[gkafkg8y8]

It's ok to try tackling a big problem, as long as you know when pause for a while and come back to it later.

What if Ramanujan had been told by Hardy to stay home and stop working on big things that he hadn't had sufficient experience in? While there will ever only be one Ramanujan, he wouldn't have developed into what he did had he restricted himself. He made a lot of mistakes, and that didn't kill his career nor did it stop him from producing many great works.

Similarly, Bezos obsessed about a simple online bookstore website. Jobs obsessed over details for a small number of devices. Torvalds obsessed over an operating system he wrote. DHH obsessed over a web application framework open source project for his company. If you obsess over something, it has a much better chance for success.

If you believe in it, and you see a path to it, don't give up.

[mathgenius]

Ramanujan produced a constant stream of results and wasn't at all obsessed with one big problem to solve.

Terrance Tao is talking about the "hide in the attic for 10 years working on one problem" attitude. And this he warns against.

As for business development, I'm pretty sure Jobs/Bezos etc actually produced something in fairly short order, ie. the MVP came out quickly. This approach of release early, release often seems to be exactly what Tao would endorse.

[joe_the_user]

Yes, Ramanujan just floated around dealing with whatever number theories inspired him, sometimes in a nearly mystical way so he's not a good example.

Andrew Wiles is a better example, since he hit in plain sight working on Fermat's Last Theorem.

"He dedicated all of his research time to this problem for over six years in near-total secrecy, covering up his efforts by releasing prior work in small segments as separate papers and confiding only in his wife."

https://en.wikipedia.org/wiki/Andrew_Wiles

[Ma8ee]

Exactly. He proves the author's very well. Wiles was tenured, had published in the field already, and made sure that he could continue publishing while working on the Big Problem.

[nwjtkjn]

Tenured at Princeton, had already solved some fairly big problems in the field, and it helped that FLT had recently been "reduced" to proving a conjecture about elliptic curves which were already very much in Wiles's wheelhouse.

Not to take away from his achievement, but I think it is not stressed enough how much the proof depends on work from previous decades that a priori had nothing to do with Fermat.

[glaberficken]

Note that with Andrew Wiles all the secrecy and seclusion almost exploded on his face. When he first came public with the Fermat proof someone found a flaw in it within 2 months.

It took another 2 years (he was ready to give up by then) to finally come up with a "fix" for the flaw that had been found.

So in the end he was only successful after exposing it to the public for scrutiny and breaking down the problem into something smaller.

[joe_the_user]

Sure but if Wiles hadn't been secret, he'd be making progress reports all along and plausibly the person who made the fix would be the one who credited with the proof.

It's kind of shame that the quest for credit works this way, secrecy has all sorts of costs but in this instance it clearly had benefits too.

[rjtobin]

Context is important here I think. This is part of a series of posts containing career advice for mathematicians at various stages ([1]), and not life advice in general. So I don't believe Tao was addressing cases like Torvalds etc.

This post appears in the "Graduate level" section. At this point many open problems become accessible, while at the same time many grad students (emerging from being a big fish in a little pond) are looking to make a name for themselves. So a common trap is for people at this point to obsess over famous problems, to the exclusion of tackling less exciting but more tractable problems, and Tao is warning against this.

[1] https://terrytao.wordpress.com/career-advice/

[deepnotderp]

Agreed. Many a promising mathematician has been lost to the riemann hypothesis.

[rolltack]

I completely agree. Digging deep in the weeds and pulling yourself out over an over again is how most impactful problems get solved. It's time consuming and the truest test of patience. It's very fulfilling to live this way, even if it seems like world is moving at a much faster pace

[xrisk]

I think this is confirmation bias at work here.

[chr1]

> What if Ramanujan had been told by Hardy to stay home and stop working on big things that he hadn't had sufficient experience in?

he wouldn't die from tuberculosis so early?