The Best Math YouTube Videos

1 ~ A Beautiful Mind: The Documentary of John Nash

The Hollywood version of the movie A Beautiful Mind is entertaining, but this documentary shows you a more accurate and detailed version of the story of brilliant mathematician and Nobel Laureate John Nash. 

2 ~ Fields Medalist Cédric Villani - TED Lecture

The charismatic French mathematician Cédric Villani gives a short tour of what it means to be a mathematician in the general sense of the word and also more specifically in the context of his own story of researching entropy and the Boltzmann equation.  

3 ~ BBC: The Epic Story of Fermat's Last Theorem

The full BBC program on the story behind the famous proof of the 350 year old problem of Fermat's Last Theorem.  After centuries of mathematical build-up by dozens of mathematicians and decades of work by Andrew Wiles, the theorem was finally confirmed to be proven in 1994. 

This dramatic story is told in greater detail in Simon Singh's bestselling book, Fermat's Enigma.

4 ~ What is the Poincare Conjecture?

In the year 2000, the Clay Mathematics Institute posted a $1 million dollar prize for anyone who could solve any of the seven fiendishly difficult & unsolved "Millennium Prize Problems."  

CMI created the Millennium Prize Problems in order to encourage more mathematicians to work on these seven special problems, which come scattered from across a wide range of fields of mathematics. 

These problems are considered deep and important since their proofs are expected to contain a lot of newly-invented mathematical tools which will spur on all sorts of new research directions.  In fact, the years of attempts at these problems have already generated piles of new research that contain valuable results, independent of the progress toward the bigger Millennium Prize Problem.

In 2002 and 2003, a Russian mathematician working alone quietly posted his impressively original solution to one of the problems, the Poincare Conjecture.  After several years of deliberation, the mathematics community has carefully combed through the new mathematics in the proof and concluded that the first of the seven problems really has been solved.

This YouTube video shows a short, funny, analogy-based explanation of the solved Poincare Conjecture and the reclusive mathematician who cracked it.

5 ~ Terry Tao's UCLA Lecture on Structure & Randomness in Prime Numbers (for general audiences)

Child prodigies in mathematics may be pretty rare, but Terence Tao is the rarest kind: his talent has been long-lasting and he has a generous and personable character, to say the least. 

Tao has moved well beyond his early precocious years in Australia (at age 8 he earned a 760 on the math section of the SAT!) to become a world class mathematician who has worked at UCLA since earning a full professorship at the unbelievably young age of 24.

Even more incredible might be his ability to remain widely liked and respected as a kind and modest mathematician despite having earned almost all of the highest awards and prizes mathematics has to offer.

He is also unusual in being a prolific math writer of everything from essays of general interest to graduate level textbooks to incredibly heady research papers in any of the four math research areas that captures his wide-ranging interest.

His blog is very well-trafficked (deservedly so), and he has compiled chunks of his blog into published books here and here.

This video features a full-length talk Tao gave at UCLA.  It is aimed at those with no background in prime numbers, and it features a wide-ranging introductory look at some of the surprising secrets hidden in the subtle patterns of the prime numbers.

6 ~ How to Turn a Sphere Inside-Out

Mathematicians have proven the startling fact that a hollow sphere (like a beach ball) can be turned inside out without tearing or puncturing it (but while allowing it to intersect itself.) 

This video is a stunningly-animated and well narrated two-part guide for the non-mathematician and it gives a bird's eye view of how this strange fact could possibly be true.

7 ~ Möbius Transformations Revealed

Möbius transformations are a sophisticated type of transformation in the complex plane.  Nonetheless, experts and non-experts alike will appreciate this stunning visualization of the basic effect this advanced tool has on distorting space.