Years ago I recall the question of whether complex numbers vs real numbers gave #neuralnetworks a greater ability to learn ?
I don't recall the answer
does anyone know?
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#maths
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« 380 ans de mystère enfin résolu » : des #mathématiciens ( #maths ) percent le secret ultime du #théorème des #cercles de #Descartes avec une #démonstration fulgurante
Innovant - L'actualité des innovations · « 380 ans de mystère enfin résolu » : des mathématiciens percent le secret ultime du théorème des cercles de Descartes avec une démonstration fulgurante - InnovantLes mathématiques ont récemment connu une avancée majeure grâce à des chercheurs de l'université Monash. Ils ont résolu un casse-tête géométrique vieux de plusieurs siècles, lié au célèbre théorème des cercles de Descartes. Cette découverte n'est pas seulement un exploit intellectuel, elle ouvre aussi de nouvelles perspectives en géométrie et au-delà. Quelles implications cela pourrait-il
« 380 ans de mystère enfin résolu » : des #mathématiciens ( #maths ) percent le secret ultime du #théorème des #cercles de #Descartes avec une #démonstration fulgurante
www.innovant.fr/2025/04/08/3...
« 380 ans de mystère enfin rés...
Bluesky SocialBluesky
Replied in thread
ѦਹѤʞ @JacquesTimmermans
...Suddenly three became an infinity. Maths is often like this and I think it’s generally a hint that one is moving in the right direction.
#maths #mathematics
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@JacquesTimmermans
I recall learning about the quaternions surprisingly early in life and becoming somewhat obsessed with them and other related algebras I managed to discover along the way all of which seemed to provide sensible finite numbers of solutions to various problems; then suddenly realising one day, some years later, that Hamilton had not only found three square roots of minus one but that *every point* on the unit imaginary sphere is a square root of minus one...
#maths #mathematics
"How do we know that a particular set of postulates, say those of elementary algebra, will never lead to a contradiction? The answer to this disposes once and for all of the hoary myth of absolute truth for the conclusions of pure mathematics. We do not know [...] that a particular set of postulates is self-consistent and that it will never lead to a contradiction." – Eric Temple Bell (1883-1960)
#quote #mathematics #math #maths
![Portrait of Eric Temple Bell, and a quote : "How do we know that a particular set of postulates, say those of elementary algebra, will never lead to a contradiction? The answer to this disposes once and for all of the hoary myth of absolute truth for the conclusions of pure mathematics. We do not know [...] that a particular set of postulates is self-consistent and that it will never lead to a contradiction."](https://media.mathstodon.xyz/media_attachments/files/114/303/173/993/456/523/original/1dddfb1441c29548.png "Portrait of Eric Temple Bell, and a quote : \"How do we know that a particular set of postulates, say those of elementary algebra, will never lead to a contradiction? The answer to this disposes once and for all of the hoary myth of absolute truth for the conclusions of pure mathematics. We do not know [...] that a particular set of postulates is self-consistent and that it will never lead to a contradiction.\"")
"Comment savons-nous qu'un ensemble particulier de postulats, disons ceux de l'algèbre élémentaire, ne conduira jamais à une contradiction ? La réponse à cette question élimine une fois pour toutes le vieux mythe de la vérité absolue des conclusions des mathématiques pures. Nous ne savons pas [...] si un ensemble particulier de postulats est cohérent, et s'il ne conduira jamais à une contradiction." – Eric Temple Bell (1883-1960)
#citation #mathématiques #maths #math
![Portrait d'Eric Temple Bell, et une citation : "Comment savons-nous qu'un ensemble particulier de postulats, disons ceux de l'algèbre élémentaire, ne conduira jamais à une contradiction ? La réponse à cette question élimine une fois pour toutes le vieux mythe de la vérité absolue des conclusions des mathématiques pures. Nous ne savons pas [...] si un ensemble particulier de postulats est cohérent, et s'il ne conduira jamais à une contradiction."](https://media.mathstodon.xyz/media_attachments/files/114/303/172/702/724/213/original/b09fd21a7c0083d3.png "Portrait d'Eric Temple Bell, et une citation : \"Comment savons-nous qu'un ensemble particulier de postulats, disons ceux de l'algèbre élémentaire, ne conduira jamais à une contradiction ? La réponse à cette question élimine une fois pour toutes le vieux mythe de la vérité absolue des conclusions des mathématiques pures. Nous ne savons pas [...] si un ensemble particulier de postulats est cohérent, et s'il ne conduira jamais à une contradiction.\"")
As a mathematician, I am upset by *anyone* who starts by setting ε < 0.
Theorem of the Day (April 8, 2025) : The Second Isomorphism Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/GroupTheory/SecondIsomorphism/TotDIsomorphism2.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#35
Yesterday was day 1 of the 3 day International Meeting of the STACK community.
It was inspiring to be around so many smart people working on improving #maths education. There was good coverage of the use of JSXGraph for creating questions with graphics that students can interact with . Recent developments in Large Language Models and #AI have made it much easier to create the #Javascript code required for #JSXGraph .
sites.google.comSTACK 2025 - ScheduleThe schedule is as follows. All in person participants will be provided with a site plan to help you find the rooms. All remote participants will be emailed a Zoom link. The workshops, discussions, talks and network meetings are all available for both in person and remote participants.
The icon 5️⃣
Math nerds, what is your favorite equation or expression and why?
Mine is : Δx · Δp ≥ ħ / 2
Because I find poetic that uncertainty is native to reality, it isn’t a failure, it’s fundamental feature!
my new ~10 seconds hardcore investigation game with 250 lvls 
Find Tau-do! 
24 lvls per second!! 
GIF
**Explaining the Trump Tariff Equation**
Stand-up Maths
#Video length: eighteen minutes and twenty-five seconds.
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@glyph
I hear you.
My favourite (perhaps less jarring?) example is when a court declares they have found someone guilty, and that their threshold of guilt is "on balance of odds".
I look at the lawyers and the witnesses and realise that none of them has studied actuarial or probability mathematics. I wouldn't even trust them to understand a bet on the horses. For a scientist to watch them is like observing a cargo cult. Worse, I am sure, is for a scientist to find themselves on the receiving end of such a court.
I would offer the meagre consolation that you can see the feedback loops that drive them to behave so, where they think themselves to have free will.
Replied in thread
@JacquesTimmermans
Would it be pedantic of me to point out that
\[\frac{1}{a}+\frac{1}{b}=\frac{1}{13}\]
does not imply a+b=1 and ab=13
but that a+b=k and ab=13k
for some arbitrary k
and that modifying the quadratic thus would give solutions
\[\frac{k+\sqrt{k(k-52)}}{2}\]
and
\[\frac{k-\sqrt{k(k-52)}}{2}\]
?
"L'une des principales fins des mathématiques, quand elles sont correctement enseignées, est d'éveiller chez l'apprenant la foi en la raison, la confiance dans la vérité de ce qui a été démontré et dans la valeur de la démonstration." – Bertrand Russell (1872-1970)
#citation #mathématiques #maths #math
"One of the chief ends served by mathematics, when rightly taught, is to awaken the learner's belief in reason, his confidence in the truth of what has been demonstrated, and in the value of demonstration." – Bertrand Russell (1872-1970)
#quote #mathematics #math #maths
Saw a @codepen demo using... a lot! of elements (screen 1) and quite a bit of #CSS to create a simple loader, so I forked it and made a 1 div version (screen 2) in under 30 CSS declarations (gradients, mask, variables to only change --c0 and --c1 values for 2nd loader): https://codepen.io/thebabydino/pen/PwoLJLR
