What seperates the Greatest mathematicians from the greats

there are alot of great mathematicians in history, past, present

but some are of course greater than others, an elite few

what is it

>natural intelligence plays a role
> is it luck based, happen to have the right opportunities etc.
>study more than the average mathematician

what is it?

the true GOAT coming through

he's good

but this is the true GOAT

There isn't a monolithic answer to this question. It's as varied as there are mathematicians. You'll have people whose parents forced them to do maths 10+ hours a day and who end up being very prolific and have people who do math

some rare people are incredibly thoughtful, gifted, and driven

Some people have a gift. Ramajuan recreated modern mathematics in his bedroom with just a shitty elementary text.

But here's a nice quote.

>How to become a mathematician?
"I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up." -Paul Halmos.

I think the most important factor is whether or not there is, at their prime, a good enough question to answer in their field and whether or not it's possible to answer it.

Three dimensions, user: depth, breadth, and length.

depth: actual importance of results, the deeper (that is, the more useful to later people), the better, and the more, the better. This is why Newton is genuinely good, for example, though one doesn't want to read the historical documents.

breadth: ability to weigh meaningfully across topics, and not just get stuck in one area. Wanna know why Ted Kaczynski isn't known as a BRILLIANT mathematician, and instead merely as a good/competent one? Because he cut his own career short to go live innawoods, and his professionial output focsed around a topic in complex analysis known as boundary functions.

length: you have to be long-lived enough to build up your corpus in a meaningful way, and keep amassing it in your own terms. This is what Euclid, Grothendieck, Euler, Gauss and Erdos all have in common. Obviously Galois and Riemann made their contributions, but they were both cut short, which stops them from serious GOAT discussion.

really you just have to do maths all the time and enjoy it.
grothendieck, ramanujan, gauss, euler, etc. basically lived, breathed, became math, because it just came naturally to them.
you can shut yourself in your room and do math 12+ hours a day but if you don't get enjoyment out of it you'll go insane.
if you aren't already like this then you probably can't make yourself like it.
it's ok, there is more to life than technical perfection in one narrow area of human knowledge.
even if you are not a "great" you can probably still make important and interesting contributions to math. it's all about hard work in the face of intimidating odds.
good luck user.

> Ramajuan recreated modern mathematics in his bedroom with just a shitty elementary text.
Out of curiosity, does anyone know which books he had?