RE: Studying Mathematics Thread
October 2, 2018 at 7:58 am
(This post was last modified: October 2, 2018 at 8:10 am by polymath257.)
(October 2, 2018 at 7:40 am)LastPoet Wrote:(October 1, 2018 at 8:06 am)polymath257 Wrote: I just want to say that this is still very much true today. Computers help some with computations. They are good for writing up results. But the *real* ideas happen on paper or the black (marker) board. Reams of paper are used before the first key on the computer is hit.
Indeed. Computers with some software are nice mostly for presentation and whatnot. It is too time consuming and dostracting havint to hotkey the math symbols in, makes your train of though less efficient.
Good ol paper or a chalk/marker board. I made my own, my ex boss has a factory that uses nice white acrylic and has tools, so I asked him if I could do one on a saturday. 1.5 * 1 meter with the support to keep it standing. He offered me the materials. It was nice of him. Still have it, but I could replace the whiteboard, Acrylic tends to get yellowish over time.
There is a specialist typesetting language called TeX (or LaTeX) that is now standard for mathematics papers. No hotkeys, but there is a learning curve for how to use it. MiKTeX is the most often used Windoze port.
(October 2, 2018 at 2:51 am)Reltzik Wrote: Eh, I guess I have something I can contribute here.
Axiomatization
A very, very nice post. I only have a slight quibble about the history.
Plato was a couple of centuries *before* Euclid. So the geometry that Plato wanted for entrance to his Academy was not that of Euclid, but more likely that of Theatetus.
Second, Euclid's Elements *did* include a considerable amount of number theory. For example, his proof that there are infinitely many primes is simple and direct and used today. He also gave a condition when an even number is perfect (later showed to be the only situation where an even number is perfect by Euler).
Given your discussion of the 5th Postulate, I was also surprised that you didn't mention the rise of non-Euclidean geometry and the effect it had on the formalization movement leading up to Russell.
All said, though, well done!