#numbertheory — Public Fediverse posts

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html

#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra

Alright, future engineers!

**Modulo Arithmetic:** The remainder after division.
Ex: `10 mod 3 = 1` (since `10 = 3*3 + 1`).
Pro-Tip: Super useful for clocks & cyclical patterns – it wraps around!

#DiscreteMath #NumberTheory #STEM #StudyNotes

Alright, future engineers!
**Modular Arithmetic:** Numbers wrap around after a certain value (the modulus).
Ex: `(10 + 4) mod 12 = 14 mod 12 = 2`. Think of a clock!
Pro-Tip: It's super useful in cryptography & computer science for cycles/remainders!
#NumberTheory #DiscreteMath #STEM #StudyNotes

Alright, future engineers!
**Modulo Arithmetic:** Finding the remainder after division.
Ex: `17 mod 5 = 2`.
Pro-Tip: Crucial for cryptography, clock arithmetic, and hashing!
#DiscreteMath #NumberTheory #STEM #StudyNotes

Alright, future engineers!
**Modular Arithmetic:** Numbers wrap around after reaching a specific value (the modulus).
Ex: `10 mod 3 = 1` (since 10 = 3*3 + 1).
Pro-Tip: Think of a clock! Useful for cryptography & algorithms.
#DiscreteMath #NumberTheory #STEM #StudyNotes

Alright, future engineers!
**Modulo Arithmetic:** The remainder when an integer is divided by another.
Ex: `17 mod 5 = 2` (17 / 5 leaves 2).
Pro-Tip: Think clock arithmetic! Crucial for cryptography, hashing, and cyclic systems.
#DiscreteMath #NumberTheory #STEM #StudyNotes

Niels Abel was born 224 years ago, on August 5, 1802. At just 21, he proved that no general algebraic formula can solve equations of degree 5, a problem that had challenged mathematicians for roughly 250 years.

Short on money, Abel paid the printer himself and condensed his proof into just six pages to keep costs down. He sent a copy to Gauss, but never received a response.

Abel died of tuberculosis at just 26. Two days later, a letter arrived announcing that he had been appointed professor in Berlin.

A breakthrough recognized too late.

#NielsAbel #Mathematics #MathHistory #HistoryOfMathematics #Mathematician #Algebra #AbstractAlgebra #QuinticEquation #Quintic #GaloisTheory #MathematicalHistory #MathFacts #ScienceHistory #STEMHistory #STEM #MathematicalBreakthrough #MathematicalGenius #Norway #NorwegianHistory #CarlFriedrichGauss #Equations #NumberTheory #PureMathematics #MathEducation #ScienceCommunication #OnThisDay #August5 #History #MathematicsLovers #MathTwitter

Alright, future engineers!
**Modular Arithmetic:** Operations focusing on the remainder after division.
Ex: `17 mod 5 = 2`.
Pro-Tip: Think 'clock arithmetic'! Essential for hashing & crypto.
#DiscreteMath #NumberTheory #STEM #StudyNotes

On May 20, 2026, OpenAI made an announcement that shook the mathematical world. An internal AI model, one not available to the public, had come up with a counterexample to the “unit distance” problem, a conjecture made in 1946 by Paul Erdős, the prolific, itinerant Hungarian mathematician. Erdős posed thousands of questions, but this one was special: It was both simple to explain and mathematically deep. It was the first historically significant proof to come from an AI model. Though the model’s result wasn’t definitive, human mathematicians would substantially improve on it within weeks, it was innovative, bringing in ideas from a distant branch of math that no one had successfully applied to this problem before. And it was influential: Within a few days, related techniques were used to solve other important problems. Then on August 1, OpenAI announced that an unreleased model named Astra made 10 additional mathematical advances, including finding solutions to three more problems posed by Erdős. Many mathematicians have hailed developments such as these as a phase transition in the mathematical capability of AI models. These models are “changing dramatically the way mathematical research is being done,” said Noga Alon of Princeton University, who has solved dozens of Erdős problems over his decades-long career.

https://www.quantamagazine.org/why-the-legendary-erdos-problems-are-falling-to-ai-20260803

#AI #Erdős #Erdos #ErdősProblems #PaulErdős #OpenAI #Revolution #ArtificialIntelligence #QuantaMagazine #Maths #Math #NumberTheory #MathRevolution

Probability,
теорія ймовірностей, теория вероятностей
#Probability,
#теоріяймовірностей, #теориявероятностей
t.me/scilib_yura15cbx/193

Number theory
Теория чисел, Теорія чисел
#Number theory
#Теориячисел, #Теоріячисел
t.me/scilib_yura15cbx/192

References, Collected works
Література, Зібрання праць,
Ссылки, Собрание сочинений
t.me/scilib_yura15cbx/190

Symmetry and groups
Симметрия и группы,
Симетрія і групи
#Symmetry
t.me/scilib_yura15cbx/189

Philosophy of mathematics
Філософія математики, Философия математики
t.me/scilib_yura15cbx/188

Mathematical physics
Математическая физика, Математична фізика
#Mathematical physics
#Математическаяфизика, #Математичнафізика
t.me/scilib_yura15cbx/187

Optimization and control
Оптимізація та контроль, Оптимизация и контроль
t.me/scilib_yura15cbx/186

Optimal control
Оптимальный контроль, Оптимальний контроль
#Optimal control
#Оптимальныйконтроль, #Оптимальнийконтроль
t.me/scilib_yura15cbx/185

Numerical methods
Чисельні методи, Численные методы
#Numerical methods
#Чисельніметоди, #Численныеметоды
t.me/scilib_yura15cbx/184

