"I think proofs by contradiction are a mistake. [...] In all the cases I have looked at, you can transform a proof by contradiction into a proof in which everything you’re saying is true and you learn more that way." – David Blackwell (1919-2010)
#quote #mathematics #math #maths

"Je pense que le raisonnement par l'absurde est une erreur. [...] Dans tous les cas que j'ai examinés, on peut transformer un raisonnement par l'absurde en une preuve dans laquelle tout ce qu'on dit est vrai, et on en apprend plus de cette façon." – David Blackwell (1919-2010)
#citation #mathématiques #maths #math

Truncated ‘cuboctahedron’ mapped from continuous polynomial x^80+y^80+z^80+.6133^80((y+z)^80+(z+x)^80+(x+y)^80+(y-z)^80+(z-x)^80+(x-y)^80)+.5286^80((x+y+z)^80+(x+y-z)^80+(x-y+z)^80+(-x+y+z)^80)-1=0. An Archimedean solid, it has 26 regular faces (6 octagonal, 8 hexagonal and 12 square), 48 vertices and 72 equal edges. It is not a true truncation of the cuboctahedron which instead results in 12 rectangular faces rather than square. However, with a bit of (mathematical) stretching, the requisite all edges equal condition can be met. #Maths #Mathematics #Math #polyhedron

https://en.wikipedia.org/wiki/Truncated_cuboctahedron

Theorem of the Day (April 23, 2025) : Bailey’s Theorem on Latin Squares
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Statistics/Bailey/TotDBailey.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#56
#mathematics #maths #math #theorem @Theoremoftheday

Here's the question for April 23rd 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.

An excellent video from Quanta Magazine about a group of people solving the BB5 computational Halting Problem.

12-minute video: https://youtu.be/rmx3FBPzDuk

Another bifurcation diagram, not made over breakfast. This is of \[ f(x) = \left(\frac{1}{2}+\sin(Ax/2)\right)\left( \frac{1}{2}+\sin(Ax+\frac{\pi}{2} \right) \]

I found out a little about the #MoodleStack Meclib library at the STACK25 conference in Durham. However it was only today I realised quite what a useful thing it could be. This is summed up by the tag on the github repo.

“JSXGraph-based dynamic and interactive images in Moodle STACK questions without even touching JavaScript”

https://github.com/mkraska/meclib
#moodle #edtech #educaiton #maths #math #mathematics

"For me, and I suppose for most mathematicians, there is another reality, which I will call "mathematical reality"; and there is no sort of agreement about the nature of mathematical reality among either mathematicians or philosophers. Some hold that it is "mental" and that in some sense we construct it, others that it is outside and independent of us." – Godfrey Harold Hardy (1877-1947)
#quote #mathematics #math #maths

"Pour moi, et je suppose pour la plupart des mathématiciens, il existe une autre réalité, que j'appellerai "réalité mathématique" ; et il n'y a aucun accord d'aucune sorte sur la nature de la réalité mathématique, que ce soit parmi les mathématiciens ou les philosophes. Certains soutiennent qu'elle est "mentale" et que, en un sens, nous la construisons, d'autres qu'elle est extérieure et indépendante de nous." – Godfrey Harold Hardy (1877-1947)
#citation #mathématiques #maths #math

Theorem of the Day (April 22, 2025) : A Theorem of Erdös and Wilson on Edge Colouring
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/CombinatorialTheory/ErdosWilson/TotDErdosWilson.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#117
#mathematics #maths #math #theorem @Theoremoftheday

On Tuesday, 29th July 2025 I'm in Liverpool as part of the IMA-funded event "Automated grading in mathematics & statistics: beyond the basics"

The plan is to gather people who know a bit about a few different maths assessment systems and think about how to fairly mark more complicated questions. I'll be representing @numbas.

There's also a strand about AI that I'm not interested in at all.

Info and free registration at https://pcwww.liv.ac.uk/~itho17/workshop2025/

Here's the question for April 22nd 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.

22 avril 1929 : #CeJourLà naissance de Michael Atiyah (†11/1/2019), mathématicien britannique d'origine libanaise, médaillé Fields en 1966 notamment pour ses travaux en K-théorie et sa preuve, avec Isadore Singer, du théorème de l'indice d'Atiyah-Singer.
https://fr.wikipedia.org/wiki/Michael_Atiyah
#mathématiques #maths #math

The Opposite of Infinity

https://www.youtube.com/watch?v=WYijIV5JrKg

"Sans un minimum d’ouverture à la beauté des choses, j’aurais été bien incapable de "fonctionner" comme mathématicien, même à un régime des plus modestes – et je doute que quiconque puisse faire travail utile en mathématiques, s’il ne reste vivant en lui, tant soit peu, ce sens de la beauté." – Alexandre Grothendieck (1928-2014)
#citation #mathématiques #maths #math

"Without a minimum of openness to the beauty of things, I would have been quite unable to "function" as a mathematician, even at a modest level – and I doubt that anyone could do useful work in mathematics if that sense of beauty didn't remain alive in them, at least to some extent." – Alexandre Grothendieck (1928-2014)
#quote #mathematics #math #maths

Theorem of the Day (April 21, 2025) : Sokal’s Theorem on Chromatic Roots
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/MathPhysics/Sokal/TotDSokal.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#169
#mathematics #maths #math #theorem @Theoremoftheday

Source : Youtube / Numberphile

https://www.youtube.com/watch?v=hKpa9ntjgeo
#mathematics #math #maths #youtube