4 ms·

> mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who

> mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Yes, Hardy was a great mathematician and he did say this --- but most mathematicians have tremendous respect for peers who strive for clear exposition in their lectures, their papers, and (if they write them) their books. I am a professional mathematician, and Hardy's attitude is one I have never heard expressed by any of my peers. "A Mathematician's Apology" is a fascinating read, but his description of mathematicians' attitudes is certainly not accurate today. It indeed can be boring to reconstruct your thoughts in a way so that others can understand -- but many of us make the effort anyway, and doing so often leads to new insights.

infinity0 9y ago
The full paragraph (in fact, the very first paragraph of the essay) reads: > It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds. I interpreted "men who explain" not as mathematicians that can explain their work well, but as people who try to explain mathematics in a "lay" way to cater for a large audience, whose explanation can very often become inaccurate, non-mathematical or just downright false, yet still get public credit for seeming to know the field very well, despite these inaccuracies, and even though they are not directly pushing the advancement of the field itself. It's of course a good thing to try to reconstruct your own thoughts, but I wouldn't say it's unreasonable for a mathematician to omit doing that. Could you go into more detail on the examples you mention, where doing so led to new insights?
- impendia 9y ago
  > Could you go into more detail on the examples you mention, where doing so led to new insights? Good question. It's a bit hard to do so (especially without going into mind-numbing technical detail) -- in math you never quite know where insights really come from. "Fortune prepares the prepared mind." But generally speaking, I would say that good exposition gets you thinking about: Why does the technique work? What is the key insight? What are its limitations? And if you think about such questions, you naturally get a better sense of for which other questions your techniques are also likely to work.

infinity0 9y ago

The full paragraph (in fact, the very first paragraph of the essay) reads: > It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds. I interpreted "men who explain" not as mathematicians that can explain their work well, but as people who try to explain mathematics in a "lay" way to cater for a large audience, whose explanation can very often become inaccurate, non-mathematical or just downright false, yet still get public credit for seeming to know the field very well, despite these inaccuracies, and even though they are not directly pushing the advancement of the field itself. It's of course a good thing to try to reconstruct your own thoughts, but I wouldn't say it's unreasonable for a mathematician to omit doing that. Could you go into more detail on the examples you mention, where doing so led to new insights?

impendia 9y ago
> Could you go into more detail on the examples you mention, where doing so led to new insights? Good question. It's a bit hard to do so (especially without going into mind-numbing technical detail) -- in math you never quite know where insights really come from. "Fortune prepares the prepared mind." But generally speaking, I would say that good exposition gets you thinking about: Why does the technique work? What is the key insight? What are its limitations? And if you think about such questions, you naturally get a better sense of for which other questions your techniques are also likely to work.