Many consider mathematics to both a science - in the sense that it seeks truth - and an art -- in the sense that it seeks beauty. We'll talk with a mathematician about what makes something beautiful in mathematics - after this on Earth and Sky.
DB: This is Earth and Sky, on beauty in mathematics. The bedrock of mathematics is the proof - the logical argument that something is or is not true. But often there are many ways to prove the same thing, and mathematicians tend to choose what they see as the most "beautiful" solution. We asked Dr. Hendrik Lenstra, a mathematician at the University of California at Berkeley, about what makes something beautiful in mathematics:
(Tape 0:09:04-0:09:52) What makes something beautiful in mathematics is not very different from what makes things beautiful in other branches of human pursuit. It is sort of a sense of economy, a sense of harmony, the idea that things go together well. If you construct a proof, then you want the proof to be not too long. You want the proof to be sort of natural, you like that it flows in the way, that well, the water goes, you know, in a little river perhaps. But then what can also be beautiful is exactly the other way around - when suddenly there happens something completely unexpected.(Tape 0:11:13-0:11:20) Beautiful proofs, well, maybe it is in the eyes of the beholder.
DB: Thanks to Dr. Hendrik Lenstra for speaking with us. And with thanks to the National Science Foundation, I'm Deborah Byrd, for Joel Block, for Earth and Sky.
Author: Beverly Wachtel
Thanks to the following individual for aiding in the preparation of this script:
Dr. Hendrik Lenstra
Department of Mathematics
University of California
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