Bill Thurston’s “On Proof and Progress” or as I prefer: “Why do I, as an individual, matter?”

Math prof to class: “Who is the most famous mathematician of all time?”

Brave student: “Gauss!”

Math prof: “Close! But Gauss is only the second most famous mathematician”

Student: “Who’s the most famous then?”

Math Prof: “Ted Kaczynski”

 The above was a real conversation that happened in a math class at Wisconsin.

I used to wonder to myself: “I love math but will any of my work even matter to real people?” Maybe you’ve also wondered if you and your work is important to anyone else at all. 

Well, a grad student mentor at Wisconsin was kind enough to direct me to the following two articles. The first is a post by celebrated Field’s Medalist Bill Thurston on math overflow (a.k.a. the serious math forum for professionals) answering a question from a student who is wondering why they should even try in math if they’re not a genius.

http://mathoverflow.net/questions/43690/whats-a-mathematician-to-do/44213#44213

The second is a longer article by Thurston explaining his views in more detail.

https://arxiv.org/abs/math/9404236

My take away from reading these:

  1. Individual geniuses are not that important in the long run
  2. Math as a whole subject is important to society
  3. Math as a subject needs a community of scholars to keep it alive. Being a part of this community and giving back to this community is important.

Side remark: In the second article it is interesting to see that Thurston developed a niche sub-field of topology on his own, but he regrets that he solved all the easy problems in his new field. Instead he wished that he had left the easy problems alone so that future mathematicians could solve them and then be inspired to add to this subfield.

June 3rd Update: I forgot to mention that Terry Tao also writes roughly the same argument on his blog under the career advice tab.

 

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