8 ms·

Mathematical Chronology

139 points by kercker 9y ago

h3ctic 9y ago
Wondering how much from the last 100 years has been left out
- swampers 9y ago
  Probably a huge amount given that ~50% of the mathematicians* who have ever been alive are alive today. Source: Pure Mathematics Hons BSc, St Andrews - I took the St Andrews "History of Mathematics" course this site's information is used in. *For a given value of 'mathematician'. And 'alive', I guess.
  - mbrd 9y ago
    Nice to see another St Andrews person on HN - I took that course too! I only wrote two essays during my four year degree, one for this class! (I wrote about Alexander Aitken, a gifted mental arithmetician)
laichzeit0 9y ago
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 ?
jordigh 9y ago
A guy I knew used to say that this is why computer science is so much easier to learn than number theory. It's thousands of years of number theory to learn vs a few dozen years of computer science. On top of that, the recent historical explosion of computer science is also accompanied by perhaps an even larger explosion of number theory.
- deleted 9y ago
  [deleted]
- deleted 9y ago
  [deleted]
- posterboy 9y ago
  Also, mathematics has to be discovered and remembered, whereas half the internet seemingly consists only of programming tutorials and documentation. Edit: In the end there is no difference, however. Both are structural sciences. I guess you meant the maths in a CS degree.
tempodox 9y ago
Fascinating. Nitpick: It would be even nicer if the images on the main page were annotated with the person's name. I recognized e.g. Einstein and Turing, but who are all the others?
- kercker 9y ago
  You can try this link: http://www-history.mcs.st-andrews.ac.uk/Miscellaneous/bg_picture.html http://www-history.mcs.st-andrews.ac.uk/Miscellaneous/bg_pic...
metakermit 9y ago
Pro tip – Cmd/Ctrl+F for "independently". Research redundancy :)
decasteve 9y ago
If we consider the topical chronology/lineage stemming from Euclid's Elements, and how much of our world relies on Mathematics, one could argue that it is the most influential book ever written.
journeeman 9y ago
It doesn't seem to mention the works of the Indian mathematicians from Kerala, India on calculus. I think their work predated that of Newton and Leibniz.
- ralfd 9y ago
  Interesting, but (wiki): > Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series).[2] However, they did not formulate a systematic theory of differentiation and integration, nor is there any direct evidence of their results being transmitted outside Kerala.
- krsree 9y ago
  Madhava of Sangamagrama is mentioned
samdoidge 9y ago
Highlight: 'About 1950BC Babylonians solve quadratic equations.'
williamblake 9y ago
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 an engineer. After observing them, the engineer went on to ask the largest US companies in such business if they could make one. Only one responded and the answer was interesting. The place is real and the boxes, some as much as 90 tons (or the weight of more than fifty Prius cars) are not going anywhere. It's not in the books, nor is anything that explains it in the timeline but you can see it in person and test if for yourself. This place is only one of many that, by their nature and existence, question the conventional timeline of history There is also a mathematician that, with some help from others, is doing a rigorous mathematical review of the conventional timeline of history and apparently there are some major problems with what has previously been accepted, written and taught. Does anyone know who I am referring to here? How many people here are aware of the Serapeum mentioned above? Where does that level of precision work fit in with the timeline?
- pluteoid 9y ago
  The qualities of the Saqqara boxes are entirely consistent with what we know about the mathematical and engineering sophistication of ancient Egyptians. There is nothing well-verified "not in the books" that upends the "conventional timeline". The only people claiming otherwise are Discovery Channel nutcase types who want you to believe, without real evidence, often with fake evidence, and always with fatuous reasoning, that angels and aliens intervened in ancient human history. https://nathandickey.wordpress.com/2014/02/03/demythologizing-the-giant-stone-boxes-of-egypt/ https://nathandickey.wordpress.com/2014/02/03/demythologizin...
  - williamblake 9y ago
    I'm sorry that I have given you the impression that I or others like myself who discuss these questions believe in ancient aliens. I realize that this is a topic of confusion for many "debunkers". I don't accept belief as a valuable tool the process of discovering the truth, nor do I deem it necessary in the practice of science. Unbiased observation, free from belief is important. And denotative language seems to be more effective than connotative language, at least as far as these kings of arguments are concerned. Logical argument is better than the disparagement of persons and groups when arguing and making a point. And staying on topic is also a good thing. There is a growing discussion regarding belief systems within academia and various conventional sciences such as archeology. This seems to be a problem and if it is not cleaned up fairly quickly and replaced with something more logical, evidence-based, reality-accepting and legitimately scientific, the term "pseudoscience" will likely be used against those coming from the conventional side of these topics. I don't see anything relevant from your link that explains the precision of the boxes I mentioned above. What do you know about ancient Egyptian mathematics and engineering that relates to this subject? I have read the entire page you linked to, so forgive me in advance for missing it.
