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It was something like 1500 years between the discovery of squareroot 2 and squareroot -1. If you view mathematics as the exploration of progressively stranger
by SomeStupidPoint 9y ago
It was something like 1500 years between the discovery of squareroot 2 and squareroot -1.
If you view mathematics as the exploration of progressively stranger objects, that there's such a gap between discovering two roots should make us cautious of discounting things after a 100 year search.
We don't know what we don't know.
- jcranmer 9y ago> It was something like 1500 years between the discovery of squareroot 2 and squareroot -1. It was something like 200 years between the discovery of sqrt(-1) and more-or-less universal acceptance of -1 as a number in the first place (yes, imaginary numbers predate the universal acceptance of negative numbers). European mathematics in particular favored geometric interpretation of numbers over algebraic interpretations until relatively recently, and while irrational numbers come about very easily in geometry, negative numbers don't have an immediately obvious interpretation, particularly if you exclude it is a convention of directionality.
- pvg 9y agoThe irrationality of the square root of 2 was known long (longer than 1500 years) before the invention of complex numbers, never mind root 2 itself. But whatever the duration, there wasn't relatively uninterrupted, continuous study of mathematics over it - that's a fairly recent thing. Mathematical (and other) knowledge was routinely lost or not seriously pursued at all. This supposed 'gap' between two fairly arbitrary discoveries doesn't inform our understanding of the development of mathematics itself as much as you seem to think.