Hacker News with Generative AI: Number Theory

Mathematician solves algebra's oldest problem using intriguing number sequences (phys.org)
A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations.
Mathematics, Algebra, Number Theory
53 points by amichail 7 days ago | 51 comments
Mathematician solves algebra's oldest problem using new number sequences (phys.org)
A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations.
Mathematics, Algebra, Number Theory, Research
8 points by pseudolus 7 days ago | 0 comments
The Periodic Table of Primes (2024) (ssrn.com)
Over millennia, nobody has been able to predict where prime numbers sprout or how they spread.
Mathematics, Number Theory, Prime Numbers
7 points by toss1 14 days ago | 1 comments
Reptends and Reciprocals (gregegan.net)
Is there an integer d whose reciprocal, 1/d, has a decimal representation with a recurring block of digits exactly 10 digits long, containing all ten decimal digits?
Mathematics, Number Theory, Puzzles
13 points by pavel_lishin 16 days ago | 2 comments
Is 1 Prime, and Does It Matter? (wordpress.com)
If you ask a person on the street whether 1 is a prime number, they’ll probably pause, try to remember what they were taught, and say “no” (or “yes” or “I don’t remember”). Or maybe they’ll cross the street in a hurry. On the other hand, if you ask a mathematician, there’s a good chance they’ll say “That’s an excellent question” or “It’s kind of an interesting story…”
Mathematics, Number Theory, Prime Numbers
92 points by jamespropp 18 days ago | 151 comments
A cute proof that makes e natural (poshenloh.com)
This webpage pulls out the part of the article which uses Pre-Calculus language to explain what is so natural about e, while intuitively connecting the following two important properties:
Mathematics, Proof, Number Theory
101 points by georgecmu 22 days ago | 43 comments
Loader's Number (fandom.com)
Mathematics, Number Theory, Trivia
63 points by lisper 34 days ago | 10 comments
Lehmer's Continued Fraction Factorization Algorithm (leetarxiv.substack.com)
In 1931, at Stanford University, D.H Lehmer and R.E. Powers1 published a general integer factorization algorithm based on the theory of continued fractions.2
Mathematics, Algorithms, Number Theory
18 points by muragekibicho 40 days ago | 5 comments
Peano's Axioms (principlesofcryptography.com)
Thinking of numbers intuitively brings to mind the simplest and most fundamental set of numbers, namely the set of natural numbers. These numbers are used to count objects like cars, books, pens, etc. If we associate natural numbers such as 1, 2, 3, etc. with counting, then with what corresponding concepts do we relate numbers like -4, \sqrt{3} \text{ and } \frac{22}{7}?
Mathematics, Number Theory, Set Theory
91 points by ulugh 46 days ago | 33 comments
Powers of 2 with all even digits (oeis.org)
Powers of 2 with all even digits.
Mathematics, Number Theory
265 points by Hbruz0 50 days ago | 116 comments
Ten Digit Problems (2011) [pdf] (ox.ac.uk)
Mathematics, Research Papers, Number Theory
54 points by cpp_frog 63 days ago | 2 comments
Quaternions and spherical trigonometry (wordpress.com)
Hamilton’s quaternion number system is a non-commutative extension of the complex numbers, consisting of numbers of the form where are real numbers, and are anti-commuting square roots of with , , . While they are non-commutative, they do keep many other properties of the complex numbers:
Mathematics, Algebra, Number Theory, Geometry
124 points by t55 99 days ago | 48 comments
Where do those undergraduate divisibility problems come from? (grossack.site)
Oftentimes in your “intro to proofs” class or your first “discrete math” class or something similar, you’ll be shown problems of the form “prove that for $n^6 + n^3 + 2n^2 + 2n$ is a multiple of $6$ for every $n$”… But where do these problems come from? And have you ever stopped to think how magical this is?
