"Category theory is a universal modeling language."
Background.
Success is founded on information. A tight connection between success (in anything) and information. It follows that we should (if we want to be more successful) study what information is.
Grant proposals. These are several grant proposals, some funded, some in the pipeline, others not funded, that explain various facets of my research project.
Introductory talk (video, slides).
Blog post, on John Baez's blog Azimuth, about my motivations for studying this subject. (Here's a .pdf version.)
Category: Mathematics
👓 News re proofs of the ABC conjecture & Riemann Hypothesis | John D. Cook
There have been a couple news stories regarding proofs of major theorems. First, an update on Shinichi Mochizuki’s proof of the abc conjecture, then an announcement that Sir Michael Atiyah claims to have proven the Riemann hypothesis.
👓 Famed mathematician claims proof of 160-year-old Riemann hypothesis | New Scientist
Michael Atiyah, a famed UK mathematician, claims that he has a "simple proof" of the Riemann hypothesis, a key unsolved question about the nature of prime numbers
👓 Titans of Mathematics Clash Over Epic Proof of ABC Conjecture | Quanta Magazine
Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.
👓 Curve-Fitting | xkcd
Cauchy-Lorentz: "Something alarmingly mathematical is happening, and you should probably pause to Google my name and check what field I originally worked in."
👓 Additional thoughts on the Ted Hill paper | Timothy Gowers
First, I’d like to thank the large number of commenters on my previous post for keeping the discussion surprisingly calm and respectful given the topic discussed. In that spirit, and to try t…
Highlights, Quotes, Annotations, & Marginalia
Our prehistoric ancestors were not doing higher mathematics, so we would need to think of some way that being on the spectrum could have caused a man at that time to become highly attractive to women. ❧
One needs to remember that it isn’t always the men that themselves need to propagate the genes directly (ie, they don’t mate with someone to hand their genes down to their progeny directly). Perhaps a man on the autism spectrum, while not necessarily attractive himself, has traits which improve the lives and fitness of the offspring of his sister’s children? Then it’s not his specific genes which are passed on as a result, but those of his sister’s which have a proportion of his genes since they both share their parent’s genes in common.
September 19, 2018 at 03:35PM
variability amongst males ❧
Does it need to be a mate-related thing? Why not an environmental one. I seem to recall that external temperature had a marked effect on the sexual selection within alligator populations such that a several degree change during gestation would swing the sex proportion one way or another. Could these effects of environment have caused a greater variability?
Further, what other factors may be at play? What about in sea horse populations where males carry the young? Does this make a difference?
September 19, 2018 at 03:41PM
👓 Has an uncomfortable truth been suppressed? | Timothy Gowers
Update to post, added 11th September. As expected, there is another side to the story discussed below. See this statement about the decision by the Mathematical Intelligencer and this one about the…
I will say that far more people have now either heard about or read Hill’s paper than would have ever otherwise been aware of it had it actually gone ahead and actually been published and kept up. This is definitely an academic case of the Barbara Streisand effect, though done somewhat in reverse.
🔖 A Brief Introduction to the Basics of Game Theory by Matthew O. Jackson | SSRN
I provide a (very) brief introduction to game theory. I have developed these notes to provide quick access to some of the basics of game theory; mainly as an aid for students in courses in which I assumed familiarity with game theory but did not require it as a prerequisite.
🔖 [1809.05923] What is Applied Category Theory? by Tai-Danae Bradley
This is a collection of introductory, expository notes on applied category theory, inspired by the 2018 Applied Category Theory Workshop, and in these notes we take a leisurely stroll through two themes (functorial semantics and compositionality), two constructions (monoidal categories and decorated cospans) and two examples (chemical reaction networks and natural language processing) within the field. [PDF]
Friends! I am so happy to share that my little booklet “What is Applied Category Theory?” is now available on the arXiv. It’s a collection of introductory, expository notes inspired by the ACT workshop that took place earlier this year. Enjoy! https://t.co/EPYP19z14x pic.twitter.com/O4uVhj401s
— Tai-Danae Bradley (@math3ma) September 18, 2018
See also Notes on Applied Category Theory
🎧 “Malcolm Gladwell’s 12 Rules for Life” Season 3 Episode 7 | Revisionist History
"Crucial life lessons from the end of hockey games, Idris Elba, and some Wall Street guys with a lot of time on their hands."
