A 23‑year‑old amateur named Liam Price teamed up with ChatGPT to solve the 60‑year‑old Erdős primitive‑sets conjecture in just 80 minutes, using a novel “vibe mathing” approach that bypassed traditional number‑theoretic methods and surprised leading mathematicians including Terence Tao.
The 2026 Breakthrough Prize announced its New Horizons in Mathematics winners—Wang Hong, Yunqing Tang, Otis Chodosh and Vesselin Dimitrov—highlighting Wang's solution of the Kakeya conjecture, Tang and Dimitrov's breakthroughs on the unbounded denominators conjecture and a new irrationality result, and Chodosh's advances in differential geometry, with a total prize pool of $18.75 million.
The Riemann Hypothesis, a 1859 conjecture linking the zeros of the ζ(s) function to the exact distribution of prime numbers, remains the most celebrated unsolved problem in mathematics, influencing number theory, cryptography, physics, and countless downstream theorems.
This guide explains how to use PHP together with the GMP library to perform modular inverse calculations on large integers, covering installation of the GMP extension, loading it in code, implementing the inverse function, and important usage notes for cryptographic applications.
The article explores the mathematical definition of prime numbers, their cultural characterization as possessing a masculine, indestructible quality in Chinese tradition, explains their rigid structure, discusses the unpredictable distribution of primes, and connects these ideas to the profound Riemann Hypothesis that seeks a hidden order in prime patterns.
This article explains how to perform large‑integer modular inverse calculations using PHP and the GMP library, covering installation of the GMP extension, loading it in code, and demonstrating the gmp_invert() function with example code and important considerations for correct results.
From its appearance as a rescue signal in a thriller film to its role as a triangular number, a sum of primes, and a culturally charged symbol, this article explores the many mathematical properties and cultural meanings of the number 666.
This article explains what Armstrong (narcissistic) numbers are, demonstrates how to determine them for three‑digit, n‑digit, and range‑based cases, and provides clear Python code examples with sample outputs to help readers grasp the concept and implement the checks.
This article traces the historical origins of the Goldbach conjecture, explains its equivalent formulations involving prime numbers and almost‑primes, reviews the series of partial results such as the 9+9 and 1+2 theorems, and discusses why the full conjecture remains unproven today.
The author tackles a elementary school three‑digit logic puzzle—determining a number that meets specific divisibility and digit‑sum conditions—by first reasoning through the constraints and then using a short Python brute‑force script, ultimately revealing the unique solution abc = 168.
A third‑grader’s bulb‑toggling puzzle is solved by showing that a bulb stays on only when its number is a perfect square, leading to 14 lit bulbs out of 200, and a simple Ruby program is used to demonstrate the result.
A father turned his daughter's third‑grade math challenge—finding a five‑digit number that becomes its reverse when multiplied by four—into a collaborative coding exercise, showcasing three distinct Oracle SQL solutions that generate and test digit permutations to reveal the unique answer.
