“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.


el·e·gant   [el-i-guhnt]
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.

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

Can be confused:  elegant, eloquent (see synonym note at eloquent).

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.

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