It is sort of like that. You can propose any axiomatic system you want. Matiyasevich proved that Hilbert's 10th problem was unsolvable. This 10th problem was to find a universal method for solving Diophantine equations. This turns out to to mean there is no axiomatic system for solving p-adic number systems. There are then an infinite number of such number systems. You can build them almost as you want.
LC On Monday, September 13, 2021 at 1:32:18 PM UTC-5 Brent wrote: > That's interesting. Does Coq let you change axioms? In what Feynman > called "Persian" mathematics, you're interested in what axioms support a > given theorem, not the other way around as in "Greek" mathematics. > > My wife (who's a mechanical engineer) were just discussing how calculus is > regarded as the "hard mathematics" in college. But I wonder if it's a > matter of how it's taught. When she and I went school a lot of calculus > was learning tricks and approximations to do integration. Conceptually it > wasn't that hard. And in applications, nobody worries much about the > tricks anymore because they just give it a computer. Mathematica knows the > tricks and there's easy numerical integration algorithms. Does that mean > we are losing contact with how it actually works...not at all. Those > tricks and approximations just obfuscated "what was really going on". > > I wonder how calculus is taught now in high school and undergrad college > courses? ISTM is could be much clearer and conceptual and easier to learn. > > Brent > > > On 9/13/2021 2:49 AM, Lawrence Crowell wrote: > > I am learning about Coq, which is a theorem proving/proof checking system. > The one problem with this or some AI code generating system is that we > humans will start losing more contact with how things actually work. > > LC > > On Friday, September 10, 2021 at 5:38:38 AM UTC-5 [email protected] > wrote: > >> From The New York Times: >> >> A.I. Can Now Write Its Own Computer Code. That’s Good News for Humans. >> >> A new technology called Codex generates programs in 12 coding languages >> and even translates between them. But it is not a threat to professional >> programmers. >> >> >> https://www.nytimes.com/2021/09/09/technology/codex-artificial-intelligence-coding.html?smid=em-share >> > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/453c2c88-fcf0-4fac-9129-7798ad3b8f07n%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/453c2c88-fcf0-4fac-9129-7798ad3b8f07n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5544271f-0ade-400b-a2bc-aef24cf69cebn%40googlegroups.com.
