Taxicabs and Sums of Two Cubes: An Excursion in Mathematics
Professor Joseph H. Silverman
Brown University
Some numbers, such as
9 = 13 + 23 and 370 = 33 + 73,
can be written as a sum of two cubes. Are there numbers that can be written as a sum of two cubes in two (or more) essentially different ways? This elementary question will lead us into beautiful areas of mathematics where number theory, geometry, algebra, calculus, and even internet security, interact in surprising ways. The talk will be accessible to undergraduates at all levels.
Dr. Joseph H. Silverman is Royce Professor of Mathematics at Brown University and a leading expert in the theory of elliptic curves. He received his Ph.D. at Harvard University in 1982 and has authored eight books and more than 100 research articles. Among his honors are Sloan and Guggenheim fellowships, a Steele Prize for Mathematical Exposition from the American Mathematical Society (AMS), a Distinguished Teaching Award from the Mathematical Association of America, and being named a Fellow of the AMS. Professor Silverman is also an active researcher in cryptography and a co-inventor of the NTRU cryptosystem. He has supervised 31 Ph.D. students and is an avid teacher and mathematics education advocate.
