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!)

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!

Not wanting your child to be permanently compared to you for their entire career is entirely understandable

> But what he deemed being posited as true

Implicit in the "correctness" of this motive is the idea that unless you're #1 in your field, you are nothing (depression implies strong feelings of worthlessness).

I don't know if you think that's a great lesson to teach your kids as a parent, but I don't.

It’s unusual to tell others not to do something because you’re projecting they’re secretly doing it to compete with you, or that they’ll be depressed when they don’t do what you did.

Doubly so when the rationale is “I’m so fucking awesome”

Triply so when it’s something you’re passionate about, presumably inherently.

Quadruply so when it’s your child. Its tough as a kid hearing your parents come up with elongated excuses why you can’t dream and work towards a future.

When you let people find their own way, you might even learn something from it (ex. 70 yo Gauss learns he didn’t need to tie his mental state to his work because his son doesn’t suddenly become depressed from not matching dads output)

Re: second half, sounds about right, confused at relevancy though (is the idea the child would only do it to pursue nepotistic spoils and an additional reason is the spoils aren’t even good?)