Tag: math

Math from the future

Mochizuki had invented a new branch of his discipline, one that is astonishingly abstract even by the standards of pure maths. “Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space. Mochizuki has estimated that it would take a maths graduate student ~10 years to be able to understand his work, and Fesenko believes that it would take even an expert in arithmetic geometry some 500 hours. So far, only 4 mathematicians have been able to read the entire proof.

Mathematica for pure math

mr. wolfram is prone to hyperbole, but at least he’s not boring.

But could we systematically extend the Wolfram Language to cover the whole range of pure mathematics—and make a kind of “Mathematica Pura”? The answer is unquestionably yes. It’ll be fascinating to do, but it’ll take lots of difficult language design. One might think that somehow mathematical notation would already have solved the whole problem. But there’s actually only a quite small set of constructs and concepts that can be represented with any degree of standardization in mathematical notation—and indeed many of these are already in the Wolfram Language.

First cellular automaton?

But given that the Vigenčre cipher was viewed as uncrackable, was there a perceived need for anything else? I suspect that the urge to invent new encryption methods has always been strong: if you have a cool idea based on your own field of expertise, you will suggest it (after all, if you cannot break it, it must be unbreakable!). In fact, the use of a transformation of the previous column seems to be like an autokey cipher. The first real autokey cipher was suggested ion 1556 by Cardano in De Subtilitate, but the first useful on was invented in 1564 by Giovan Battista Bellaso. Vigenčre published one in 1586. Liber Soyga was mentioned by Dee in 1583. Could the Soyga automaton be the result of somebody working on an autokey method, perhaps getting the bright idea of applying it again and again to itself? It would seem to fit into the time. Of course, the border between cryptography and angelic communication might have been blurry. Maybe the tables were seen as both. Sufficiently advanced cryptography is indistinguishable from magic.

Twin Primes Conjecture

similar excitement to andrew wiles & fermat’s last theorem from a few years ago. you can follow progress here

an obscure mathematician — one whose talents had gone so unrecognized that he had worked at a Subway restaurant to make ends meet — garnered worldwide attention and accolades from the mathematics community for settling a long-standing open question about prime numbers, those numbers divisible by only 1 and themselves. Yitang Zhang showed that even though primes get increasingly rare as you go further out along the number line, you will never stop finding pairs of primes separated by at most 70M. His finding was the first time anyone had managed to put a finite bound on the gaps between prime numbers, representing a major leap toward proving the centuries-old twin primes conjecture