Theorem of the Day (February 7, 2026) : A Theorem of Schur on Real-Rootedness
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Analysis/SchurRealZeros/TotDSchurRealZeros.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#148
#MATH
![Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
A Theorem of Schur on Real-Rootedness : Let f (x) = a0 +a1 x+. . .+am x^m and g(x) = b0 +b1 x+. . .+bn x^n be polynomials in R[x] and suppose that f and g have only real zeros and that all the zeros of g have the same sign. Then the polynomial f (x) ⊙ g(x) = ∑_(k=0)^(min(m,n)) k!ak bk x^k has only real zeros and if a0 and b0 are both nonzero then these zeros are distinct.](https://files.mastodon.social/cache/media_attachments/files/116/028/998/186/592/864/original/f82b04a77fe56368.png)
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Long-Sought Proof Tames Some of Math’s Unruliest Equations
Source : Quanta Magazine / Paulina Rowińska
https://www.quantamagazine.org/long-sought-proof-tames-some-of-maths-unruliest-equations-20260206/
#mathematics #maths #math
Thomaths 32 - La Combinatoire
Source : Youtube / Thomaths
https://www.youtube.com/watch?v=82Nkx3MxSTI
#mathématiques #maths #math #Youtube
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A117048: Prime numbers that are expressible as the sum of two positive triangular numbers
A117048 ➡️ https://oeis.org/A117048
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Decomposition into weight × level + jump of prime numbers in 3D, threejs - webGL (log(weight), log(level), log(jump))
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A116700: "Early bird" numbers: write the natural numbers in a string 12345678910111213.... Sequence gives numbers that occur in the string ahead of their natural place, sorted into increasing order (cf. A117804).
A116700 ➡️ https://oeis.org/A116700
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Rust: building arbitrary precision integers (badly)
https://artificialworlds.net/blog/2026/02/06/arbitrary-precision-integers/
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Problem for February 7th from the 2026 AMS Daily Epsilon of Math Calendar
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A new hectoc for you:
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Teaching category theory to engineers (part 4)
https://joe-moeller.com/2026/02/06/teaching-category-theory-to-engineers-part-4/
7 février 1883 : #CeJourLà naissance de Eric Temple Bell (†21/12/1960), mathématicien et écrivain américain d'origine écossaise, dont les travaux portent sur la théorie des nombres (cf. les séries de Bell, les nombres de Bell, les polynômes de Bell).
https://fr.wikipedia.org/wiki/Eric_Temple_Bell
#mathématiques #maths #math
7 février 1877 : #CeJourLà naissance de Godfrey Harold Hardy (†1/12/1947), mathématicien britannique dont les travaux portent sur l'analyse et la théorie des nombres. Il est aussi connu pour avoir "découvert" et collaboré avec Srinivasa Ramanujan.
https://fr.wikipedia.org/wiki/Godfrey_Harold_Hardy
#mathématiques #maths #math
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"We present a diverse set of 10 research-level math questions, drawn from algebraic combinatorics, spectral graph theory, algebraic topology, stochastic analysis, symplectic geometry, representation theory, lattices in Lie groups, tensor analysis, and numerical linear algebra. Each question arose naturally in the research process of the authors and has been answered with a proof of roughly five pages or less, but the answers have not yet been posted online."
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