Category: Math Breakthroughs
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Why You Can’t Draw These 4 Shapes Exactly
With only an unmarked straightedge and a compass, ancient geometers could bisect angles, build equilateral triangles and draw regular pentagons. Yet four simple-sounding tasks resisted every attempt for millennia. The reason turned out to be algebraic: once constructions are translated into equations, it becomes clear why squaring the circle, doubling the cube, trisecting an angle… read more
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The Most Controversial Proof in Mathematics Ever
Mathematics rests on a promise: if a proof is correct, a trained mathematician should be able to check it. Shinichi Mochizuki's claimed proof of the ABC conjecture has tested that promise, dividing proponents of his theory from prominent critics. This article explains the conjecture, why it matters, and the disagreement about whether the proposed argument… read more
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Every Unsolved Prime Number Problem
Brocard’s Conjecture Twin, Cousin, and Sexy Primes Palindromic Primes Euclid Numbers Goldbach’s Conjecture Brocard’s Conjecture A prime number is a positive whole number that has exactly two divisors: 1 and itself. Pick a prime number greater than 2, like 3. Then take the next prime number after that, in this case 5. Then take the… read more
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Every Unsolved Geometry Problem that Sounds Easy – Part 2
Five More Geometry Problems That Are Way Harder Than They Look Tripod Packing The Thomson Problem The Levi-Hadwiger Conjecture Heesch’s Problem Kalai’s 3ᵈ Conjecture Tripod Packing Let’s start with a cube existing at some fixed location in 3D space. (This problem can be easier to comprehend if you think of the cubes as Minecraft blocks,… read more
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Unsolved Problems in Graph Theory Explained
Graph theory has uncovered many secrets of networks and relationships, but some problems remain unsolved. Here are three famous unsolved problems in graph theory, the Total Coloring Conjecture, the Hadwiger Conjecture, and the 1-Factorization Conjecture, and why they continue to puzzle mathematicians. Building Blocks of Graph Theory 1-Factorization Conjecture Unfriendly Partition Conjecture Hadwiger Conjecture Total… read more
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Fibonacci and the Birth of Modern Math
Leonardo de Pisa Fundamentally Changed Math Discovering the Fibonacci Series Ancient Indian Discoveries in Sanskrit Texts The Golden Number (Phi, φ) The Golden Spiral From Roman Numerals to Hindu-Arabic Numbers Fascinating Facts About the Fibonacci Sequence Leonardo de Pisa Fundamentally Changed Math mathematics is related to Natural Sciences the result of human logic a language… read more
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Every Method to Complete the Square Explained
Completing the Square: Why It’s Actually About Squares If you’ve ever taken an algebra class, you’ve probably been asked to solve for x. Before you get to quadratic equations, you usually start with linear equations, which are equations that can be put in the form ax + b = 0 for a ≠ 0. Once… read more
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Every Unsolved Geometry Problem that Sounds Easy
Five Geometry Problems That Look Simple but Remain Unsolved Square Packing Bellman’s Lost in a Forest Problem Ulam’s Packing Conjecture Lebesgue’s Universal Covering Problem Moser’s Worm Problem Kobon’s Triangle Problem Five Geometry Problems That Look Simple but Remain Unsolved Square Packing A unit square is a square with a side length of one unit. Suppose… read more
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Every Unsolved Math Problem that Sounds Easy – Part 2
Six Deceptively Simple Unsolved Problems in Mathematics Mersenne Primes Perfect Numbers The Rational Distance Problem The Moving Sofa Problem The Inscribed Square Problem The Ramsey Theory Problem Six Deceptively Simple Unsolved Problems in Mathematics Mersenne Primes One unsolved problem in mathematics concerns whether or not there are infinitely many Mersenne primes. In order to understand… read more
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How Every Dimensions Actually Work (You Probably Didn’t Know)
Every Dimension Explained Zero Dimension (0D) One Dimension (1D) Second Dimension (2D) Third Dimension (3D) Fourth Dimension (4D Spacetime) Higher Dimensions in Mathematics Functional and Infinite Dimensions Fractals and Fractional Dimensions Curved and Warped Dimensions Applications and Modern Theories Every Dimension Explained Zero Dimension (0D) Zero dimension corresponds to the point, defined since antiquity as… read more
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