Theorem of the Day (July 12, 2025) : Neumann’s Separation Lemma
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/GroupTheory/PMNeumann/TotDNeumann.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#64
#mathematics #maths #math #theorem @Theoremoftheday

my brain isn't working

did I get the type on the last line right?

---

if x was x:β then the type would be β→...

but here x is x:Πα:*.(α→α) and naively that means the type is Πα:*.(α→α) →...

I'm partly worried that α should be σ but then I remember that α is bound so irrelevant outside the scope of the Π

I'm begrudgingly impressed by overleaf - an online latex editor and previewer.

They managed to include useful latex packages, have good documentation and tutorials, have a UI that isn't too complicated and headache-inducing.

I still use offline lyx for my projects, but overleaf is good for generating small snippets of typeset maths.

Begrudging? Well, I wanted to create an online version of lyx (no latex code) but never managed to find time.

https://www.overleaf.com/

"Mon enthousiasme pour les mathématiques avait peut-être eu pour base principale mon horreur pour l'hypocrisie [...]. Suivant moi, l'hypocrisie était impossible en mathématiques et, dans ma simplicité juvénile, je pensais qu'il en était ainsi dans toutes les sciences où j'avais ouï dire qu'elles s'appliquaient." – Stendhal (1783-1842)
#citation #mathématiques #maths #math

"My enthusiasm for mathematics was based principally perhaps on my horror of hypocrisy [...]. In my opinion, hypocrisy wasn’t possible in mathematics and, in my youthful simplicity, I thought the same went for all the sciences in which I had heard it said they were applied." – Stendhal (1783-1842)
#quote #mathematics #math #maths

**Mathematicians are chasing a number that may reveal the edge of maths**

https://www.newscientist.com/article/2487058-mathematicians-are-chasing-a-number-that-may-reveal-the-edge-of-maths/.

Is it normal to do this kind of thing?

λα,β:* . x:α→β, y: α . xy : Πα,β:*. (α→β) →α →β

That is, to have non-trivial types for objects like x?

--

To make that clearer ...

So instead of just doing x:α, y:β we do things like x:α→β→β and y:β→α

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1/2

Theorem of the Day (July 11, 2025) : The Eratosthenes–Legendre Sieve
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/NumberTheory/LegendreSieve/TotDELSieve.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#207
#mathematics #maths #math #theorem @Theoremoftheday

Do you guys know what saddens me the most at the moment?

The fact that we keep multiplying sin and cos function parameters by π or 𝜏 for the function to immediately undo this and move it back into normalized range.

"Mathematics is the science which uses easy words for hard ideas. In this it differs from any other science." – Edward Kasner et James Newman
#quote #mathematics #math #maths

"La mathématique est la science qui utilise des mots faciles pour des idées difficiles. En cela, elle diffère de toute autre science." – Edward Kasner et James Newman
#citation #mathématiques #maths #math

Sometimes (often) I have this mathematical urge, this instinct, to just name everything with one letter, then I switch to capitalized ones when I run out of them, and then I feel frustrated for not being able to use some Unicode character instead of pi, tau, phi, ...

This is honestly starting to frighten me, especially since I'm actually taking a liking to it.

This is a sickness, please help me.

Theorem of the Day (July 10, 2025) : The Fundamental Theorem of Algebra
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Algebra/FundamentalAlgebra/TotDFTA.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#6
#mathematics #maths #math #theorem @Theoremoftheday

10 juillet 1682: #CeJourLà naissance de Roger Cotes (†5/6/1716), mathématicien britannique qui a collaboré avec Isaac Newton, dont les travaux portent notamment sur les logarithmes, le calcul intégral et l'analyse numérique (cf. formules de Newton-Cotes).
https://fr.wikipedia.org/wiki/Roger_Cotes
#mathématiques #maths #math

Double Maths First Thing: Issue 2C
Source : The Aperiodical / Colin Beveridge

https://aperiodical.com/2025/07/double-maths-first-thing-issue-2c/
#mathematics #maths #math @aperiodical @icecolbeveridge

Is this correct?

---

In the context β:*, the type of

Πγ:*.γ

is

β → β

---

"In mathematics it is new ways of looking at old things which seem to be the most prolific sources of far-reaching discoveries. A particular fact may have been known for centuries, and it may have been sterile or of only minor interest all that time, when suddenly some original mind glimpses it from a new angle and perceives the gateway to an empire." – Eric Temple Bell (1883-1960)
#quote #mathematics #math #maths