4 ms·

I'm not a mathematician, but I've always been fascinated by two specific periods in the history of mathematics: Around 1750-1850 where you have Gauss, Fourier,

I'm not a mathematician, but I've always been fascinated by two specific periods in the history of mathematics: Around 1750-1850 where you have Gauss, Fourier, Poisson, Laplace, Navier, Cauchy, Lagrange, Euler. That's just... insane. And then the mathematics that happened around ~1940.. Kolmogorov, Fisher, Poincaré, Gödel, Von Neumann, Church, Turing... Just crazy.

lordnacho 9y ago
Funnily enough, I think the same. The first is the stuff you do in school. Always good to have context, which sadly there's little time for. The second is fundamentals and computing stuff, and stats. There's a good chance you'll have to use a computer to calculate things over large datasets sometime in your life. Crypto is interesting as well.
WhitneyLand 9y ago
I'd love to be able to watch a simple video interview with these guys. Something like...Dr. Gödel, could we take just a few of your notable insights and have you walk us through how the fuck you managed to come up with them?
- mrkgnao 9y ago
  As I understand it, a significant portion of the cleverness is in the audacity of encoding something liar paradox-like into a formal logical framework (and perhaps also the precision with which logics were specified and differentiated from one another).
- pdm55 9y ago
  some insights https://www.webofstories.com/story/search?q=math&max=20&p=1&sp=&ch= https://www.webofstories.com/story/search?q=math&max=20&p=1&...
mrkgnao 9y ago
Well, a couple decades later we have the era-defining unification of geometry, algebra, and number theory building on the work of Noether, Hilbert, Weil, and so on. To drop a few names, we had Grothendieck, Serre, Deligne, Wiles, Illusie, (the elder) Artin ... and it's continued to this day. Wiles' proof of FLT built upon this beautiful synthesis of ideas, for example.
AlexDanger 9y ago
I imagine there are some testable hypotheses around this very interesting question. 1.) What, if any, of mathematics has been invented concurrently in different regions (say within 10-20 years) without collaboration or knowledge of other derived work? 2.) To what extent is the rate of mathematical development associated with war or advances in knowledge sharing? Be it radio, printing press, persuing weapons development, crypto, or mass migration (eg post ww2). I think 1.) comes about via natural scientific progress. Some mathematical ideas are dependent on the right set of tools being invented or environmental necessity. How many people independently came up with ballastics equations once soldiers starting flinging big rocks at each other? The 2.) Question is very interesting to me. What is the network effect of mathematicians sharing ideas? What happens when the 10 smartest mathematicians in the world end up all working at the same elite university? Why isnt this just accelerating mathematical progress in the 21st century? Are breakthroughs harder now? Does the internet and peer review journals provide too much noise? Or is it simply that progress is so fast now we don't think of these things as extraordinary ?

lordnacho 9y ago

Funnily enough, I think the same. The first is the stuff you do in school. Always good to have context, which sadly there's little time for. The second is fundamentals and computing stuff, and stats. There's a good chance you'll have to use a computer to calculate things over large datasets sometime in your life. Crypto is interesting as well.

WhitneyLand 9y ago

I'd love to be able to watch a simple video interview with these guys. Something like...Dr. Gödel, could we take just a few of your notable insights and have you walk us through how the fuck you managed to come up with them?

mrkgnao 9y ago
As I understand it, a significant portion of the cleverness is in the audacity of encoding something liar paradox-like into a formal logical framework (and perhaps also the precision with which logics were specified and differentiated from one another).
pdm55 9y ago
some insights https://www.webofstories.com/story/search?q=math&max=20&p=1&sp=&ch= https://www.webofstories.com/story/search?q=math&max=20&p=1&...

mrkgnao 9y ago

Well, a couple decades later we have the era-defining unification of geometry, algebra, and number theory building on the work of Noether, Hilbert, Weil, and so on. To drop a few names, we had Grothendieck, Serre, Deligne, Wiles, Illusie, (the elder) Artin ... and it's continued to this day. Wiles' proof of FLT built upon this beautiful synthesis of ideas, for example.

AlexDanger 9y ago

I imagine there are some testable hypotheses around this very interesting question. 1.) What, if any, of mathematics has been invented concurrently in different regions (say within 10-20 years) without collaboration or knowledge of other derived work? 2.) To what extent is the rate of mathematical development associated with war or advances in knowledge sharing? Be it radio, printing press, persuing weapons development, crypto, or mass migration (eg post ww2). I think 1.) comes about via natural scientific progress. Some mathematical ideas are dependent on the right set of tools being invented or environmental necessity. How many people independently came up with ballastics equations once soldiers starting flinging big rocks at each other? The 2.) Question is very interesting to me. What is the network effect of mathematicians sharing ideas? What happens when the 10 smartest mathematicians in the world end up all working at the same elite university? Why isnt this just accelerating mathematical progress in the 21st century? Are breakthroughs harder now? Does the internet and peer review journals provide too much noise? Or is it simply that progress is so fast now we don't think of these things as extraordinary ?