Ideal
/aɪˈdiːəl/noun
A standard of perfection, or in algebra a subset of a ring closed under multiplication by any element.
The Greek roots
Literally: “belonging to the form”
The story of the word
Plato's ἰδέα is what you see when you see a thing's form, built on ἰδεῖν, to see, and its career runs through Late Latin idealis, existing only as an idea. The mathematical sense began as something close to a joke: Kummer introduced 'ideal numbers' in the 1840s, fictions invented to rescue unique factorization, objects that did not exist but behaved as though they did. Dedekind then made them respectable as the ideals of ring theory, and the name for a useful fiction became the name for a real object.
- How it travelled
- Ancient Greek → Late Latin → French → English
- First recorded
- 1610s
The same roots elsewhere
Other languages reached for exactly the same Greek pieces.
Same family
In a sentence
Every ideal in the integers is generated by a single number.
The plan was sound in the ideal case and useless in February.