[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.