Why Mathematicians Call a Proof Elegant
Elegant means graceful and unfussy. In science and mathematics it is high praise for a solution that does the most with the least.
Elegant describes beauty that comes from restraint: a plain dress, a clean line, a room with nothing extra in it. Mathematicians borrowed the word for proofs, and there it has a precise flavour — an elegant proof is short, surprising and uses no more machinery than it must.
- Graceful and stylish. *An elegant dress.*
- Pleasingly simple and effective. *An elegant solution to the problem.*
- Refined in manner. *Elegant manners.*
Word forms
| Form | Word | Example |
|---|---|---|
| Adjective | elegant | An elegant curve. |
| Adverb | elegantly | Elegantly dressed. |
| Noun | elegance | Quiet elegance. |
| Opposite | inelegant | An inelegant fix. |
| Related | graceful | A graceful movement. |
How it is used in a sentence
- The building is elegant without being showy.Elegance and display pull in opposite directions.
- It is an elegant solution: two lines of code instead of forty.In engineering, elegant means economical.
- She made an inelegant landing but stayed upright.Inelegant is gentler than clumsy.
Nearby words, with their differences
- Elegant — beautiful through simplicity and proportion
- Graceful — beautiful in movement
- Stylish — fashionable, which elegance need not be
- Sophisticated — worldly and complex, sometimes the opposite of elegant
- Elegant variation — a writing fault: swapping in synonyms just to avoid repeating a word
From Latin *elegans*, tasteful, related to *eligere*, to select — the same root as *elect*. The idea sits inside the word: elegance is a matter of what has been chosen, and of what has been left out.
Can a person be elegant?
Yes, and it usually refers to how they dress and carry themselves rather than to their face.
What is an elegant proof?
One that reaches a result briefly and clearly, often by an unexpected route, using the fewest assumptions.