mathlib VS learnxinyminutes-docs

It's been on my mind lately as well. I was trying out `symbolics.jl` (a CAS written in Julia), and it turned out that it didn't support symbolic integration beyond simple linear functions or polynomials (at least back then, things have changed now it seems). Implementing a generic algorithm for finding integrals is hard, but I was expecting more from that CAS since this seems to be implemented in most other CASs. The thing is that every single CAS that covers general maths knowledge will have to implement the same algorithm, while it's hard to do it even once!

I feel like at least a large part of the functionality of a general purpose CAS can be written down once, and every CAS out there could benefit from it, similar to what the Language Server Protocol did for programming tools. They also had to rewrite the same tool for some language multiple times because there are lots of editors out there, and the LSP cut the time investment down a lot. They did have to invest a large amount of time to get LSP up and running, and it'll have to be maintained, but I think it's orders of magnitudes more efficient than having every tool developed and maintained for every single (programming language, editor) pair out there.

Main problem is like you said how to write down mathematical knowledge in a way that all CASs can understand it. I've been learning about Mathlib lately [0], which seems like a great starting point for this. It is as far as I know one of the first machine readable libraries of mathematical knowledge; it has a large community which has been pushing it continuously forward for years into research-level mathematics and covering the entire undergraduate maths curriculum and it's still accelerating. If some kind of protocol can be designed to read from libraries like this and turn it into CAS code, that would be a major step towards making the CAS ecosystem more sustainable I think.

It's not exactly what you were talking about, as in, this would allow multiple CASs to co-exist and benefit from each other, but I think that's better than having one massive CAS that has a monopoly. No software is perfect, but having a diverse set of choices that are open source would be more than enough to satisfy everyone.

(I have posted about this before on the Lean Zulip forum, it's open to everyone to read without an account [1])

[0] https://leanprover-community.github.io/

Kinda agree but Mathlib and its documentation makes for a big corpus to learn by example from. Not ideal but it helps.

https://github.com/leanprover-community/mathlib

https://github.com/leanprover-community/mathlib

https://1lab.dev/

You can watch the next generation, or participate, right now.

Still, there are many useful tools based on these ideas, used by programmers and mathematicians alike. What you describe sounds rather like Datalog (e.g. Soufflé Datalog), where you supply some rules and an initial fact, and the system repeatedly expands out the set of facts until nothing new can be derived. (This has to be finite, if you want to get anywhere.) In Prolog (e.g. SWI Prolog) you also supply a set of rules and facts, but instead of a fact as your starting point, you give a query containing some unknown variables, and the system tries to find an assignment of the variables that proves the query. And finally there is a rich array of theorem provers and proof assistants such as Agda, Coq, Lean, and Twelf, which can all be used to help check your reasoning or explore new ideas.

For the math that you mention, I would suggest looking at mathlib (https://github.com/leanprover-community/mathlib). I agree that the foundations of Coq are somewhat distanced from the foundations most mathematicians are trained in. Lean/mathlib might be a bit more familiar, not sure. That said, I don't see any obstacles to developing classical real analysis or linear algebra in Coq, once you've gotten used to writing proofs in it.

At this point I would go with Lean because of mathlib. Mathlib's goal is to formalize modern mathematics, so many of the theorems you would need for analysis should already be there for you.

I think about that every day. Lean's mathlib is a gigantic (with respect to this kind of project) code base and each function, each definition has a precise and rigorous natural language counterpart (in a maths book, somewhere).

It's been around since 2013, although there are LLM that interact with Lean to do automated theorem proving. Anyway, you can learn more about Lean here. I enjoyed their natural numbers game (which reminds, me I should finish the last two levels)

> Sure, maybe for some esoteric edge cases, but 5 mins on https://learnxinyminutes.com/ should get you 80% of the way there, and an afternoon looking at big projects or guidelines/examples should you another 18% of the way.

Not for C++, and even for other languages, it's not the language that's hard, it's the idioms.

Python written by experts can be well-nigh incomprehensible (you can save typing out exactly one line if you use list-comprehensions everywhere!).

Someone who knows Javascript well still needs to know all the nooks and crannies of the popular frameworks.

Java with the most popular frameworks (Spring/Boot/etc) can be impossible for a non-Java programmer to reason about (where's all this fucking magic coming from? Where is it documented? What are the other magic words I can put into comments?)

C# is turning into a C++ wannabe as far as comprehension complexity goes.

Right now, the quickest onboarding I've seen by far are Go codebases.

The knowledge tree required to contribute to a codebase can exists on a Deep axis and a Wide axis. C++ goes Deep and Wide. Go and C are the only projects I've seen that goes neither deep nor wide.

Learn x in y minutes: Concise tutorials to learn various programming languages and tools quickly.

StackOverflow's making their own competing LLM for all this stuff.

IMO, one of the biggest problems with the way people use LLMs right now, is that they're being treated as a single oracle: to know Java, it must be trained on examples of Java.

It would be much better if their language comprehension abilities were kept separated from their knowledge (and there are development efforts in this direction), so in this example it would be trained to be able to be able to read a Java tutorial rather than by actually reading a Java tutorial, so when the overall system is asked to write something in Java, the language model within the system decides to do this by opening https://learnxinyminutes.com and combining the user query with the webpage.

I think this will help make the models more compact, which is a benefit all by itself, but it would also mean that knowledge can be updated much more easily.

Someone would have to actually do this in order to see if those benefits are worth the extra cost of having to load a potentially huge a tutorial into the context window, and likewise the extent to which a more compact training set makes the language comprehension worse.

The project was created and is maintained by Adam Bard, but is open sourced with over 1.7k contributors since 2013

https://github.com/adambard/learnxinyminutes-docs

So you have studied programming for at least 5 years, what kinds of programs have you written? Apparently you have already applied your skills, since you have "created a good reputation among developers"? Why a time-frame of 20 years, why not 20 months or 20 weeks? Heck, you can learn a lot in even 20 days!

Once you have learned a few languages, libraries and frameworks then learning new stuff becomes much easier. At that point I'd recommend to check the website https://learnxinyminutes.com. Meanwhile, continue asking questions here and elsewhere :)

An other tip, if you are into computer science and algorithms stuff I recommend you try to solve problems which are posted at https://codegolf.stackexchange.com. You don't need to try solving them in less than X characters, but just to get them solved by any means necessary. And don't take too much bad influence from the posted solutions.

If you want a brief overview, go to https://learnxinyminutes.com/ and look for Javascript. I guess it should be roughly the time it took to learn C++ or possibly less, but JS has its own quirks. Often learning a second language is difficult as the first.

Very light compared to the other resources people have linked for you, but I love https://learnxinyminutes.com/