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Part of me wants to reconstruct all of math up to calculus from scratch and document it all and then create a knowledge map so someone can see how any advanced idea is derrived from the most elementary ideas.
Partly I want to do this for myself just because I have a hard time remembering some derrivations, particularly in calculus where you have to go back to limits to show it.
@yellowbeard Story of my life... i should be doing real work and not contemplating reinventing math :)
@freemo @yellowbeard
finding news ways to gain an overview of math is perhaps the most important life work there is. Not only would this help you, it would help countless generations to come. Imagine how much lost learning energy can be saved/captured with an overview of how all the math pieces fit together. Imagine how many students who are currently 'lost in math space' would suddenly find math simple, usable, an maybe even fun. Start with an overview, maybe a wiki?
@freemo could polish http://us.metamath.org from set theory
Or there are several systems in type theory.
@jmw150 I heard of metamath before.. i really should try and get into it.
@freemo it is more like a database.
Systems like Coq are more fun though I think. The standard library is proofs for a bunch of undergrad math like the dedikind cut construction of reals. Real numbers at your fingertips. 😁
@jmw150 metamath is definately not just a database. It is a special language you can use to write proofs and have a system automatically verify the validity of a proof as well as render the proof as a webpage.
That ability to confirm the validity of a proof is what I usually hear people talk about when they have mentioned metamath.
@freemo It's a really fun time. That's how I was taught Calculus. It was theory that we had to prove.
Its how i was taught too, but i have forgotten so much of the derivation and find it hard to dig up sometimes. Thus id like to document it somewhere in a wiki format.. a wiki of derrivtions and cheat sheets.
@freemo Or maybe a dive from Trigonometry to the Derivative and Integral.
@freemo ok hilbert, just don't do it like you do combinatorics
@namark lol... if i ever started such a project I probably just setup some example pages and structure it and hope others helped... I dont have time for something like this on my own. I am no Hilbert thats for sure :)
