A detailed explanation of the Chinese Remainder Theorem (CRT), originating from ancient Chinese arithmetic texts, covering its mathematical principles to its important applications in modern public-key cryptography (RSA cryptography).
A detailed explanation of the famous topological theorem, the 'Hairy Ball Theorem', from intuitive understanding to rigorous mathematical proof, and its real-world applications in meteorology and computer graphics.
The 'Seven Bridges of Königsberg' problem solved by the 18th-century mathematician Leonhard Euler. This article delves deeply into the history and mathematical background of how this problem pioneered new fields of modern mathematics, such as graph theory and topology.
From the doubts about Euclid's parallel postulate, to the establishment of non-Euclidean geometry by Gauss, Bolyai, Lobachevsky, and Riemann, and leading to Einstein's general theory of relativity, we explain the magnificent history of mathematics and physics.
An easy-to-understand explanation of the physical background and mathematical difficulties of the 'Yang-Mills Equation and Mass Gap Problem', one of the Millennium Prize Problems.
A deep dive into the existence and smoothness of the Navier-Stokes equations, one of the Millennium Prize Problems of the Clay Mathematics Institute.
A deep dive into the 'Remarkable Theorem' discovered by Carl Friedrich Gauss, from its mathematical background to its everyday application when eating pizza.
A deep explanation of the Prime Number Theorem, a monumental achievement in mathematics regarding the regularity of prime number appearances. From the prime-counting function to its relationship with the Riemann Hypothesis.
A detailed mathematical explanation of the Birch and Swinnerton-Dyer Conjecture (BSD Conjecture), one of the Millennium Prize Problems, from the basics of elliptic curves to its deep connection with L-functions.
Fermat's Last Theorem, the most famous unsolved problem in the history of mathematics. How was this difficult problem, which rejected the challenges of many genius mathematicians for 360 years after the death of Pierre de Fermat, proven by Andrew Wiles? We explain its dramatic history and mathematical background in detail.
What is Galois Theory? Why is there no formula for solving equations of degree 5 or higher? We will explain the foundations of group theory left by Évariste Galois and the beauty of symmetry in mathematics in an easy-to-understand way.
A comprehensive guide to the Hodge Conjecture, one of the Clay Mathematics Institute's Millennium Prize Problems, exploring its role as a bridge between algebraic geometry and topology and its deep mathematical background.
A detailed explanation of the full picture of the 'Poincaré Conjecture' that troubled mathematicians for over 100 years, the basics of topology, and the story of the dramatic proof by Grigori Perelman.
A detailed explanation of the Twin Prime Conjecture, an unsolved problem in mathematics, including its history, partial solutions, and the latest research trends.
Delve deeply into the history of the Continuum Hypothesis (CH) proposed by Georg Cantor, its mathematical background, and the proofs of its independence by Gödel and Cohen.
A deep explanation of the background and meaning of Euler's identity, considered the most beautiful equation in the history of mathematics.
We explain in detail the history of the Four Color Theorem, a difficult problem in the mathematical world, proof approaches, and the significance of computer-assisted proofs.
A detailed explanation of 'Goldbach's Conjecture', one of the most famous unsolved problems in mathematics, covering its history, meaning, and significance in modern mathematics.
An in-depth look at the overview of the ABC Conjecture and the groundbreaking approach by Professor Shinichi Mochizuki using Inter-Universal Teichmüller Theory (IUT Theory).
An explanation of the Law of Large Numbers, a crucial theorem in probability theory. We delve deep into casino profit structures, rigorous mathematical definitions (weak and strong laws), with diagrams and Python code.
