Pretty big book news (in a couple of ways)! The Univalent Foundations Program at the Institute for Advanced Study in Princeton has released a 470-page textbook resetting the foundations of mathematics on homotopy type theory. It’s called Homotopy Type Theory: Univalent Foundations of Mathematics.
Do you ever collect too much fun maths stuff to keep to yourself, and then start a website just so you’ve got somewhere to put it? That happens to me sometimes.
In case you’re new to this: every now and then I encounter a paper or a book or an article that grabs my interest but isn’t directly useful for anything. It might be about some niche sub-sub-subtopic I’ve never heard of, or it might talk about something old from a new angle, or it might just have a funny title. I put these things in my Interesting Esoterica collection on Mendeley. And then when I’ve gathered up enough, I collect them here.
In this post the titles are links to the original sources, and I try to add some interpretation or explanation of why I think each thing is interesting below the abstract.
Some things might not be freely available, or even available for a reasonable price. Sorry.
A sympathetic story for you this Saturday.
Andy has a problem. He can’t solve it on his own – he needs your help. This problem vexed Andy so much that he spent four years trying to solve it on his own, to no avail. It really is a very difficult problem. Finally in 1997, out of what must have been sheer desperation, Andy reached out to his fellow man: maybe some kindly type out there could find a solution to his problem, which he would gladly reward with a small consideration.
Can you help a soul in need?
Update 17/06/2013: The gap is down to 60,744. That’s a whole order of magnitude down from where it started!
When Yitang Zhang unexpectedly announced a proof that that there are infinitely many pairs of primes less than 70 million apart from each other – a step on the way to the twin primes conjecture – certain internet wags amused themselves and a minority of others with the question, “is it a bigger jump from infinity to 70 million, or from 70 million to 2?”.
Of course the answer is that it’s a really short distance from 70 million to 2, and here’s my evidence: the bound of 70 million has in just over three weeks been reduced to just a shade over 100,000.
The Online Encyclopedia of Integer Sequences contains over 200,000 sequences. It contains classics, curios, thousands of derivatives entered purely for completeness’s sake, short sequences whose completion would be a huge mathematical achievement, and some entries which are just downright silly.
For a lark, David and I have decided to review some of the Encyclopedia’s sequences. We’re rating sequences on four axes: Novelty, Aesthetics, Explicability and Completeness.
Following last week’s palaver, we’re going to do our best to be serious this time. Game faces on.
A052486
Achilles numbers – powerful but imperfect: writing n=product(p_i^e_i) then none of the e_i=1 (i.e. powerful(1)) but the highest common factor of the e_i>1 is 1 (so not perfect powers).72, 108, 200, 288, 392, 432, 500, 648, 675, 800, 864, 968, 972, 1125, 1152, 1323, 1352, 1372, 1568, 1800, 1944, 2000, 2312, 2592, 2700, 2888, 3087, 3200, 3267, 3456, 3528, 3872, 3888, 4000, 4232, 4500, 4563, 4608, 5000, 5292, 5324, 5400, 5408, 5488, ...
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of May, is now online at Wild About Math!.
The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.
Silly maths stories, like buses with a taxi sneaking into the bus lane behind them, come along four at a time, it seems. None of these stories merits being reported on here on its own, but we felt the fact that they all came to our attention so close to each other deserved recognition.