**A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode**

“_....the hyper-Catalan numbers 𝐶𝐦 count the number of subdivisions of a polygon into a given number of triangles, quadrilaterals, pentagons, etc. (its type 𝐦), and we show that their generating series solves a polynomial equation of a particular geometric form. This solution is straightforwardly extended to solve the general univariate polynomial equation._”

Wildberger, N. J. and Rubine, D. (2025) ‘A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode’, The American Mathematical Monthly, pp. 1–20. doi: https://doi.org/10.1080/00029890.2025.2460966.

Theorem of the Day (May 1st, 2025) : Lamé’s Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Binomial/Lame/TotDLame.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#87

#mathematics #maths #math #theorem @Theoremoftheday

Source : Quanta Magazine / Jordana Cepelewicz

https://www.quantamagazine.org/mathematical-beauty-truth-and-proof-in-the-age-of-ai-20250430/
#mathematics #maths #math #proofs

Ain't that grand?

https://mathstodon.xyz/@nbourbaki

Bourbaki lives! And Nicolas may have to be revived in his original form, if geopolitics continue down this trend.

https://www.bourbaki.fr/TEXTES/Exp1231-Hairer.pdf

Do you represent a #museum, #gallery, or other cultural organisation in #Scotland?

2025's FREE online #Maths in #Museums training from National Museums Scotland in partnership with Maths Week Scotland is on Weds 28 May, 10am-3pm.

Find out more & sign up here: https://my.nms.ac.uk/0/17854

This free Maths in Museums event features:
- Presentations and exercises led by me (https://tkbriggs.co.uk/services/maths-in-museums/)!
- How to get involved in Maths Week Scotland
- Case studies from museums who've done it before
- Maths in the Curriculum for Excellence (from Education Scotland)
- Meet & share skills with peers

This event is for people associated with a museum, gallery, library (etc) that holds a public collection in Scotland who want to gain knowledge, skills and confidence in creating maths-focused programming and events, such as for schools and families.

Here's the link again: https://my.nms.ac.uk/0/17854

A Prime Minister can only be divided by itself or one.

Theorem of the Day (April 30, 2025) : The Piff-Welsh Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/CombinatorialTheory/PiffWelsh/TotDPiffWelsh.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#141

#mathematics #maths #math #theorem @Theoremoftheday

Here's the question for April 29th from the AMS Daily Epsilon of Math Calendar. For those unfamiliar with the calendar, the answer is always the day of the month. Looking for imaginative solutions is the aim.

**The Periodic Table of Primes**

“_We identify 48 integers out of a period of 2x3x5x7=210 to be the roots of all primes as well as composites without factors of 2, 3, 5, and 7. Each prime, twin primes, or composite without factors of 2, 3, 5 and 7 is an offspring of the 48 integers uniquely allocated on the PTP._”

Li, Han-Lin and Fang, Shu-Cherng and Kuo, Way, The Periodic Table of Primes (April 6, 2024). Available at SSRN: https://dx.doi.org/10.2139/ssrn.4742238.

The Thompson Problem.
https://www.youtube.com/watch?v=dNTnk1VFoJY
#GolfBalls #polyhedra #Goldberg
#maths #mathematics #geometry #electrons

Who wants to win $10,000 ?
https://www.youtube.com/watch?v=stpiBy6gWOA
#maths #mathematics #MagicSquares #Numberphile

Matt Parker learns some sudoku solving techniques for a problem he was not convinced was human solvable. He wrote a python program to brute force the solution. But Simon and Mark solved it in about an hour.

Matt had already figured out which of the actors in the puzzle were the liars, so that jumpstarted the solve.

https://www.youtube.com/watch?v=WFZ6AMTXUJk

Code&Demo https://sketchpunklabs.github.io/threejs_proto/code/webgl/maths/wind_map.html

Here's a basic proto of creating a wind system. A way to visualize wind dir plus run compute to get wind dir at a certain spot. Gonna use it someday to animate cloths, hair & grass. #opensource, enjoy !

Ok, this is really interesting

https://www.livescience.com/physics-mathematics/mathematics/mathematicians-just-solved-a-125-year-old-problem-uniting-3-theories-in-physics

"Nowadays, it is not easy to follow an academic career, but you should keep in mind that you can do many different things with mathematics, working at university is not the unique option." – Margarida Mendes Lopes (1955–)
#quote #mathematics #math #maths