partycoder 9y ago
It would be good to include the setbacks caused by religious intervention. You can find some of it here in this other timeline: http://superstringtheory.com/history/history1.html http://superstringtheory.com/history/history1.html e.g: Hypatia, Galileo, Kepler, Copernicus... and many more.
- fjdlwlv 9y ago
  Galileo's wasn't held back by religious intervention against science. Even debates about heliocentrism weren't interfering with math.
WhitneyLand 9y ago
Please anyone, what is best timeline metaphor you know of? This is great stuff, but I immediately want to interactively browse through the information. For different parts be able to dive deeper, see high level views, different categories, taxonomies, links to related topics. Not trying to reinvent Wikipedia or hypermedia. But specifically to timelines with a lot of density, it seems there ought to be some nice user interface that could be leveraged for these scenarios.
- marxidad 9y ago
  I like the UI for timelines in Chrome Developer Tools or sound waveform editing programs, like Adobe Audition.
- perilunar 9y ago
  I've played with the vis.js timelines a bit and quite like them: http://visjs.org/timeline_examples.html http://visjs.org/timeline_examples.html
mrybczyn 9y ago
Fantastic, I wish I had read this back in elementary / high school. Will review with the kids! Not having this context in mathematics teaching is criminal.
Herodotus38 9y ago
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?
- ihm 9y ago
  I'm surprised Gromov and Thurston's contributions to geometry in the 70s-00s aren't emphasized more. Some things I think should be on there from my admittedly limited point of view: - 1982/87: Yao and then later Goldreich-Micali-Wigderson prove the "fundamental theorem of cryptography", which essentially states that any computational functionality can be achieved "efficiently" and securely. I.e., given k parties with one input each and any function F of k inputs and k outputs, the parties can communicate so that each learns their output of the function on all the inputs, and nothing else. - 2003: Perelman's proof of the geometrization conjecture.
- kercker 9y ago
  - 2013: Yitang Zhang's work on the gap between prime numbers.
- mrkgnao 9y ago
  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
chus9000 9y ago
Here you have the chronology in an infographic made with an automatic tool that I'm working on: http://history.takethejuice.com/output/MTQ5Njk0MDc1NC1NYXRoZW1hdGljYWwgQ2hyb25vbG9neQ== http://history.takethejuice.com/output/MTQ5Njk0MDc1NC1NYXRoZ...
imh 9y ago
>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.
du_bing 9y ago
A typo: 1991 Quidong Wang finds infinite series solutions to the n-body problem (with minor exceptions). The name is Qiudong Wang.
lorddoig 9y ago
I wish I knew St Andrews was home to a cool mathematics department and the progenitor of Idris when I was there, filling my body with mind-altering chemicals.
mrkgnao 9y ago
> 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_published_a_proof_of_resolution_of/ https://www.reddit.com/r/math/comments/6aqwbo/hironaka_publi...
- ice109 9y ago
  >can work with instead what can you actually do with these "smoother" varieties?
  - mrkgnao 9y ago
    They are much closer to the curves and solids we're familiar with from everyday experience. For example: you have well-defined tangents at every point for a smooth curve, but a self-intersecting curve doesn't. So many techniques and a lot of intuition carries over into the abstract algebraic setting. More generally, algebraic geometry is a central field of math because it is, basically, about solving polynomial equations. It's one of the most "well-connected" fields of mathematics today. Number theory, differential geometry, complex geometry, even differential equations: all these fields benefit from their interactions with modern algebraic geometry. (Also biology, I've heard. Lior Pachter is a name I remember in this connection.)
macawfish 9y ago
No mention of William Clifford?
drio 9y ago
This is great. Thank you for sharing. These days I am working on trying to understand the Fourier transform (1807). It is great fun. I finally understand the equation and how it works. Pure beauty. Now I am in the process to use it in practice. I am planning to write about it and perhaps write some visualizations to help others understand. This post made me think about a crazy idea I had. I wanted to write periodic posts to talk about the work of all these great mathematicians. I also wanted to have a place where people could buy gear (t-shirts). The same way people is very proud of wearing a sports guy t-shirt (Lebron 23), I'd love to see people wearing t-shirts with mathematicians names (Fourier 10). It's crazy I know.
- drio 9y ago
  Also, what are your favorite books/resources about the history of Mathematics? Something with similar contents to this resource but perhaps connecting the different discoveries.
- fjdlwlv 9y ago
  https://www.quantamagazine.org/ https://www.quantamagazine.org/ does what you describe
- pdm55 9y ago
  An interesting book, written by an interesting group, is "Who is Fourier". They seem to be mainly undergraduates in Japan who learn and teach each other new languages. They took on a similar task to explain Fourier Transforms to each other. Their motivation was to understand the mathematics of languages.
iamandoni 9y ago
> Adleman, Rivest, and Shamir introduce public-key codes, a system for passing secret messages using large primes and a key which can be published. My OCD wishes they would have said Rivest, Shamir, and Adleman like the algorithm is named after

