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Mathematical Chronology

www-history.mcs.st-andrews.ac.uk

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Re: Mathematical Chronology

#31

Post by imh »

>1591

>Viète writes In artem analyticam isagoge (Introduction to the analytical art), using letters as symbols for quantities, both known and unknown. He uses vowels for the unknowns and consonants for known quantities. Descartes, later, introduces the use of letters x, y ... at the end of the alphabet for unknowns.

This may be my favorite point in the history of mathematics. Using placeholders for things (variables) and efficient notation makes reasoning easy. It's such an obvious thing now, but I think it's amazing.

Re: Mathematical Chronology

#34

Post by mrkgnao »

> 1964

> Hironaka solves a major problem concerning the resolution of singularities on an algebraic variety.

Essentially, sometimes the varieties (which are geometric objects like curves, surfaces, etc.) studied in algebraic geometry are singular: they might have singularities, like nasty self-crossings or sharp edges. Hironaka's result lets you take a "bad" variety and "resolve its singularities", giving you a good (nonsingular) variety which you can work with instead.

This is in "characteristic zero", i.e. over fields like the real or complex numbers. We also have fields of positive characteristic, e.g. the integers modulo any prime number. Over such fields, I understand that this is a much harder problem to solve.

The aforesaid Heisuke Hironaka is 86 now.

In March of this year, he published a (purported) proof of resolution of singularities in positive characteristic.

The /r/math thread has some good explanations.

https://www.reddit.com/r/math/comments/6aqwbo/hironaka_publi...

Re: Mathematical Chronology

#35

Post by mrkgnao »

laichzeit0 wrote: post #4

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.

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.

Re: Mathematical Chronology

#36

Post by mrkgnao »

WhitneyLand wrote: post #23
laichzeit0 wrote: post #4

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.

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?

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).

Re: Mathematical Chronology

#37

Post by mrkgnao »

Herodotus38 wrote: post #25

Too bad it ends at 2000, though I understand that 17 years ago may still be too soon to know what should count as history. Does anybody have a suggestion of what they think will eventually be included in such a timeline covering the last 20 years if it were made in 2100?

I made a top-level parent comment about a result from March 2017. Otherwise, things that either will become part of history, or suggest directions for work that will:

* Green-Tao theorem, and lots of other work involving Terry Tao

* Yitang Zhang's work on prime gaps, and subsequent improvements

* Bhargava and collaborators' work on elliptic curves

* The introduction of algebraic topology methods into algebraic geometry (aka "simplicial"/"derived" stuff, see Jacob Lurie)

* Homotopy type theory

* Mochizuki/ABC stuff

* Peter Scholze's work in arithmetic geometry

Re: Mathematical Chronology

#39

Post by dfan »

garrybelka wrote: post #28
williamblake wrote: post #14

There is a network of artificial tunnels in Egypt called the Serapeum of Saqqara. It contains at least 24 large boxes made from single pieces of solid granite, allegedly moved there from a very interesting granite quarry several hundred miles away, then hollowed out to a mirror finish and a precision of a few ten-thousandths of an inch as tested by a precision machinist with a precision toolmaker's square who is also…

That mathematician is Fomenko. An entertaining read though history and linguistics experts just laugh at it. https://en.wikipedia.org/wiki/Anatoly_Fomenko https://en.wikipedia.org/wiki/New_Chronology_(Fomenko)

Garry Kasparov is a Fomenko fan! As conspiracy theories go, I have to admit that it is pretty good.

Re: Mathematical Chronology

#40

Post by AlexDanger »

laichzeit0 wrote: post #4

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.

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 ?

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