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Mathematics arose from ancient humans need to count and measure. Even the invention\discovery of Calculus was in service to physics. It has probably only been

Mathematics arose from ancient humans need to count and measure. Even the invention\discovery of Calculus was in service to physics. It has probably only been 300 years or so since Mathematics has been symbolic, before that it was more geometric and more attached to the physical world. Leibniz (late 1600s) helped to popularize negative numbers. At the time most mathematicians thought they were "absurd" and "fictitious". No, not highly abstract from the beginning.

elliotec 1y ago
Sorry what? Ancient humans invented symbols to count. How is that not symbolic? Geometry is “attached” to the physical world… but in an abstract way… but you can point to the thing your measuring maybe so it doesn’t count… Abstraction was perfected if not invented by mathematics.
- Ekaros 1y ago
  Symbolic here refers of doing math with place holders, be it letters or something. Ancient world had notations for recording numbers. But much less so to do math with them. Say like long division.
empath75 1y ago
Almost from the first time people started writing about mathematics, they were writing about it in an abstract way. The Egyptians and the Babylonians kept things relatively concrete and mostly stuck to word problems (although lists of pythagorean triples is evidence for very early "number theory"), but Greece, China and India were all working in abstractions relatively early.
- hollerith 1y ago
  In particular, ancient Greek geometry at least after 300 BC proceeded from axioms, which is a central component of the abstract approach.
compressedgas 1y ago
> Leibniz (late 1600s) helped to popularize negative numbers. Wasn't that imaginary numbers?
anthk 1y ago
Archimedes did Calculus before Newton. https://en.wikipedia.org/wiki/The_Method_of_Mechanical_Theorems https://en.wikipedia.org/wiki/The_Method_of_Mechanical_Theor...
- Jensson 1y ago
  He didn't connect the dots, so no he didn't do calculus even if he did some things related to it.

elliotec 1y ago

Sorry what? Ancient humans invented symbols to count. How is that not symbolic? Geometry is “attached” to the physical world… but in an abstract way… but you can point to the thing your measuring maybe so it doesn’t count… Abstraction was perfected if not invented by mathematics.

Ekaros 1y ago
Symbolic here refers of doing math with place holders, be it letters or something. Ancient world had notations for recording numbers. But much less so to do math with them. Say like long division.

empath75 1y ago

Almost from the first time people started writing about mathematics, they were writing about it in an abstract way. The Egyptians and the Babylonians kept things relatively concrete and mostly stuck to word problems (although lists of pythagorean triples is evidence for very early "number theory"), but Greece, China and India were all working in abstractions relatively early.

hollerith 1y ago
In particular, ancient Greek geometry at least after 300 BC proceeded from axioms, which is a central component of the abstract approach.

compressedgas 1y ago

> Leibniz (late 1600s) helped to popularize negative numbers. Wasn't that imaginary numbers?

anthk 1y ago

Archimedes did Calculus before Newton. https://en.wikipedia.org/wiki/The_Method_of_Mechanical_Theorems https://en.wikipedia.org/wiki/The_Method_of_Mechanical_Theor...

Jensson 1y ago
He didn't connect the dots, so no he didn't do calculus even if he did some things related to it.