Mathematical Chronology
www-history.mcs.st-andrews.ac.uk
www-history.mcs.st-andrews.ac.uk
And then the mathematics that happened around ~1940.. Kolmogorov, Fisher, Poincaré, Gödel, Von Neumann, Church, Turing...
Just crazy.
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.
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.
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 ?
>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.
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?
https://nathandickey.wordpress.com/2014/02/03/demythologizin...
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.
It’s also not surprising that they could create a flat surface or angles that are exactly-ish 90 degrees. The Egyptians boast some of the earliest known texts on geometry, like the Rhind Papyrus (from around 1650 BCE) and the Moscow papyrus (from about 1850 BCE). The latter papyrus indicates that the Egyptians could approximate pi (as 3.16049) and find the volume of a truncated pyramid. It stands to reason that 500 years later, they would be able to carve a flat surface and make a corner of exactly-ish 90 degrees.
Not an exaggeration, just an extremely long time spent hand grinding/polishing with fine grit tools/paste.
I apologize if this is an order of magnitude beyond most peoples' understanding and experience. It's probably not your occupation, so please don't take it personally. As an example of what this degree of precision is, consider a thin hair which is about four thousandths of an inch in diameter. If you slice that diameter up ten times, you will then have something that is as small as or at least reasonably approaching this measurement.
To keep these ancient achievements in perspective though I recall working at Texas Instruments in the 70's (doing real-time process control programming). One of my friends there related to me his experience in giving a job interview, years earlier, to a young machinist, classically trained in Germany. The job seeker brought his final project as a sample of his work. A highly polished, precisely square, solid cube of polished steel, or so it appeared to my friend. It had all been made with hand tools, no fancy milling or grinding machines.
My friend marveled at it, but then the young man said "watch this" and proceeded to slide the upper half of the solid cube on a dovetailed channel that connected the upper half of the cube to the lower half. My friend, a mechanical engineer, said he had never seen anything like it; it was so carefully made that the channel was invisible to him when the cube was squared. The main shaping tool used in the construction of this cube was simply a file.
> 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...
what can you actually do with these "smoother" varieties?
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.)
Edit: In the end there is no difference, however. Both are structural sciences. I guess you meant the maths in a CS degree.
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.
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.
> 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.
http://history.takethejuice.com/output/MTQ5Njk0MDc1NC1NYXRoZ...
- 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.
* 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
You can find some of it here in this other timeline: http://superstringtheory.com/history/history1.html
e.g: Hypatia, Galileo, Kepler, Copernicus... and many more.
Even debates about heliocentrism weren't interfering with math.
My OCD wishes they would have said Rivest, Shamir, and Adleman like the algorithm is named after
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?
Will review with the kids!
Not having this context in mathematics teaching is criminal.
1991 Quidong Wang finds infinite series solutions to the n-body problem (with minor exceptions).
The name is Qiudong Wang.
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.