is certainly not stellar, as a recent paper by Greg Martin points out.

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