I was reminded the other day that one of the main reasons I decided to commit to a math major was also a book! One of my friends let me borrow Fermat’s Last Theorem, a book about the history behind the proof to the following statement made by Fermat (as stated on Wikipedia):

“If an integer n is greater than 2, then the equation aⁿ + bⁿ = cⁿ has no solutions in non-zero integers a, b, and c.”

So basically, when n = 2, we have all the Pythagorean triplets such as 3-4-5 and 5-12-13, but for n > 2, there exist no such triplets for which the equation works out. It seems deceptively simple to show, but the proof took centuries of mathematicians and many advances in the field of mathematics itself before it was proved that the theorem is true.

It was fascinating to me that this problem was simple enough to be understood by anyone who had taken pre-Algebra, but that the solution had stumped many of the greatest minds throughout history. And when I say the solution stumped them, I don’t mean that there isn’t an answer, because it was found 357 years after the problem was posed by a Princeton mathematician, Andrew Wiles, in 1995.

The book (and a documentary by the same name) goes through the history of the theorem and the stories of the mathematicians who tried to solve it. It inspired me to pursue the field because there is a sort of magic and beauty to how mathematics works. Math is a product of the human mind but can be manifested in many practical applications. Each field of it ties into other fields in unexpected ways, giving one the suspicion that there really does exist an underlying structure to the universe. The journey to solving the math problem is far more cumbersome than the answer itself, many times the answer seems obvious once stated, but the proof of it may take weeks to understand. It is this sort of feeling that answers to complicated problems exist out there and that man can figure them out that convinced me I wanted to study the field.

Some other interesting “get you excited about math” books I’ve found since then include (in increasing order of mathematical sophistication):

• A Mathematician Reads the Newspaper
• One, Two, Three… Infinity
• Journey Through Genius: The Great Theorems of Mathematics
• Euclidean and Non-Euclidean Geometry: Development and History
• All the Mathematics You Missed: But Need to Know for Graduate School

I recommend them all, especially for the “armchair mathematician.” I figure, why bother doing Sudoku puzzles as you grow older when you can just learn new maths?