From the Pythagorean Theorem to a $1,000,000 prize

Theme:

Mathematics

Content:

One of the oldest mathematical results we have as humans is the Pythagorean Theorem relating the lengths of the sides of a right triangle.  In this presentation, we give a short proof of the Pythagorean Theorem and then explore some generalizations, leading to the statement of Beal's Conjecture, the solution of which is worth $1,000,000.

Why this is important?

We tend to think of mathematics as an area of human knowledge in which everything is already known, but this is far from the truth.  By passing from the well known (in this case the Pythagorean Theorem) to the unknown (in this case Beal's Conjecture) in a few short minutes, I hope to inspire students to think of mathematics as the wide open frontier that it is. Perhaps it will inspire someone to prove Beal's Conjecture, just as a talk he heard as a young student inspired Andrew Wiles to prove Fermat's Last Theorem.

Key descriptors:

mathematics, Pythagorean Theorem

Suggested age range:

14-18

Speaker:

Professor James W. Anderson