Blogs about Mathematics

Soddy’s hexlet is a famous system of nine spheres in three-dimensional Euclidean space, consisting of a ring of six spheres, tangent in consecutive pairs, and a ring of three spheres, tangent in pairs, with every …

A mathematical proof is a rigorous argument based on straightforward logical rules to convince other mathematicians that a statement is true. A minor deficiency in a proof can spoil the whole argument!

So, I’m working on svylme again, for linear mixed models under complex sampling. It uses pairwise likelihood, following the basic idea from the Canadians, but extending it to settings where the design structure and model …

NYT published a brain-dead article filled with statistical fallacies (link). Since the Times has people on staff who know statistics, the real explanation for such an article is "story-first thinking". Data mined to support a …

$\newcommand\R{\mathbb{R}}\newcommand\C{\mathbb{C}}\newcommand\Z{\mathbb{Z}}$ The singular value decomposition is usually defined for a matrix. Here, we will show directly that any linear map between inner product spaces has a singular value decomposition. The singular value decomposition of a …

Yosi Rinott, Tomer Shoham, and I wrote our third paper regarding our statistical study of the Google 2019 supremacy experiment. Our paper presents statistical analysis that may shed light on the quality and reliability of …

For the book Computational Intractability: A Guide to Algorithmic Lower Boundsby Demaine-Gasarch-Hajiaghayi (See here for a link to a first draft.) we had to make some choices about which notation to use. One of the …

Link to announcement on ASA website. First Winner . Nancy Reid University of Toronto For contributions to the foundations of statistics that significantly advanced the frontiers of statistics and for insight that transformed understanding of …

The other day I went to the cinema and watched M3GAN, a true movie masterpiece1 about the death and carnage that ensues when you simply train your extremely complex ML model and don’t do proper …

Large language models, have improved and become more main stream. I discuss this in the video below with AI Researcher Xavier Garcia.

This issue’s interviewee is Katharine Ott, who is an Associate Professor of Mathematics at Bates College. In this interview, which was conducted by Ken Fan and Raegan Phillips, Katharine discusses a wide range of topics, …

An “einstein” that doesn’t need flipping Siobhan Roberts is a Canadian science journalist, biographer, and historian of mathematics. She has an article that appeared in print in yesterday’s New York Times. It is on a …

This will be a talk for the Axe Histoire et Philosophie des mathématiques, Séminaire PhilMath Intersem 2023, a collaborative event sponsored by the University of Notre Dame and le laboratoire SPHERE, Paris. The Intersem runs …

Here’s a curious fact. The graphs of cotangent and secant cross at the same height as the graphs of tangent and cosecant, and this common height is the square root of the golden ratio φ. …

Learn how to use properties to add dynamic behaviour to your attributes. (If you are new here and have no idea what a Pydon't is, you may want to read the Pydon't Manifesto.) Introduction Properties, …

I wrote two blog articles on this theme back in 2010: Commutative separable algebras. Commutative separable algebras II. Now for rather different reasons I’m returning to it. A separable algebra AA over a commutative ring …

I have a google play (which plays streaming music) and it’s really terrible for classical music. If you choose virtually any piece of classical music and then flip forward three songs you invariably end up …

Henning Krause: Completions of triangulated categories are lecture notes on (you'd never guess) completions of triangulated categories. It's amazing how useful completion has turned out to be in this subject, and these lecture notes are …

I like a close, hard-fought game as much as the next baseball fan, and I’ve seen a lot of those lately, but there is a peculiar and specific pleasure to the game in which the …

You saw the workshop, now read the book. The National Academies of Sciences, Engineering, and Medicine report Toward a 21st Century National Data Infrastructure: Enhancing Survey Programs by Using Multiple Data Sources is available for …