Revisionist History wades into the crowded self-help marketplace, with some help with from a band of math whizzes and Hollywood screenwriters. It's late in a hockey game, and you're losing. When should you pull your goalie? And what if you used that same logic when a bad guy breaks into your house and holds your entire family hostage? We think the unthinkable, so you don’t have to.
Pulling the Goalie: Hockey and Investment Implications on SSRN.
👓 Election Update: Democrats’ Chances In The 13 Romney-Clinton Districts | Five Thirty Eight
Welcome to our Election Update for Thursday, Sept. 13! The biggest update: We now have a Senate forecast to go with our House forecast! The “Classic” version of the Senate forecast currently gives Democrats a 1 in 3 chance of flipping the upper chamber. Meanwhile, the “Classic” version of our House forecast hasn’t really changed much since yesterday: Democrats still have a 5 in 6 chance of winning control. Across thousands of simulations, Democrats’ average gain was 39 seats.
👓 Why Le’Veon Bell Might Make More Money If He Ends His Holdout Now | Five Thirty Eight
Last weekend, Steelers running back Le’Veon Bell sat out the first game of the regular season rather than play under the NFL franchise tag. Slated to earn $14.5 million in guaranteed money in 2018, Bell loses out on $855,529 each week he fails to report. The franchise tag would make Bell the third highest paid running back in the NFL this season — but only if he actually plays. Around the league, there is a wide range of speculation on how long Bell’s holdout will last. ESPN’s Adam Schefter reports that his sources believe Bell could be back by the end of September, while others note his holdout could conceivably last through Week 10.
👓 Statement by Amie Wilkinson addressing unfounded allegations. | Amie Wilkinson
This statement addresses some unfounded allegations about my personal involvement with the publishing of Ted Hill's preprint "An evolutionary theory for the variability hypothesis" (and the earlier version of this paper co-authored with Sergei Tabachnikov). As a number of erroneous statements have been made, I think it's important to state formally what transpired and my beliefs overall about academic freedom and integrity. I first saw the publicly-available paper of Hill and Tabachnikov on 9/6/17, listed to appear in The Mathematical Intelligencer. While the original link has been taken down, the version of the paper that was publicly available on the arxiv at that time is here. I sent an email, on 9/7/17, to the Editor-in-Chief of The Mathematical Intelligencer, about the paper of Hill and Tabachnikov. In it, I criticized the scientific merits of the paper and the decision to accept it for publication, but I never made the suggestion that the decision to publish it be reversed. Instead, I suggested that the journal publish a response rebuttal article by experts in the field to accompany the article. One day later, on 9/8/17, the editor wrote to me that she had decided not to publish the paper. I had no involvement in any editorial decisions concerning Hill's revised version of this paper in The New York Journal of Mathematics. Any indications or commentary otherwise are completely unfounded. I would like to make clear my own views on academic freedom and the integrity of the editorial process. I believe that discussion of scientific merits of research should never be stifled. This is consistent with my original suggestion to bring in outside experts to rebut the Hill-Tabachnikov paper. Invoking purely mathematical arguments to explain scientific phenomena without serious engagement with science and data is an offense against both mathematics and science.
👓 Holly Krieger | Cambridge
Born and raised near Chicago, Dr Holly Krieger completed the undergraduate mathematics honors program at University of Illinois at Urbana-Champaign. She went on to a master's degree and a Ph.D. from the University of Illinois at Chicago, with initial research interests during graduate school were primarily in arithmetic and Diophantine geometry. Under the guidance of Laura DeMarco and Ramin Takloo-Bighash, her thesis work focused on the emerging field of arithmetic dynamics, which studies the relationship between dynamics of one complex variable and the arithmetic geometry of abelian varieties.
📺 The Dollar Game – Numberphile | YouTube
With Dr Holly Krieger from Murray Edwards College, University of Cambridge.