Physicists Vote on 'Most Beautiful Equations of All Time'

illusion by donguriko

http://www.ritsumei.ac.jp/~akitaoka/donguriko.gif

Physics and mathematics periodicals frequently hold polls  for readers to vote on the equation they most admire. The results hold fairly stable from poll to poll. Here are some excerpts about these results:

“Some were nominated for the sheer beauty of their simplicity, some for the breadth of knowledge they capture, others for historical importance.

“The top vote-getters in the magazine poll were Maxwell's equations - a set of four that describe the interplay between electric and magnetic fields - and Euler's equation, a purely mathematical construct that finds wide use in theoretical physics" ["in a dead heat" the poll said]."Among the other nominees were the all-familiar E=mc2 from Einstein, which equates energy and matter; the Pythagorean theorem; and Isaac Newton's F=ma.

“Dr. Brian Greene, a theorist at Columbia University and author of ‘The Elegant Universe,’ cites Einstein's general relativity equations, which describe how matter warps the fabric of space, and the Schrödinger equation, the fundamental equation of quantum mechanics.

"’With a mere handful of symbols, those equations describe almost all phenomena in the universe,’ he said.

“Dr. Neil deGrasse Tyson, director of the Hayden Planetarium, said he was disappointed that E=mc2 did not receive more votes. ‘I think the general physics community, they're a little bored with the equation,’ he said.

“A half-dozen of Dr. Crease's respondents, including Richard Harrison of Calgary, Alberta, chose one of the simplest possible equations:

“Mr. Harrison wrote: ‘ '1 + 1 = 2' is the fairy tale of mathematics. . .’ ”

Leonhard Eulerby Emanuel Handmann 1756?

I found in my reading that it is probably Euler's Identity formula that stirs the imaginations of mathematicians the most: 

"[Euler's equation] combines rational and irrational numbers to get zero," Dr. Crease said. "It's bizarre." 

". . . called 'the most remarkable formula in mathematics' by Richard Feynman, for its single uses of the notions of addition, multiplication, exponentiation, and equality, and the single uses of the important constants 0, 1, e, i and π. 

" After proving Euler's Identity during a lecture, Benjamin Peirce, a noted American 19th Century philosopher/mathematician and a professor at Harvard University, stated that ‘It is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth.’ "

* * * *

also from New York Times:

by George Johnson

Published: September 24, 2002

Here They Are, Science's 10 Most Beautiful Experiments

Note: this poll is for experiments, not equations

Here’s the list of ten

This website includes ANIMATED ICONS to explain each experiment:

http://physics-animations.com/Physics/English/top10.htm

* * *

I thought I would tackle by what term to call these: the difference between an equation and a theorem; in my understanding, an equation is based on experience, a theorem on reasoning; and somewhere, a formulafits into this. But I saw that even some mathematicians found the borderline vague; that lets me off the hook.

THIS IS NOT ONE SMOOTH DIRECT QUOTE, BUT A COMBINATION INTERWEAVING THE FOLLOWING THREE SOURCES:

from NYT: 

2004:   http://www.nytimes.com/2004/10/24/weekinreview/24chan.html

2002:  http://query.nytimes.com/gst/fullpage.html?res=9D06E6D91439F937A1575AC0A9649C8B63

fr Wikipedia:  http://en.wikipedia.org/wiki/Euler's_identity and other Euler entries.