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number theory
Riemann Hypothesis: The Conjecture That Controls Prime Numbers
The Riemann hypothesis claims all nontrivial zeros of the zeta function lie on a single line. If true, it pins down exactly how...
Mersenne Primes: The Largest Primes Ever Found
A Mersenne prime is a prime number of the form 2^n - 1, where n is itself prime. Only 52 are known. Learn...
Langlands Program: Mathematics' Bridge Between Worlds
The Langlands program connects number theory and representation theory, proposing that prime numbers and symmetry share deep, hidden structures.
Prime Numbers: Definition, Properties, and Why They Matter
A prime number is a natural number greater than 1 whose only factors are 1 and itself. Primes are the atoms of arithmetic.
Fermat's Last Theorem: The 358-Year Proof
Fermat's Last Theorem states that no three positive integers can satisfy a^n + b^n = c^n for any integer n greater than 2....
Fibonacci Numbers: Nature's Hidden Sequence
Fibonacci numbers are integers where each equals the sum of the two before it. The pattern links pure mathematics to nature.
Composite Numbers: The Building Blocks of Arithmetic
A composite number is a positive integer greater than 1 that can be divided evenly by at least one number other than 1...
The Prime Number Proof That Borrowed From the Wrong Field
Ben Green and Mehtaab Sawhney proved infinitely many primes fit p² + 4q² by importing Gowers norms from combinatorics - a tool nobody...
Unsolved Math Problems That Sound Deceptively Easy
Unsolved math problems from the Collatz conjecture to twin primes sound simple enough for grade school. No mathematician alive can solve them.
