Number Theory
Faltings’s Theorem and the Mordell Conjecture
On the number of rational solutions to polynomials.
Number Theory
Prime Numbers
The Twin Prime Conjecture
Are there infinitely many primes p such that p + 2 is prime?
Prime Numbers
The Infinity of Primes
We present two proofs of one of the great theorems in number theory, namely that there are infinitely many primes.
Number Theory
How to Prove That e is Irrational
Two Simple Proofs of the Irrationality of e
Number Theory
A Formula For Fibonacci Sequence
Fibonacci numbers are one of the most captivating things in mathematics. They hold a special place in almost every mathematician’s heart…
Number Theory
The Invention Of Zero
Assigning Value To The Concept Of Nothing
Number Theory
Proving The Existence of Transcendental Numbers
… and how to compare the infinite?
Number Theory
The History of Euler’s Number (e)
From Napier Table’s To Bernoulli’s Compounding Interest
Mathematics
Unexpected Beauty in Primes
The Visualization of Primes & Its Potential Significance
Ramanujan
The Hardy-Ramanujan Number
The two different ways 1729 is expressible as the sum of two cubes are 1³ + 12³ and 9³ + 10³. The number has since become known as the Hardy-Ramanujan number, the second so-called “taxicab number”
Mathematics
Fermat's Little Theorem
Understanding Pierre de Fermat’s observation about prime numbers
Mathematics
The Prime Numbers Cross: Hint of a Deeper Pattern?
I have always been fascinated with “origins”: the origin of life on Earth, the origin of human beings, the origin of the Universe, and of…