## Unsolved Math Problems

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

http://mathworld.wolfram.com/UnsolvedProblems.html

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.

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## BBC Podcasts: A Brief History of Mathematics

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

http://www.bbc.co.uk/podcasts/series/maths

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.

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## 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.

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## Portrait of John Conway

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

http://www.dailyprincetonian.com/2012/03/01/30161/

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.

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## 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**:

http://video.google.com/videoplay?docid=8269328330690408516

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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## The Euler Archive

This is a great on-line resource hosted by the Math Department at **Dartmouth University**: a comprehensive collection of the works of (and about) **Leonhard Euler**.

http://www.math.dartmouth.edu/~euler/

Euler, indisputably one of the greatest mathematicians in history, authored over 800 papers in his lifetime, touching on every area of mathematics then in existence. In addition, Euler made significant contributions to physics, astronomy, and applied sciences as well.

The archive features historical and biographical information, related resources, and digital copies of over 800 original documents.

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## Biographies of Female Mathematicians

This is another nice resource provided by the School of Math and Statistics at the University of St. Andrews, Scotland: a collection of biographies of female mathematicians.

http://www-history.mcs.st-and.ac.uk/Indexes/Women.html

There are around 150 mathematicians profiled here. Each profile consists of a biography, a list of references, and links to other internet resources on the individual.

Among those profiled here are Maria Agnesi (of the **Witch of Agnesi** cubic curve), Emmy Noether (of **Noetherian Ring **fame), and Mary Ellen Rudin (topologist, and wife of Walter Rudin, a noted figure in Real Analysis).

A general collection of biographies is also available, as well as a fun-to-browse library of curves.

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