Monthly Archives: September 2013

Andrew Wiles and Fermat’s Last Theorem

In 1995, Andrew Wiles proved Fermat’s Last Theorem, a problem that had stumped mathematicians for over 350 years.

WilesFermat

Andrew Wiles (Left) and Pierre de Fermat (Right)

Never heard of Fermat’s Last Theorem? Well, to explain, let’s start with the Pythagorean Theorem. As you may know, the Pythagorean Theorem states that for right angle triangles, a2+b2=c2, where c  is the length of the hypotenuse, and a and b are the lengths of the other 2 sides. We know that there are a number of positive whole number solutions to the Pythagorean Theorem: 3, 4, and 5; 6, 8, and 10; etc.

In 1637, Pierre de Fermat, a French lawyer and amateur mathematician, conjectured that there are no positive whole number solutions for an+bn=cn for values of n>2. So, in other words, there are no positive whole number solutions for a3+b3=c3, or a4+b4=c4, etc. He claimed to have a proof, but did not have room in the margin of the book (Arithmetica) where he wrote this conjecture. For over 350 years, mathematicians tried to discover Fermat’s proof but were unsuccessful. Wiles finally proved the theorem, but he used some modern techniques that would have been unknown to Fermat, which makes ones wonder if Fermat had some other simpler proof that has yet to be discovered.

If you are interested in learning more about Fermat’s Last Theorem, there is a great book and a documentary (both by Simon Singh) that you should check out.

fermats-enigma

The book, Fermat’s Enigma, provides a detailed and interesting account of Andrew Wiles quest to solve Fermat’s Last Theorem, including explanations of the math appropriate for non-mathematicians. Singh gives us the entire story of Fermat’s Last Theorem starting from Fermat himself and covering the mathematicians along the way that attempted to solve the proof or provided important breakthroughs used by Wiles in his successful proof. Simon Singh wrote the book after producing a documentary about Wiles’ journey for the BBC. The documentary, Fermat’s Last Theorem does not provide as much detail, or course, but I love how, through the interviews with Wiles, you really get a sense of how much of himself he pored into this problem. This problem, which he first learned about from a library book at the age of 10, truly was his life’s work. You can hear the emotion in his voice when he describes how important it was to him and how he felt when he finally completed the proof. The documentary was also produced in the U.S. as The Proof by NOVA, but it isn’t available online. You can see the BBC version in full on YouTube (embedded below).

How to Fall in Love with Math

 

Manil Suri, a mathematics professor at the University of Maryland, had a great op-ed in the New York Times this past weekend called How to Fall in Love with Math. Suri argues that even those of us without advanced knowledge of math can appreciate its power and beauty. He writes:

Despite what most people suppose, many profound mathematical ideas don’t require advanced skills to appreciate. One can develop a fairly good understanding of the power and elegance of calculus, say, without actually being able to use it to solve scientific or engineering problems.

Think of it this way: you can appreciate art without acquiring the ability to paint, or enjoy a symphony without being able to read music. Math also deserves to be enjoyed for its own sake, without being constantly subjected to the question, “When will I use this?”

I highly recommend heading over to read the whole piece.

Math: What is it good for?

A new school year has begun, and soon I will have a new group of after-school math club students. At the first session, I always like to just talk to the kids about why math is important, in terms of future careers, as well as, in everyday life. After all, few are going to grow up to be mathematicians, so why do they need all this math anyway?

I start by asking them to think of ways they or the grown-ups in their family use math:

  • Dividing something to share,
  • Dealing with money – shopping, tipping, budgeting
  • Art and craft projects (measuring, buying the right amount of supplies),
  • Home improvement projects,
  • Time management

Next, we think about some of the careers that use math:

  • Scientists and engineers
  • Computer programmers
  • Medical professionals (doctors, nurses, technicians),
  • Designers
  • Contractors and landscapers
  • Bankers, accountants, and other finance professionals
  • Anyone who owns a business – budgets and accounting

This year, I plan to also show them how math is important in lots of fields and shows up often in scientific articles. Here are just a few recent headlines:

In the past, I have finished off the lesson, by showing this video about designing the Mars Curiosity Lander. Lots of math and WAY COOL!

This year, I plan to show this great video about why math is cool and interesting and important for many kinds of careers.