Lmst

The official solutions to the textbook I'm following says that prime 53 can't be expressed as the difference of two squares.

Im confused.

53=27²−26²

Am I going mad?

#maths #numbertheory

You might have noticed that 53 is a prime number and so cannot be expressed as
the difference of two squares.

(3/3) ... effectue calculs arithmétiques des arpentages #maths #science.

#year1642 #histoire #climat

"Aucun avertissement plus impressionnant ne peut être donné à ceux qui voudraient restreindre la connaissance et la recherche à ce qui est apparemment utile, que la réflexion selon laquelle les coniques ont été étudiées pendant dix-huit cents ans comme une simple science abstraite, sans penser à une quelconque utilité autre que celle de satisfaire la soif de connaissance des mathématiciens, et qu'ensuite [...]"– Alfred North Whitehead (1861–1947)
#citation #mathématiques #maths #math

Portrait photographique d'Alfred North Whitehead, et une citation : "Aucun avertissement plus impressionnant ne peut être donné à ceux qui voudraient restreindre la connaissance et la recherche à ce qui est apparemment utile, que la réflexion selon laquelle les coniques ont été étudiées pendant dix-huit cents ans comme une simple science abstraite, sans penser à une quelconque utilité autre que celle de satisfaire la soif de connaissance des mathématiciens, et qu'ensuite, à la fin de cette longue période d'étude abstraite, elles se sont révélées être la clé nécessaire pour parvenir à la connaissance de l'une des lois les plus importantes de la nature."

"No more impressive warning can be given to those who would confine knowledge and research to what is apparently useful, than the reflection that conic sections were studied for eighteen hundred years merely as an abstract science, without a thought of any utility other than to satisfy the craving for knowledge on the part of mathematicians, and that then at the end of this long period of abstract study [...]" – Alfred North Whitehead (1861–1947)
#quote #mathematics #maths #math

Photographic portrait of Alfred North Whitehead, and a quote : "No more impressive warning can be given to those who would confine knowledge and research to what is apparently useful, than the reflection that conic sections were studied for eighteen hundred years merely as an abstract science, without a thought of any utility other than to satisfy the craving for knowledge on the part of mathematicians, and that then at the end of this long period of abstract study, they were found to be the necessary key with which to attain the knowledge of one of the most important laws of nature."

I am delighted that this news is finally public and thrilled that Pure Maths at the University of Liverpool is part of this programme. This generous funding will enable us to build sustainable, high-impact research teams, pursue more ambitious projects, and nurture the next generation of UK mathematicians, whilst strengthening the long-term foundations of mathematical research in the UK.

I am grateful to Anna Pratoussevitch, Oleg Karpenkov, and Jon Woolf for helping to make this happen, as well as XTX Markets for stepping in to support UK Mathematics.

https://www.xtxmarkets.com/news/2025-pure-maths-research/

#Maths

Theorem of the Day (December 1st, 2025) : Wagner’s Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/CombinatorialTheory/Wagner/TotDWagner.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#25

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.

Wagner’s Theorem : A graph G is planar if and only if it contains neither K5 nor K3,3 as a graph minor.

If you like #Maths and puzzles... why not try the #Scroggs-Advent-Calendar... it's always fun to do... and there's a ravelry group... where we discuss tricky questions... and help each other our... www.ravelry.com/discuss/wool... www.mscroggs.co.uk

mscroggs.co.uk

A052018: Numbers k with the property that the sum of the digits of k is a substring of k

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A052018.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A052018.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A052018.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of A052018 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A052018 in 2D (log(weight), log(level))

We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #natural #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of natural numbers: the fundamental theorem of arithmetic and the sieve of Eratosthenes

Graph in 2D (log(weight), log(level)) of the decomposition into weight × level + jump of natural numbers

Decomposition into weight × level + jump of prime numbers: in 2D with sequences on the OEIS: a new classification of primes

Graph in 2D (log(weight), log(level)) of the decomposition into weight × level + jump of prime numbers

A051936: Truncated triangular numbers: a(n) = n*(n+1)/2 - 9

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/Truncated_triangular_numbers.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/Truncated_triangular_numbers.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Truncated_triangular_numbers.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of truncated triangular numbers in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of truncated triangular numbers in 2D (log(weight), log(level))

@appassionato

A similar one to this just arrived on my doorsteps:

"The Secret Lives of Numbers - A Global History of Mathematics and it's Unsung Trailblazers"

Kate Kitagawa & Timothy Revell.

My current "favorite math book" is Schaum's Outlines on Group Theory. Published in 1968, it's printed in a typewriter font and is actually quite good and has lots of problems.

#books
#nonfiction
#mathematics
#maths

Here's the question for December 1st from the AMS Daily Epsilon of Math Calendar
@DailyEpsilon

#math #maths #mathematics #mathstodon

1er décembre 1792 : #CeJourLà naissance de Nikolaï Lobatchevski (†24/2/1856), mathématicien russe. Il a été l'un des 1ers (avec Gauss et Bolyai) à étudier en détail une géométrie non euclidienne (géométrie hyperbolique), et le 1er à publier ses recherches
https://fr.wikipedia.org/wiki/Nikola%C3%AF_Ivanovitch_Lobatchevski
#mathématiques #maths #math

1/7
This air-quote #Mathematics unquote article https://www.quantamagazine.org/a-new-bridge-links-the-strange-math-of-infinity-to-computer-science-20251121/ keeps appearing in my feed, and I initially made some comments the first time, debunking it from a #Maths point-of-view, but given how it keeps popping up I think I need to do a more thorough #MathsMonday thread about it

Firstly, the author is a Physics journo, so you can take what he says about #math with a grain of salt (for some reason I see a lot of them doing this overreach, instead of checking with a Mathematician)…

OED definition of "finite", which includes "limited in size or extent", and shows that the root word is "finish"

The Unreasonable Elegance of Mathematics by Stefan Steinerberger, 2025

This book offers an introduction to the nature of mathematics, its history, and some of the curious individuals who have shaped it. It explores a range of fundamental ideas that can be appreciated without prior mathematical training. Highlighting the human side of mathematics and its shared lineage with philosophy, the book embraces the subject’s colorful history,

#books
#nonfiction
#mathematics
#maths

Based on a course taught to non-science majors, it is intended for anyone with an interest in mathematics—including those whose last experience with algebra was less than enjoyable.

A051795: Doubly balanced primes: primes which are averages of both their immediate and their second neighbors

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/Doubly_balanced_primes.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/Doubly_balanced_primes.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Doubly_balanced_primes.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of doubly balanced primes in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of doubly balanced primes in 2D (log(weight), log(level))

My data have not been verified but my work is highly reproducible.
- Downloads (csv, img, dump) ➡️ https://decompwlj.com/
- Algorithms ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump#Algorithms

#decompwlj #math #mathematics #maths #sequence #OEIS #Downloads #Algorithms #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research #PARIGP

Algorithm of the decomposition into weight × level + jump in PARI/GP from the OEIS Wiki

A051750: Primes whose cubes lack zeros

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A051750.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A051750.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A051750.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of A051750 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A051750 in 2D (log(weight), log(level))

(239/...)
- La Cité du Vatican est autonome à 100 % via les énergies renouvelables solaires.
- en #maths : https://mastodon.gougere.fr/@PierreCo

#year2025 #anthropocene #climat #climate #climatechange #climatecrisis

"The history of mathematics is important also as a valuable contribution to the history of civilisation. Human progress is closely identified with scientific thought. Mathematical and physical researches are a reliable record of intellectual progress."– Florian Cajori (1859–1930)
#quote #mathematics #maths #math

#maths

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