Prime Numbers
Erdős’ Proof of the Infinitude of Primes
Let’s take a look at an unusual proof that there are infinitely many prime numbers.
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Calculus
Let’s Derive the Power Rule from Scratch!
From nothing but the definitions of derivatives and exponentiation, we’ll prove one of the first derivative rules you’ll learn in college
Complex Analysis
There is no such thing as √-1
What are complex numbers, after all?
Probability Theory
Probabilities: One Problem, Two Answers.
Why probabilities can sometimes be confusing.
Fractal
Fractal Geometry
From Gaston Julia to Benoit Mandelbrot
Classical Mechanics
A Geometric Intuition for Energy Conservation
In a sense, Conservation of Energy is just Conservation of Area.
Cognition
The Psychology Behind Mathematical Thinking
The mystery behind how our human mind works
Analysis
The Link Between Hypothesis Testing and Proof by Contradiction
Hypothesis testing has some similarities with one of the simplest methods of proof from mathematical logic: Proof by contradiction…
Infinity
Hilbert’s Hotel: You’re Missing the Best Bit!
Infinity, enumerating the rationals and elegant solutions to innocuous problems.
Arithmetic
The Fundamental Theorem of Arithmetic
Over 2,300 years ago Euclid proved the Fundamental Theorem of Arithmetic. Now it is our turn.
Physics
Approaches to Solving Problems in Physics
Becoming a master at physics requires a lot of work, but learning the techniques and guidelines in this article is taking the first step.
Philosophy
Why Mathematics Isn’t Much Different From Religion
Exploring faith