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Why Ellipses Are Not Elliptic Curves

by Adrian Rice and Ezra Brown

Year of Award:2013


Publication Information: Mathematics Magazine, vol. 85, 2012, pp. 163-176

Summary: (Adapted from the MathFest 2013 Prizes and Awards Booklet) This article explores where the related names came from, despite the core differences in these two famous mathematical objects. The authors begin with a brief history of ellipses, starting in Ancient Greece and ending with Jacobi and Eisenstein working with the doubly periodic properties of elliptic functions. The authors then trace elliptic curves from Ancient Greece to Fermat and Newton and return to Eisenstein to connect the two concepts.

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About the Author: (From the MathFest 2013 Prizes and Awards Booklet)

Ezra (Bud) Brown grew up in New Orleans, has degrees from Rice and Louisiana State University, and has been at Virginia Tech since 1969, where he is currently Alumni Distinguished Professor of Mathematics. His research interests include number theory and combinatorics, and elliptic curves have fascinated him for a long time. He particularly enjoys discovering connections between apparently unrelated areas of mathematics and working with students who are engaged in research. He has been a frequent contributor to the MAA journals, and he recently served a term as the MD/DCNA Section Governor. In his spare time, Bud enjoys singing (from opera to rock and roll), playing jazz piano, and solving word puzzles. Under the direction of his wife Jo, he has become a fairly tolerable gardener, and the two of them enjoy kayaking. He occasionally bakes biscuits for his students, and he once won a karaoke contest.

Adrian Rice received a B.Sc. in mathematics from University College London in 1992 and a Ph.D. in the history of mathematics from Middlesex University in 1997 for a dissertation on Augustus De Morgan. He is currently a Professor of Mathematics at Randolph-Macon College in Ashland, Virginia. His research focuses on nineteenth- and early twentieth-century mathematics, on which he has published research papers, articles and books, including Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800-1945, edited with Karen Hunger Parshall, The London Mathematical Society Book of Presidents, 1865-1965, written with Susan Oakes and Alan Pears, and Mathematics in Victorian Britain, edited with Raymond Flood and Robin Wilson. In his spare time, he enjoys reading, travel, and spending time with his wife and young son.

Subject classification(s): Algebra and Number Theory | Algebra | Geometry and Topology | Algebraic Geometry
Publication Date: 
Sunday, August 18, 2013