“Everything should be made as simple as possible, but no simpler.”

- Albert Einstein


It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.
  • "On the Method of Theoretical Physics" The Herbert Spencer Lecture, delivered at Oxford (10 June 1933); also published in Philosophy of Science, Vol. 1, No. 2 (April 1934), pp. 163-169., p. 165. [thanks to Dr. Techie @ www.wordorigins.org and JSTOR]
  • There is a quote attributed to Einstein that may have arisen as a paraphrase of the above quote, commonly given as “Everything should be made as simple as possible, but no simpler.” or “Make things as simple as possible, but not simpler.” See this article from the Quote Investigator for a discussion of where these later variants may have arisen.


An elegant solution is one that is as simple as possible.




Elegant



el·e·gant   [el-i-guhnt]
adjective
1.tastefully fine or luxurious in dress, style, design, etc.: elegant furnishings.
2.gracefully refined and dignified, as in tastes, habits, or literary style: an elegant young gentleman; an elegant prosodist.
3.graceful in form or movement: an elegant wave of the hand.
4.appropriate to refined taste: a man devoted to elegant pursuits.
5. excellent; fine; superior: an absolutely elegant wine.


Origin:
1400–50; late Middle English (< Middle French ) < Latin ēlegant- (stem of ēlegāns ) tasteful, choice, equivalent to ēleg- (akin to ēlig- select; see elect) + -ant- -ant; orig. present participle of lost v.

Related forms
el·e·gant·ly, adverb
hy·per·el·e·gant, adjective
hy·per·el·e·gant·ly, adverb
o·ver·el·e·gant, adjective
o·ver·el·e·gant·ly, adverb
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Can be confused:  elegant, eloquent (see synonym note at eloquent).

Synonyms
1. See fine. 2. polished, courtly.


Elegance in Math

I'm a huge fan of Tom Lehrer and have mentioned him a number of times before. I just came across an interview with him from 2000 in which he discussed his dual life as a mathematician and performer. I especially loved this quote, on the concept of "elegance" in mathematics:
I think the construction part, the math, how to say it, the logical mind, the precision, is the same that's involved in math as in lyrics.... And I guess in music too. It's gotta come out right. It's like a puzzle, to write a song. The idea of fitting all the pieces so it exactly comes right, the right word at the end of the sentence, and the rhyme goes there and not there. Mathematicians, as opposed to natural scientists, are so interested in elegance. That's the word you hear in mathematics all the time. "This proof is elegant!" It doesn't really matter what it proves. "Look at this -- isn't that amazing!" And it comes out at the end. It's neat. It's not just that it's proof, because there's plenty of proofs that are just boring proofs. But every now and then there's a really elegant proof.
I have tried many times to capture and define the euphoria of achieving some kind of mathematical beauty or elegance -- almost always in vain. Erdos said it well:
Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you.

  1. Mathematical beauty - Wikipedia, the free encyclopedia



    en.wikipedia.org/wiki/Mathematical_beauty
    This article is in the category Elementary mathematics, but no reliable sources ... Mathematicians describe an especially pleasing method of proof as elegant.

  2. Beauty in method - Beauty in results - Beauty in experience
  3. Most Elegant Math Equations Ever - Science Forums



    www.scienceforums.net/.../31453-most-elegant-math-equations-ever/
    19 posts - 13 authors - Jul 12, 2008
    In your opinion, what equations, solutions, or sets are the most elegant math equations ever solved or conceived of? Personally, I like Euler's ...
  1. In math, "elegant" means "cool"!



    www.learnnc.org/lp/pages/784
    An elegant solution to a math problem is one that requires less time and work. Encouraging students to find such solutions will help them build number sense or ...
  1. Elegance



    www.thisisthegreenroom.com/2011/elegance/
    Elegance. September 19, 2011 in Math,Quotes. I'm a huge fan of Tom Lehrer and have mentioned him a number of times before. I just came across an interview ...
  1. That long thread about elegant math



    www.physicsforums.com › PF LoungeGeneral Discussion
    5 posts - 4 authors - Jul 19, 2006
    That long thread about elegant math General Discussion discussion.
  2. Does the elegant proof to the Fermats last theorem exists?- 10 posts - Jul 3, 2012
  3. Writing mathematical proofs has greatly improved my life- 26 posts - Feb 1, 2012
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  5. Snark Patrol: Elegant Math



    snarkpatrol.blogspot.com/2005/04/elegant-math.html
    Apr 27, 2005 –
    Elegant Math. This is one of the hardest concepts to explain to non-scientists. You see strange mathematical squiggles, I see five lines of ...
  1. Poincaré on Mathematical Elegance | Vita Smid ~ Zephyrus ...



    ze.phyr.us/poincare-on-mathematical-elegance
    Poincaré on Mathematical Elegance. “Mathematicians attach a great importance to the elegance of their results, and this is not mere dilettantism. What is it that ...
  1. "The elegance of mathematical logic and proofs" - NYU supplement



    www.essayforum.com/.../elegance-mathematical-logic-proofs-nyu- ...
    Dec 5, 2010 –
    Prompt 1: Why do you choose your anticipated academic area of study and NYU ? The elegance of mathematical logic and proofs has always ...