139 points by kercker 9y ago

h3ctic 9y ago

Wondering how much from the last 100 years has been left out

swampers 9y ago
Probably a huge amount given that ~50% of the mathematicians* who have ever been alive are alive today. Source: Pure Mathematics Hons BSc, St Andrews - I took the St Andrews "History of Mathematics" course this site's information is used in. *For a given value of 'mathematician'. And 'alive', I guess.
- mbrd 9y ago
  Nice to see another St Andrews person on HN - I took that course too! I only wrote two essays during my four year degree, one for this class! (I wrote about Alexander Aitken, a gifted mental arithmetician)

laichzeit0 9y ago

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 ?

jordigh 9y ago

A guy I knew used to say that this is why computer science is so much easier to learn than number theory. It's thousands of years of number theory to learn vs a few dozen years of computer science. On top of that, the recent historical explosion of computer science is also accompanied by perhaps an even larger explosion of number theory.

deleted 9y ago
[deleted]
deleted 9y ago
[deleted]
posterboy 9y ago
Also, mathematics has to be discovered and remembered, whereas half the internet seemingly consists only of programming tutorials and documentation. Edit: In the end there is no difference, however. Both are structural sciences. I guess you meant the maths in a CS degree.

tempodox 9y ago

Fascinating. Nitpick: It would be even nicer if the images on the main page were annotated with the person's name. I recognized e.g. Einstein and Turing, but who are all the others?

kercker 9y ago
You can try this link: http://www-history.mcs.st-andrews.ac.uk/Miscellaneous/bg_picture.html http://www-history.mcs.st-andrews.ac.uk/Miscellaneous/bg_pic...

metakermit 9y ago

Pro tip – Cmd/Ctrl+F for "independently". Research redundancy :)

decasteve 9y ago

If we consider the topical chronology/lineage stemming from Euclid's Elements, and how much of our world relies on Mathematics, one could argue that it is the most influential book ever written.