Lecture notes
Конспекты лекций, Конспект лекцiй
t.me/scilib_yura15cbx/183

Encyclopaediae, School-level
Енциклопедії, Шкільний рівень
Энциклопедии, школьный уровень
t.me/scilib_yura15cbx/182

Games, game theory
Ігри, теорія ігор
Игры, теория игр
#Games, #game theory
#Ігри, ₽теоріяігор
#Игры, #теорияигр
t.me/scilib_yura15cbx/181

Geometry and topology
Геометрия и топология
Геометрія і топологія
#Geometry and #topology
#Геометрия и #топология
#Геометрія і #топологія
t.me/scilib_yura15cbx/180

Biography, history
Биография, история
Біографія, історія
#Biography, #history
#Биография, #история
#Біографія, #історія
t.me/scilib_yura15cbx/178

Mams_ Proceedings AMS
Праці AMS, Труды АМС
t.me/scilib_yura15cbx/177

Algebra, Алгебра
#Algebra, #Алгебра
t.me/scilib_yura15cbx/176

Optical devices
Оптика, оптические устройства, технологии, инжинерия
#Optical devices

t.me/scilib_yura15cbx/173

From a Mathematical Curiosity to the Foundation of Internet Security 🧮🧐🔐✨

In 1636, Pierre de Fermat made a remarkable observation: if you take an integer a, raise it to a prime power p, and then subtract a, the result is always divisible by p. In other words, for a prime p,

aᵖ ≡ a (mod p).

For example, when p = 5:
2⁵ − 2 = 30, which is divisible by 5, and
3⁵ − 3 = 240, which is also divisible by 5.

Fermat found this property elegant and tried to spark interest in this curious corner of mathematics. Not everyone was impressed. John Wallis reportedly dismissed such results, remarking, “Big deal; I could find other relationships just as interesting without much effort, and none of them are important.”

About a century later, Leonhard Euler was encouraged by Christian Goldbach to study Fermat’s ideas. Though initially unenthusiastic, Euler soon uncovered deeper structure within them. His work laid much of the foundation for what we now call modern number theory.

#Mathematics #Math #NumberTheory #Fermat #Euler #EulerTheorem #FermatsLittleTheorem #ModularArithmetic #RSA #Cryptography #CyberSecurity #HistoryOfMathematics #MathHistory #PrimeNumbers #EulerTotient #AbstractMath #PureMathematics #STEM #ScienceCommunication #MathEducation #EducationalContent #DidYouKnow #MathematicalBeauty #InternetSecurity #Encryption #Curiosity #Innovation #History #Learning #Knowledge

The ‘Lonely Runner’ Problem Only Appears Simple

https://web.brid.gy/r/https://www.wired.com/story/the-lonely-runner-problem-only-appears-simple/

Number theory was the one area of mathematics on which Pierre de Fermat (1607–65) worked throughout his life, and he found it ‘very beautiful and very subtle’.

Among other results, he said that the Polygonal Number Theorem (which asserts that every natural number is the sum of at most $n$ $n$-gonal numbers) was ‘a most beautiful and wholly general proposition […] this marvellous proposition’.

(He offered no proof of this result, but claimed to have one in a marginal note to Diophantus' Arithmetica; this was the same book in which he noted what became known as Fermat's Last Theorem.)

Fermat also seems to have counted magic squares and analogous configurations as part of number theory, and wrote that: ‘I know hardly anything more beautiful in arithmetic than these numbers that some call planetary and others magic’. (The term ‘planetary’ is derived from certain treatises linking the magic squares to planets used in talismans.)

He said he had found a rule to find magic cubes (one of his examples is in the attached image) and also determined how many different ways each such cube can be arranged, which he called ‘one of the most beautiful things in arithmetic’.

1/2

[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

#Fermat #NumberTheory #HistMath #MathematicalBeauty #MagicSquare

One of the best things I saw this week: a paper uncovering alien signals in the Riemann Zeta function. April Fools always brings peak creativity. 😅

#Riemann #Zeta #ZetaFunction #RiemanZetaFunction #AprilFool #AprilFools #AprilFoolsDay #Creativity #Math #Maths #NumberTheory #PeakCreativity #Nerd #Nerds #Humor #Humour #Alien #AlienSignals

A review of V1 of the paper "On the Infinitude of Twin Primes" by Dr. Ryan Matthew Thurman ( @rythur ).
Shared in one of his posts under the url https://ef.msp.org/articles/uploads/ant/submitted/230524-Thurman/230524-Thurman-v1.pdf

#TwinPrimes #Primes #NumberTheory
#TwinPrimeConjecture #UnsolvedProblem #Proof #SolvedProblem
#Simple #Insightful #PrimeClockMethod #Modulo
#Puzzle #GameLike #Thrilled #Captivating #Excitement #Reading #ReadingRecommendation

My background for this review: a layman person without any #degree, with very weak #Math interest (I knew what were prime numbers but never heard of the twin prime conjecture) and lack of math background except for what is taught in high school and the occasional math that pop here and there from my adjacent interests in the process of thinking of process both formal and informally (mainly from #lisp lore for the #ComputerScience side and #Hegel lore for the #Philosophy side of the story)

And now, only after almost 1 month since I have read it, will I review this paper (flushed face 😳).

A paper of 10 pages of content.
The paper is very pleasant and simple to read. Managing to catch our attention and make us read it in one sitting with a child-like excitement and joy. So if you have tendencies to leave things half-done, do not fear, you will get drawn into finishing it without having to fight a moment of boringness.

1/3