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Historically, this is accurate. The whole concept of "pure math" is actually very recent and before that math was almost exclusively tied to real world problems
by erdos4d 6y ago
Historically, this is accurate. The whole concept of "pure math" is actually very recent and before that math was almost exclusively tied to real world problems that often came directly from physics.
- mettamage 6y agoHow about having some understanding of complex numbers? Wasn't it an Italian who started to use sqrt(-1)? I don't see how that'd be practical. Disclaimer: I'm not a mathematician.
- bitdizzy 6y agoThe first use of complex numbers was as intermediate quantities in the calculation of the roots of cubic polynomial functions. This use is analogous to using negative numbers in a ledger even though negative amounts of physical things don't make sense. Edit: I meant physical things like apples fam. This is an important philosophical point we don't appreciate because we are so used to them. De Morgan once wrote: "It is not our intention to follow the earlier algebraists through their different uses of negative numbers. These creations of algebra retained their existence, in the face of the obvious deficiency of rational explanation which characterized every attempt at their theory."
- Koshkin 6y agoThe complex numbers enjoy a widespread use in physics (and electrical engineering).
- 0--__-_-__--0 6y agoComplex numbers are practical, they're everywhere in classical mechanics and circuit design, off the top of my head
- erdos4d 6y agoI am, have a PhD in it at least, and complex numbers are 100% required to do quantum mechanics, so are physically motivated. In fact, many physicists consider the complex numbers to be the preferred number system of the universe for this reason.
- oytis 6y agoHistorically already ancient Greeks knew pure mathematics (e.g. Euclid's Elements), and differentiated it from its applications as far as I'm concerned. That made them pretty distinct from earlier Egyptian mathematicians who indeed were only concerned with solving practical problems without much attention to logical rigor.
- Koshkin 6y agoCuriously, many mathematical curricula used to include analytical mechanics, and some of the mathematics departments of universities around the world had the word "mechanics" in their names.
- aaplok 6y agoHistorically mathematics was part of accounting, both in Ancient China where it was used to calculate taxes, in Egypt and in Babylon. People used numbers to keep count and then developed advanced techniques to do sophisticated things like split non-rectangular land in equal parts. It wasn't until much later, and only in a tiny part of the world called Europe, that physics started using mathematical models. Even at that time and in that place, there were other disciplines making advanced use of mathematics and leading to exciting discoveries, starting from Economics. Jacobi who developed utility theory around the time of Newton. Mathematics was never a subdiscipline of physics. Important parts of mathematics were developed to support models of physics, but claiming that the parts should not exist is intellectually dishonest.