Finding the Vertex and Range (Live Examples)

Two from Turkey

what a great geometry problem!

any rational power of e is irrational!

Average Rate of Change with an Arbitrary Endpoint (Live Example)

e^pi versus pi^e -- the classic math youtube problem revisited

a nice Ramanujan sum

Interval Notation Explained from Start to Finish (Live Example)

the classic square root of 2 paradox

is this system of Diophantine equations solvable??

which regular n-gons can be formed in a lattice??

using wishful thinking to solve a differential equation

the gnarliest integral on the channel in a long time....

the first proof of the irrationality of pi!

A Complete Explanation of Hausdorff Spaces | Live Example

a nice and quick geometry problem

the best proof of the divergence of the harmonic series

2025 Putnam Exam -- Problem B1

hands down the best way to prove the sum of squares formula

infinitely many formulas for pi

the nicest proof of the Pythagorean Theorem

the most exciting number base

When Does a Function Have an Inverse? (Full Explanation + Examples)

an integral with my favorite function and a nice hidden identity

This One Example Explains Unions Better Than Any Textbook

Evaluating the viral ATM integral

how often is this integral a rational number

An identity with my favorite numbers.

What’s Inside the Symmetries of a Hexagon?

an integral infinitely nested radical

a surprisingly interesting equation

2025 AMC 12B -- All problems and solutions!!

The Identity That Shocked the World’s Best Mathematician

A Simple Trick to Prove an Equation Has No Integer Solutions - Live Example

All problems and solutions to the 2025 AMC 10A

Subgroups of Order 4 in the Alternating Group - Live Example

what an amazing approach to this crazy looking infinite series!!

Mersenne primes doubly like powers of 2.

A problem from the Asia-Pacific Math Olympiad.

Understanding GCD Properties Through Proofs - Live Example

how to count "cycled" permutations -- Stirling Numbers.

How often (Gaussian) integers are relatively prime

You’ll Never Forget Direct Proofs After Seeing This | Live Example

why only some infinite power towers are well defined.

longlisted for the IMO

How to Prove a Relation Checks All Three Boxes: Reflexive, Symmetric, Transitive - Live Breakdown

The Rogers-Ramanujan Identities

a nice technical integral

The Foundation of Pascal’s Triangle | Live Breakdown

a recursive limit problem

How many ways can we write n as the sum of two squares??

Understanding Leibniz’s Rule | Live Lecture

a completely average number theory contest problem

in a Ramanujan letter to Hardy

How to Prove Something Is a Subgroup (Step by Step)

A space where nothing is prime

How to Find All Homomorphisms from Z20 to Z12 - Live Explanation

the easiest and hardest math contest problems

how is the Pythagorean theorem related to the number of subsets??

pythagn 4K