So I was reading Euler's calculus textbook and in it he talks a lot about whether matter is infinitely divisible, or made up of indivisible atoms, and he talks about this as if it's a very important thing to consider before you get into calculus.
It's surprising because nobody talks about this type of stuff in modern math books. What gives? what's the difference between the way old-timers like Euler thought about math, and the way people today think about math?
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Back in the days they actually cared about laying a consistent foundation. Nowadays they sweep it all under the rug for convenience.
The invention of alternative facts (which gave rise to the field of postmodern mathematics) in the early 20th century by Alfred Tarski, though the credit is typically awarded to the more well-known Godel (and occasionally Turing).
fuck off, mathematics up until it was formalised was literally random shit strung together, that worked well enough. Mathematics adheres to ZF Set Theory and is entirely consistent, it had to be formalised as it got more complex.
>Mathematics adheres to ZF Set Theory and is entirely consistent
lol
>Nowadays they sweep it all under the rug for convenience.
Agreed
>Mathematics adheres to ZF Set Theory and is entirely consistent
Prove it then.
>Mathematics is entirely consistent
i will award you a phd if you prove this
>Prove it then.
>i will award you a phd if you prove this
>Requiring proof for common knowledge.
>It's surprising because nobody talks about this type of stuff in modern math books. What gives?
Because Euler was writing 80~ years before Cauchy and Weierstrass came up with (ε, δ)-definition of the limit that put calculus on a firm rigorous foundation and 160~ years before Einstein proved discrete atoms exited with his 1905 paper on Brownian motion (which was hotly debated by chemists before then).
I mean, I don't wanna be That guy, but:
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