Mathematics, Proofs, Education, Number Theory
161 points by mathgenius 109 days ago | 52 comments
Prime numbers so memorable that people hunt for them (scientificamerican.com)
Math enthusiasts challenge one another to find special prime numbers, including those that are palindromes and Smarandache numbers
Mathematics, Prime Numbers, Number Theory
185 points by georgecmu 111 days ago | 103 comments
Rational or not? This basic math question took decades to answer (quantamagazine.org)
It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question.
Mathematics, Number Theory, Science
173 points by nsoonhui 120 days ago | 137 comments
Show HN: 2025 = sum(I^3) for I = 0..9 (ycombinator.com)
This year's number is kinda fun:<p>2025 = 0^3 + 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3<p>Which is equivalent to:<p>2025 = (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) ^ 2 = 45 ^ 2<p>Next time this will happen is 1000 years from now, in 3025. See y'all then!
Mathematics, Number Theory, Programming, Show HN
12 points by temporalparts 127 days ago | 3 comments
The number pi has an evil twin (mathstodon.xyz)
Mathematics, Number Theory
579 points by pkaeding 136 days ago | 207 comments
The Year in Math (quantamagazine.org)
Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future.
Mathematics, Geometry, Number Theory, Artificial Intelligence
15 points by isaacfrond 143 days ago | 0 comments
The First 50M Prime Numbers (1975) [pdf] (mpim-bonn.mpg.de)
Mathematics, Number Theory, History, Data
93 points by quickfox 144 days ago | 39 comments
Mathematicians uncover a new way to count prime numbers (quantamagazine.org)
A new proof has brought mathematicians one step closer to understanding the hidden order of those “atoms of arithmetic,” the prime numbers.
Mathematics, Prime Numbers, Number Theory
199 points by nsoonhui 147 days ago | 88 comments
Mathematicians Uncover a New Way to Count Prime Numbers (quantamagazine.org)
A new proof has brought mathematicians one step closer to understanding the hidden order of those “atoms of arithmetic,” the prime numbers.
Mathematics, Prime Numbers, Number Theory
9 points by pseudolus 148 days ago | 0 comments
The Postage Stamp Problem (johndcook.com)
I recently stumbled upon the Postage Stamp Problem. Given two relatively prime positive numbers a and b, show that any sufficiently large number N, there exists positive integers x and y such that
Mathematics, Number Theory, Algorithms
6 points by azhenley 180 days ago | 0 comments
A Man Who Found the Biggest Prime [video] (youtube.com)
Mathematics, Prime Numbers, Number Theory, Videos
4 points by selectnull 199 days ago | 0 comments
Vampire Number (wolfram.com)
A number with an even number of digits formed by multiplying a pair of -digit numbers (where the digits are taken from the original number in any order) and together. Pairs of trailing zeros are not allowed. If is a vampire number, then and are called its "fangs."
Mathematics, Number Theory
65 points by dustfinger 199 days ago | 13 comments
New largest prime number found See all 41,024,320 digits [video] (youtube.com)
Mathematics, Prime Numbers, Number Theory, Science, Video
10 points by Alifatisk 200 days ago | 7 comments
Goldbach's Conjecture (wikipedia.org)
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.
Mathematics, Number Theory, Unsolved Problems
6 points by mkaic 206 days ago | 0 comments
Big advance on simple-sounding math problem was a century in the making (quantamagazine.org)
A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture.
Mathematics, Number Theory, Prime Numbers, Conjectures
129 points by isaacfrond 206 days ago | 40 comments
Terence Tao on O1 (mathstodon.xyz)
Mathematics, Terence Tao, Number Theory
664 points by dselsam 237 days ago | 483 comments
666 = sum(range(1,37)) and other sequences (oeis.org)
Displaying 1-10 of 1826 results found.
Mathematics, Number Theory, Sequences
12 points by wslh 247 days ago | 3 comments
Breakthrough a step toward revealing hidden structure of prime numbers (science.org)
Mathematics, Number Theory, Prime Numbers
400 points by igitur 281 days ago | 147 comments