[darkmighty]

And von Neumann lived mostly though war and 30's financial crisis. I honestly think it's more a question of (lack of) will/confidence from part of academia. I bet if had really good ideas about new languages and really wanted to dig deep on that he would be able to do so without starving.

Maryam Mirzakhani (this year's female fields Medalist) commented that she's quite a slow thinker, and left a clear impression that it's more a matter of asking important questions and actually trying to solve them with perseverence. It's just far more secure to chase the low-hanging fruits.

http://www.simonsfoundation.org/quanta/20140812-a-tenacious-...

" Another notable and enviable trait of von Neumann's was his mathematical courage. If, in the middle of a search for a counterexample, an infinite series came up, with a lot of exponentials that had quadratic exponents, many mathematicians would start with a clean sheet of paper and look for another counterexample. Not Johnny! When that happened to him, he cheerfully said: "Oh, yes, a thetafunction...", and plowed ahead with the mountainous computations. He wasn't afraid of anything."

That's an inspiration!

[tachyonbeam]

My understanding is that during the war, the american government was throwing money around liberally. Trying to do everything it could to outwit and outdo the enemy. This is part of what caused the post-war economic boom, money being distributed and more people getting a chance to prosper.

[xrange]

My understanding is that after the war, the rest of the world needed to buy stuff, but the U.S. was the only major country with an intact manufacturing base. So that's why the U.S. made 30.5% the world's manufactured goods exports in 1948, compared to 15.3% in 1938. See table XXIII on page 52 of:

http://unstats.un.org/unsd/trade/imts/Historical%20data%2019...

[e12e]

Makes one wonder what the NSA have been doing since the 80s. They're supposed to be the biggest employer of mathematicians, and since the 90s they've had their very own "war budget". Maybe in 2050 we'll say -- oh wow, look at all the great stuff that came out of the islamophobic-fuelled war on the middle east that the US spearheaded. Shame about the future ruined for half a billion people, but boy did they come up with some crazy stuff at the NSA!

[gwern]

> Makes one wonder what the NSA have been doing since the 80s. They're supposed to be the biggest employer of mathematicians, and since the 90s they've had their very own "war budget".

I wonder. Does anyone have recent sources indicating the NSA really might be the biggest employer of mathematicians? I'd also point to the Snowden and other leaks and attacks like Stuxnet - so far, everything revealed has been fairly humdrum in the sense that they are more or less what you'd expect if you threw a few billion dollars at known vulnerabilities in the Internet and current OSes. Portmapping entire countries' computers may be impressive in some respects, but not in the sense of beyond-cutting-edge cryptography/mathematics.

[e12e]

I'd say the recent revelation/allegation that NSA accidentally took down Syria's Internet connection in the recent Wired interview with Snowden and the general "vibe" of mismanagement that I get from Snowden's and Binney's accounts -- doesn't have to imply that NSA doesn't also do interesting work other than their practical attacks on global infrastructure. But it does seem clear that if they actually do interesting stuff (say, working on using multiple satellites to photograph the same area in order to extrapolate to higher resolution images than what is possible from a single lens due to atmospheric effects -- or perhaps quantum or DNA/RNA computing etc). It is clear that whatever they might be doing, it does seem to be ridiculously highly classified, just like the sibling comment's example with RSA and GCHQ.

[gwern]

While the NSA has a huge budget, it's not infinite, and what gets one promoted and what analysts are boasting about in their slides gives you a definite idea for what the organization values. Do any of the leaks sound like there might be huge contingents of mathematicians off in side-corridor making breakthroughs? Not really.

[darkmighty]

We're more likely to say "what a huge burden was NSA!". Major crypto breakthroughs created there (in either breaking something/creating something) would be kept secret for years, so it just bogs down innovation. GCHQ infamously invented public key crypto but no one was allowed to show outsiders for comment so it just died there until it was reinvented a few years later.