Category: Number Theory
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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. read more
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Every Proof That There Are Infinitely Many Primes Explained
What Is a Prime Number? Euclid’s Proof Factorial Proof Erdős’s Proof What Is a Prime Number? Think of a natural number. That is, a number used for counting, like six. Next, think of another natural number, like two. If we calculate 6 / 2, the result is 3. Since 3 is read more
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Every Equation That Changed History Explained
Timeline of Equations That Changed the World 6th Century BC: Thales’ Theorem 6th Century BC: Pythagorean Theorem 300 BC: Euclid’s Theorem 250 BC: Archimedes’ Principle of Flotation 200 BC: Conic Sections First Century AD: Heron’s Formula 1202: Fibonacci Sequence 1609: Kepler’s Laws of Planetary Motion 1614: Logarithms 1637: Cartesian Plane 1637: read more
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Every Unsolved Problem in Discrete Mathematics that sounds Easy
The Riemann Hypothesis The Navier-Stokes Problem The P versus NP Problem The Collatz Conjecture The Goldbach Conjecture The Riemann Hypothesis The Riemann hypothesis is one of the unsolved cornerstones of analytic number theory. Formulated by Bernhard Riemann in 1859, it states that all non-trivial zeros of the Riemann zeta function, denoted read more
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Every Proof that √2 is Irrational but they get increasingly more complex (pt. 2)
Continued Fractions Tennenbaum’s Proof Rational Root Theorem Applying the Rational Root Theorem to √2 Continued Fractions A continued fraction is one possible way to represent a number, consisting of a collection of nested fractions. Here we will focus on the case where the numerators of the fractions are all equal read more
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Every Unsolved Math Problem Solved
The Poincaré Conjecture Trisecting an Angle The Classification of Finite Simple Groups The Four Color Theorem The Continuum Hypothesis Fermat’s Last Theorem Gödel’s Incompleteness Theorems The Prime Number Theorem Solving Polynomials by Radicals The Poincaré Conjecture Henri Poincaré. Public domain, via Wikimedia Commons In 2000, the Clay Mathematics Institute, a nonprofit read more
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Every Dark Scandal in Math
The Murder of Hypatia The Nobel Affair The Burning of the Library of Alexandria The MIT Card Counters in Las Vegas The Air Force Cheating Scandal André Bloch’s Murders P versus NP Alan Turing Newton and Leibniz’s Calculus Wars The Drowning of Hippasus Galois’s Duel and Death The Eudaemons Cardano versus read more
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Every Unsolved Math problem that sounds Easy
The Kissing Number Problem The Goldbach Conjecture The Collatz Conjecture The Twin Prime Conjecture The Unknotting Problem The Enigma of π + e The Birch and Swinnerton-Dyer Conjecture The Riemann Hypothesis The Lonely Runner Conjecture Is γ Rational? The Kissing Number Problem A broad category of problems in math are called read more
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Why Catalan’s Constant Still Puzzles Mathematicians
Catalan’s constant is a well-known mathematical constant defined by the infinite series: It is named after the Belgian mathematician Eugène Charles Catalan, who first gave an equivalent series and expressions in terms of integrals for this constant. Where Does Catalan’s Constant Appear? Is Catalan’s Constant Rational or Irrational? Computing Catalan’s Constant read more
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the Irrational Apéry’s Constant Explained
Apéry’s Constant Overview The Riemann Zeta Function Significance Irrationality Apéry’s Constant Overview Apéry’s constant is the value of the Riemann zeta function evaluated at the argument 3. It has an approximate value of 1.202. The Riemann Zeta Function The Riemann zeta function, denoted by ζ(s), is a function of a complex read more
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