Featuring 'the wiggle', a term dating at least as far back as 2008 when Anthony Hilton talked about wiggles to the Combinatorics Study Group at Queen Mary University of London, whose very interesting archive is here webspace.maths.qmul.ac.uk/p.j.cameron/cs… (see 2008, 12 December)

The Royal Society Are you afraid to say 'combinatorics' The Royal Society?
She is a leading exponent of modern combinatorics.

Colouring a perfect graph with a number of colours equal to its clique number has remained a challenge. Progress as of 2015 is well-described by Natalie Wolchover for Quanta Magazine here quantamagazine.org/mathematicians… (thanks livecitizen for telling me)

In one dimension the theorem is an easy corollary of the Intermediate Value Theorem, see this from Plus Magazine, for example: plus.maths.org/content/maths-…

I was reading 2023 Nobel laureate Katalin Kariko's book, Breaking Through. She was brutally honest about the academic system in US.

And, here is an example section from her book.

'Put your pack of cards into some kind of order.'
'But how?'
'You decide that.'

Only one more week to submit your favourite online maths content for this month's Carnival of Maths! Find out more and submit at aperiodical.com/carnival-of-ma…

Roughly speaking, all that prevents two (even) permutations from generating all (even) permutations is them sharing a fixed point. Until 2016 this required the classification of the finite simple groups to prove arxiv.org/abs/1611.02501

'E. Landau left Brun's 1920 paper unread for a decade, apparently because he was not predisposed to believe that elementary methods as used by Brun could penetrate problems such as Goldbach's to the asserted extent' George Greaves, Sieves in Number Theory (Introduction)

I posted my lectures about asymptotics and perturbation methods back in spring 2021. They're freely available here: youtube.com/playlist?list=…

A proof 'from the book': Paul Levrie, 'A straightforward proof of Descartes's circle theorem', The Mathematical Intelligencer, 41:3 (2019), pp. 24–27. explore.lib.uliege.be/discovery/full…

Francesca Lovell-Read offers a good historical account of this theorem at merton.ox.ac.uk/sites/default/…

Review: Making Sense of Chaos: Doyne Farmer ***** - Remarkable book pulling together chaos theory and economics. Provides the first possibility that economics could become a real science. Not an easy read, but worth the effort popsciencebooks.blogspot.com/2024/05/making… #bookreview #chaos #economics

There are many related questions about group-like properties of Moufang loops. S. M. Gagola III, 'How and why Moufang loops behave like groups', Quasigroups and Related Systems, Vol. 19, No.1, 2011, pp. 1–22; online, is admirably clear and authoritative quasigroups.eu/contents/19.php

Putting Kovalevskaya's work in a modern context is Elemer Elad Rosinger, 'Can there be a general nonlinear PDE theory for existence of solutions?' hal.archives-ouvertes.fr/hal-00512015v1

There is a nice tribute to Lehrer at Gödel's Lost Letter which links to a previous short entry on this theorem rjlipton.com/2018/04/10/tom…

From the 1977 paper that introduced spherical designs. Which now have their own Wiki page - how many papers are that influential?! en.wikipedia.org/wiki/Spherical…

On how AI is transforming that most mystical and powerful of mathematical processes: Conjecture formation.
Lots of fun crafting this piece with London Institute for Mathematical Sciences director Thomas Fink!
nature.com/articles/d4158…

If you've flipped heads on a coin 10 times, what's the chance of heads on the next flip? Bayes' theorem has an (unexpected) answer. Not just for the coin but for the pursuit of science generally plus.maths.org/content/heads-… Maths4DL Chris Budd OBE

A blog post 'Mortgages, banks, and Jensen’s inequality' by John D. Cook is very instructive: johndcook.com/blog/2009/08/2…