No, Riemann Hypothesis has NOT been solved, yet!
Every few years, someone claims to have solved the Riemann Hypothesis. And every time, the mathematical community debunks it quickly.…
Real Analysis
10 Best Real Analysis Books for Math Majors
Real analysis is the rigorous foundation of calculus that math majors either love or dread. The right textbook makes the…
15 Best Measure Theory Books for Undergraduate and Graduate Students
Measure theory is the mathematical foundation of probability, integration, and functional analysis. Finding the right textbook matters enormously because bad…
Real Sequences: Definitions, Theorems, and Examples
Real sequences form the backbone of real analysis and advanced calculus. I've taught this topic to dozens of students, and…
Irrational Numbers and The Proofs of their Irrationality
How do you prove a number is irrational? You can't check infinitely many decimal places. You need a proof. I…
The Area of a Disk
The area of a disk is pi times radius squared. You memorized this in middle school. But do you know…
Triangle Inequality
The triangle inequality sounds obvious. No side of a triangle can be longer than the other two sides combined. But…
Russian Peasant Multiplication: The Ancient Method That Uses Only Doubling and Halving
Russian Peasant Multiplication is an ancient technique that multiplies any two numbers using only doubling and halving. No multiplication tables…
Everywhere Continuous, Nowhere Differentiable: The Weierstrass Function and Why It Matters
In 1872, Weierstrass presented a function that's continuous everywhere but differentiable nowhere. It shattered the assumption that smooth curves are…
Dedekind’s Theory of Real Numbers
Most math students use real numbers without ever understanding how they're constructed. Dedekind solved this with his theory of cuts.…
D’Alembert’s Ratio Test for Convergence of Series
The D'Alembert Ratio Test is one of the most reliable tools for determining whether an infinite series converges or diverges.…
Derivative of x squared is 2x or x ? Where is the fallacy?
Here's a mathematical fallacy that trips up even sharp students. Can you prove that the derivative of x squared is…