Blogs about Mathematics

Modern CPUs have \(\mathbb{F}_2\) polynomial multiplication as a single operation (\(\mathbb{M}\)). This should be useful for other kinds of bit-hacking, not just algebraic computation. Richard Palais’s historic role in promoting the use of computers in …

At the intersection of playfulness and learning, math board games offer an extraordinary opportunity to immerse yourself in the captivating world of mathematics.

Sometime in the early evening on Sunday, I looked at that day’s Antikythera post on my phone and saw that two of the equations weren’t rendering: This was in Safari. I hadn’t seen the errors …

Blocking sets are one of the central topics in finite geometry, which were originally introduced in the context of game theory under the name of `blocking coalitions’: On Finite Projective Games. I first learned about …

Or The Novice’s Guide To Achieving Mathematical Immortality This is a guest post from Barney Maunder-Taylor. A great way to achieve mathematical immortality is to solve an outstanding open question, like determining if \( \pi+e …

This is a piece of advice that I found myself giving to many early career researchers, students, and colleagues supervising and advising those as well. For years, actually. A mathematician, the joke says, is a …

The fourth in the series about every year of Numberphile. Videos about Klein bottles, infinity, and coin flips.

Quartets of datasets are trendy now, so here’s one for collinearity diagnostics. These four data sets have two candidate predictors \(x\) and \(z\) and outcome \(y\), and have very strong correlation (over 0.95) between \(x\) …

Mark also wonders about weather forecasts on his blog. He says: If we have a prediction that is inaccurate, displays sudden swings, and makes forecasts wildly divergent from its competitors, that raises some questions. As …

Roll up, roll up, roll up and welcome to the two hundred and twenty ninth Carnival of Mathematics! 229 is a prime number, and that in itself is interesting. Its the “elder” of a set …

$\newcommand\C{\mathbb{C}}$ I came up with the proof below while preparing a lecture for my complex analysis course. I learned from Sinan Gunturk that Peter Lax showed him the same proof back in 2007. Let \(O\subset\C\) …

Peter Sarnak will give the Gordon memorial lectures at the Hebrew University of Jerusalem. At the end of December 2024, Peter Sarnak will deliver the Mark Gordon memorial lecture series on Spectra of locally symmetric …

I've heard a few times recently the phrase "Information only exists in a physical state". It come from the quantum computing world where they claim quantum changes the game when it comes to representing information.As …

2024 Cruise Welcome to the December leisurely cruise: Wherever we are sailing, assume that it’s warm. This is an overview of our first set of readings for December from my Statistical Inference as Severe Testing: …

Acknowledgements The code in this post is indebted (and in some cases wholly ripped off from) work by the glorious Finn Lindgren, who emailed me some code to do this probably a decade ago. Yes …

Principal Component Analysis, or PCA, is a fundamental dimensionality reduction technique using in Machine Learning. The general goal is to transform a -dimensional problem into a -dimensional one, where is smaller than . This can …

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website. We open with the second half of our interview with Boston University Professor of Mathematics Jennifer Balakrishnan. …

My dear wife, Kathryn Farley, just woke me this Friday the 20th from a nap with something that she said was amazing. She told me it was the top most viewed video of the entire …

Is there anything new in Enumerative Combinatorics? Most experts would tell you about some interesting new theorems, beautiful bijections, advanced techniques, connections to other areas, etc. Most outsiders would simply scoff, as in “what can …

My Oxford student Emma Palmer and I have been thinking about worldly cardinals and Gödel-Bernays GBC set theory, and we recently came to a new realization. Namely, what I realized is that every worldly cardinal …