Unsolved Math Problems

This is a nice list of famous unsolved math problems from Wolfram MathWorld:


There are some well-known problems here, like the Goldbach Conjecture and the Collatz Conjecture, and some lesser-known open problems like finding an Euler Brick with an integral space diagonal.

It’s especially nice that several of these challenges are easy to explain to non-mathematicians.  For example, the Goldbach Conjecture asks “Can every even number be written as the sum of two prime numbers?”  Somewhat surprisingly, after nearly 300 years, the best answer we have is probably.

I think I’ll make this page next year’s summer homework assignment.

BBC Podcasts: A Brief History of Mathematics

This is a set of ten podcasts from the BBC titled “A Brief History of Mathematics“:


Narrated by mathematician Marcus du Sautoy, these podcasts begin with Newton, Leibniz, and Calculus, and cover other great personalities in mathematics like Euler, Fourier, Ramanujan, Poincare, and, of course, Gauss.

Each podcast is about 15 minutes in length, and all 10 are freely available for download.

Interviews with Benoit Mandelbrot

This is a collection of interview clips with mathematician Benoit Mandelbrot.


The interview is broken up into different topics like the Hausdorff Dimension, economics and mathematics, fixed points, and the birth of fractals.  In addition, Mandelbrot talks about his personal, academic, and professional life.  It’s an interesting window into a profoundly important person.

The website WebOfStories.com also offers clips of interviews of other scientists, like phsicists Murrary Gell-Mann and Freeman Dyson and Biologist Francis Crick.

Portrait of John Conway

This is a short and engaging portrait of John Conway, one of the world’s most recognized mathematicians.


Conway is decidedly eccentric, which is not uncommon in the world of mathematics.  He loves magic, juggling, and games, and has something of a a reputation as an odd chap.   But his mathematical contributions are numerous and substantial:  Conway’s Game of Life in and of itself is a remarkable mathematical construction, but he is also credited with inventing (or discovering?) surreal numbers.  Conway has also contributed to the theory of sphere packing.

The article above, from the Daily Princetonian, is a quick and lively read, a fun portrait of a brilliant and curious man.

Fermat’s Last Theorem Documentary

This is an engaging, accessible, and surprisingly moving documentary about Andrew Wiles and his lifelong pursuit of Fermat’s Last Theorem:


Although the mathematics of the proof could not possibly be explained to the layperson (there aren’t many people in the world who could really understand it in its entirety), this BBC documentary does a great job of narrating the struggles, setbacks, and triumphs of Wiles’ pursuit.

The story of the hero and the many peripheral characters (including John Conway) opens a wonderful window into the world of advanced mathematics.


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