I’ve written a lot of Lean for economic modeling (so take this with the caveat that it’s not frontier-level mathematics research) but I think this problem is overstated. If you follow good engineering standards—keep primitives composable and design abstraction well—it’s not so hard to understand enough Lean to ensure the formalized statement is correct.
In part this is possible because mathlib is very well-designed and has a very good API (in no small part because they’re willing to make breaking changes all the time), so building on top of it makes life much easier.
Or, more accurately: it's not possible to apply copyright to generated code; if you don't release it, it's a trade secret, but if you do, people can use it how they please.
A terminal AI coding assistant with a built-in math formalization engine — describe a problem in plain language and it converts it into a Lean 4 theorem and attempts a formal proof.
Interesting work. Is this a wrapper around the AUTOLEAN project (https://github.com/T3S1AMAX/autolean)?
the tricky bit is ensuring your inaccurate plain english statement is captured and formalized correctly as lean.
I’ve written a lot of Lean for economic modeling (so take this with the caveat that it’s not frontier-level mathematics research) but I think this problem is overstated. If you follow good engineering standards—keep primitives composable and design abstraction well—it’s not so hard to understand enough Lean to ensure the formalized statement is correct.
In part this is possible because mathlib is very well-designed and has a very good API (in no small part because they’re willing to make breaking changes all the time), so building on top of it makes life much easier.
What kind of economic modelling uses Lean?
Interesting, but I don't see any licensing terms, which means I can't touch it in a commercial setting.
What commercial setting do you want to use a Lean theorem-proving agent in?
Mathematics, Inc [1], I assume
[1] http://www.cs.utexas.edu/users/EWD/ewd04xx/EWD427.PDF
It's AI generated, so licensing terms are unenforceable.
Or, more accurately: it's not possible to apply copyright to generated code; if you don't release it, it's a trade secret, but if you do, people can use it how they please.
A terminal AI coding assistant with a built-in math formalization engine — describe a problem in plain language and it converts it into a Lean 4 theorem and attempts a formal proof.
Could you provide a practical example?
There is one in the quickstart:
https://math-ai-org.github.io/mathcode/#quickstart - if you look very closely, the screenshot at the top actually shows the output (and the solution).Maybe consider an integration with theoremdb.org?
To be clear, I am deep into auto-research, but hooking up slop to slop is just unlikely to produce anything valuable.
Value is in how maths is communicated: The process, frustrations, triumphs, etc.
We have to able to take generated formalizations from “it compiles” to “it is correct” before crystallizing them.
> hooking up slop to slop is just unlikely to produce anything valuable
Do you have a formal proof of that?
Premises: Garbage in implies garbage out (first principle of computer science) The input is possibly, but not necessarily garbage (definition of slop)
By the standard methods of modal logic, it follows that it is possible that the output is garbage and therefore slop by definition. QED.