The Eudoxus Real Numbers
Article by Arthan, R. D.
In collection: Unusual arithmetic
This note describes a representation of the real numbers due to Schanuel. The representation lets us construct the real numbers from first principles. Like the well-known construction of the real numbers using Dedekind cuts, the idea is inspired by the ancient Greek...
Just a few weeks ago, my colleagues and I published a review article on a problem I like to think of as the TARDIS of math: It looks small, but it's bigger on the inside, and it takes you to unexpected places. http://www.mdpi.com/2075-1680/6/3/21
I tried to make the bibliography comprehensive, but new work has come out, so it's already outdated: https://scirate.com/arxiv/1707.09911
And this morning I was sent a draft of a new paper, so it'll be outdated yet again soon
This is a good thing!
There's some good stuff in this essay, "Do Mathematicians Have Responsibilities?": http://www.math.columbia.edu/~harris/otherarticles_files/Responsibilities.pdf
The editorial board for the Journal of Algebraic Combinatorics left to continue the journal under a new name in Open Access form:
Just spent half an hour with my summer student getting into the subtleties of the conditions required for "throwing two dice" to have 36 possible outcomes.
I came up with a good example: I'm colourblind, so if we throw a red and a green die at the same time, the student can distinguish them, but I can't. So the outcomes are a property of the observer, not the trial itself.
Pentagon Tiling Proof Solves Century-Old Math Problem, _Quanta Magazine_, https://www.quantamagazine.org/pentagon-tiling-proof-solves-century-old-math-problem-20170711/
I already posted about this a couple of months ago (https://plus.google.com/100003628603413742554/posts/dC6Qo87LouC) but now there's this nice popular-press article, and confirmation on the correctness of "the most important half of Rao's proof" by Thomas Hales.
The bibliography is caught up to this week's news, and the historical overview section is more comprehensive than it was in the previous version.
Early career researchers: have you been bullied into doing bad science? Pressured to publish only in "prestigious", non-open journals?
There's a letter to sign.
Submitted a review article to a #mathematics journal.
Campus is not filled with undergrads, but the coffee place in my building is closed. Net loss.
Scientist by training, snarker by inclination. I have a blag at my wobsite, Science After Sunclipse (https://www.sunclipse.org)
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