[libraryofbabel]

One of the things I admire about many top mathematicians today like Terence Tao is that they are clearly excellent mentors to a long list of smart graduate students and are able to advance mathematics through their students as well as on their own. You can imagine a half-formed thought Terence Tao has while driving to work becoming a whole dissertation or series of papers if he throws it to the right person to work on.

In contrast, Gauss disliked teaching and also tended to hoard those good ideas until he could go through all the details and publish them in the way he wanted. Which is a little silly, as after a while he was already widely considered the best mathematician in the world and had no need to prove anything to anyone - why not share those half-finished good ideas like Fast Fourier Transforms and let others work on them! One of the best mathematicians who ever lived, but definitely not my favorite role model for how to work.

[rcxdude]

Well, in that time it was more or less how mathematics worked. It was a way of showing off, and often it would be a case of "Hey I've solved this problem, bet no-one else can". It was only later it became a lot more collaborative (and a bit more focused on publishing proofs).

[libraryofbabel]

You're correct that the culture of mathematics has changed a lot, and has become much more collaborative. The rise of the modern doctoral training system in Germany later in the 19th century is also relevant. So really Gauss's example points primarily to how much mathematics has changed. But at the same time, I think you could reasonably take Gauss to task even applying the standards of his own era - compare him with Euler, for example, who was much more open with publication and generous with his time and insights, frequently responding to letters from random people asking him mathematical questions, rather like Tao responding to random comments on his blog (which he does). I admire Euler more, and he was born 70 years before Gauss.

Of course, irascible brilliance and eccentricity has an honorable place in mathematics too - I don't want to exclude anyone. (Think Grigori Perelman and any number of other examples!)

[srean]

There's also this notion of holding themselves to their own standards.

They, Newton included, would often feel that their work was not good enough, that it was not completed and perfected yet and therefore would be ammunition for conflict and ridicule.

Gauss did not publicize his work on complex numbers because he thought he would attacked for it. To us that may seem weird, but there is no dearth of examples of people who were attacked for their mostly correct ideas.

Deadly or life changing attacks notwithstanding, I can certainly sympathize. There's not in figuring things out, but the process of communicating that can be full of tediousness and drama that one maybe tempted to do without.

[srean]

Weird typo in what I wrote. It's past the edit window. This is what I had meant to type:

There's joy in figuring things out, but the process of communicating what has been so figured can be tedious and full of drama -- the kind of drama that one maybe tempted to do without.

[hinkley]

Someone blew my mind by convincing me to read Bush’s “As we may think” which was published in 1945. Then I started digging into him and discovered he was also the second president of the ACM, was instrumental in shaping the formation of the National Science foundation (mainly by critiquing their initial plans as unworkable) and also Claude Shannon’s doctoral advisor. Because of course he was.

[libraryofbabel]

Not to mention instrumental in getting the Manhattan Project going, along with many other research projects during WWII. He basically knew everyone. I didn't know he was Shannon’s advisor though!

[PunchyHamster]

not sharing something you had no time to properly check is entirely understandable