journeeman 9y ago

It doesn't seem to mention the works of the Indian mathematicians from Kerala, India on calculus. I think their work predated that of Newton and Leibniz.

ralfd 9y ago
Interesting, but (wiki): > Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series).[2] However, they did not formulate a systematic theory of differentiation and integration, nor is there any direct evidence of their results being transmitted outside Kerala.
krsree 9y ago
Madhava of Sangamagrama is mentioned

samdoidge 9y ago

Highlight: 'About 1950BC Babylonians solve quadratic equations.'

williamblake 9y ago

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 an engineer. After observing them, the engineer went on to ask the largest US companies in such business if they could make one. Only one responded and the answer was interesting. The place is real and the boxes, some as much as 90 tons (or the weight of more than fifty Prius cars) are not going anywhere. It's not in the books, nor is anything that explains it in the timeline but you can see it in person and test if for yourself. This place is only one of many that, by their nature and existence, question the conventional timeline of history There is also a mathematician that, with some help from others, is doing a rigorous mathematical review of the conventional timeline of history and apparently there are some major problems with what has previously been accepted, written and taught. Does anyone know who I am referring to here? How many people here are aware of the Serapeum mentioned above? Where does that level of precision work fit in with the timeline?

pluteoid 9y ago
The qualities of the Saqqara boxes are entirely consistent with what we know about the mathematical and engineering sophistication of ancient Egyptians. There is nothing well-verified "not in the books" that upends the "conventional timeline". The only people claiming otherwise are Discovery Channel nutcase types who want you to believe, without real evidence, often with fake evidence, and always with fatuous reasoning, that angels and aliens intervened in ancient human history. https://nathandickey.wordpress.com/2014/02/03/demythologizing-the-giant-stone-boxes-of-egypt/ https://nathandickey.wordpress.com/2014/02/03/demythologizin...
- williamblake 9y ago
  I'm sorry that I have given you the impression that I or others like myself who discuss these questions believe in ancient aliens. I realize that this is a topic of confusion for many "debunkers". I don't accept belief as a valuable tool the process of discovering the truth, nor do I deem it necessary in the practice of science. Unbiased observation, free from belief is important. And denotative language seems to be more effective than connotative language, at least as far as these kings of arguments are concerned. Logical argument is better than the disparagement of persons and groups when arguing and making a point. And staying on topic is also a good thing. There is a growing discussion regarding belief systems within academia and various conventional sciences such as archeology. This seems to be a problem and if it is not cleaned up fairly quickly and replaced with something more logical, evidence-based, reality-accepting and legitimately scientific, the term "pseudoscience" will likely be used against those coming from the conventional side of these topics. I don't see anything relevant from your link that explains the precision of the boxes I mentioned above. What do you know about ancient Egyptian mathematics and engineering that relates to this subject? I have read the entire page you linked to, so forgive me in advance for missing it.

partycoder 9y ago

It would be good to include the setbacks caused by religious intervention. You can find some of it here in this other timeline: http://superstringtheory.com/history/history1.html http://superstringtheory.com/history/history1.html e.g: Hypatia, Galileo, Kepler, Copernicus... and many more.

fjdlwlv 9y ago
Galileo's wasn't held back by religious intervention against science. Even debates about heliocentrism weren't interfering with math.

WhitneyLand 9y ago

Please anyone, what is best timeline metaphor you know of? This is great stuff, but I immediately want to interactively browse through the information. For different parts be able to dive deeper, see high level views, different categories, taxonomies, links to related topics. Not trying to reinvent Wikipedia or hypermedia. But specifically to timelines with a lot of density, it seems there ought to be some nice user interface that could be leveraged for these scenarios.

marxidad 9y ago
I like the UI for timelines in Chrome Developer Tools or sound waveform editing programs, like Adobe Audition.
perilunar 9y ago
I've played with the vis.js timelines a bit and quite like them: http://visjs.org/timeline_examples.html http://visjs.org/timeline_examples.html

mrybczyn 9y ago

Fantastic, I wish I had read this back in elementary / high school. Will review with the kids! Not having this context in mathematics teaching is criminal.

Herodotus38 9y ago

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?

ihm 9y ago
I'm surprised Gromov and Thurston's contributions to geometry in the 70s-00s aren't emphasized more. Some things I think should be on there from my admittedly limited point of view: - 1982/87: Yao and then later Goldreich-Micali-Wigderson prove the "fundamental theorem of cryptography", which essentially states that any computational functionality can be achieved "efficiently" and securely. I.e., given k parties with one input each and any function F of k inputs and k outputs, the parties can communicate so that each learns their output of the function on all the inputs, and nothing else. - 2003: Perelman's proof of the geometrization conjecture.
kercker 9y ago
- 2013: Yitang Zhang's work on the gap between prime numbers.
mrkgnao 9y ago
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

chus9000 9y ago

Here you have the chronology in an infographic made with an automatic tool that I'm working on: http://history.takethejuice.com/output/MTQ5Njk0MDc1NC1NYXRoZW1hdGljYWwgQ2hyb25vbG9neQ== http://history.takethejuice.com/output/MTQ5Njk0MDc1NC1NYXRoZ...

imh 9y ago

>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.

du_bing 9y ago

A typo: 1991 Quidong Wang finds infinite series solutions to the n-body problem (with minor exceptions). The name is Qiudong Wang.

lorddoig 9y ago

I wish I knew St Andrews was home to a cool mathematics department and the progenitor of Idris when I was there, filling my body with mind-altering chemicals.

mrkgnao 9y ago

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

ice109 9y ago
>can work with instead what can you actually do with these "smoother" varieties?
- mrkgnao 9y ago
  They are much closer to the curves and solids we're familiar with from everyday experience. For example: you have well-defined tangents at every point for a smooth curve, but a self-intersecting curve doesn't. So many techniques and a lot of intuition carries over into the abstract algebraic setting. More generally, algebraic geometry is a central field of math because it is, basically, about solving polynomial equations. It's one of the most "well-connected" fields of mathematics today. Number theory, differential geometry, complex geometry, even differential equations: all these fields benefit from their interactions with modern algebraic geometry. (Also biology, I've heard. Lior Pachter is a name I remember in this connection.)

macawfish 9y ago

No mention of William Clifford?

drio 9y ago

This is great. Thank you for sharing. These days I am working on trying to understand the Fourier transform (1807). It is great fun. I finally understand the equation and how it works. Pure beauty. Now I am in the process to use it in practice. I am planning to write about it and perhaps write some visualizations to help others understand. This post made me think about a crazy idea I had. I wanted to write periodic posts to talk about the work of all these great mathematicians. I also wanted to have a place where people could buy gear (t-shirts). The same way people is very proud of wearing a sports guy t-shirt (Lebron 23), I'd love to see people wearing t-shirts with mathematicians names (Fourier 10). It's crazy I know.

drio 9y ago
Also, what are your favorite books/resources about the history of Mathematics? Something with similar contents to this resource but perhaps connecting the different discoveries.
fjdlwlv 9y ago
https://www.quantamagazine.org/ https://www.quantamagazine.org/ does what you describe
pdm55 9y ago
An interesting book, written by an interesting group, is "Who is Fourier". They seem to be mainly undergraduates in Japan who learn and teach each other new languages. They took on a similar task to explain Fourier Transforms to each other. Their motivation was to understand the mathematics of languages.

iamandoni 9y ago

> Adleman, Rivest, and Shamir introduce public-key codes, a system for passing secret messages using large primes and a key which can be published. My OCD wishes they would have said Rivest, Shamir, and Adleman like the algorithm is named after