Viewing profile — dellamonica

The point of the AI with respect to checking is to translate a natural language theorem and its proof into the formal system. Most of known math is not formalized because it is ver…

It is extremely well known. Lots of people have tried to solve it and it stood basically stuck for 80 years. It is getting harder every day to downplay these models. Given its elem…

The ellipse can be also encoded by just the lengths along each axis and then by a rotation in R^n (which is just a unitary matrix multiplication). So in essence, for the problem in…

Every ellipse can be encoded by the matrix A (and the geometric concept is generalized to arbitrary dimensions). Not sure I follow the physics analogy though. A unit ball is a spec…

Yes, if you don't use dotnet and is already used to Unix tooling then it is a tough sell, but otherwise the integration with dotnet is quite good.

I mean, the entire dotnet is available, you can do anything in PS though obviously that is not always the smart call. It has been very useful to me to use as a REPL on my own C# li…

What is wrong with PowerShell core? *PS core is the one based on the new versions of dotnet.

It's rather difficult to provide a good formalization but let me give it a shot. Suppose that mathematicians write papers with pen and paper in a subset of natural language without…

First of all, thank you for a thorough response. I'll need to take time to read it (and the refs in your other reply) with the care it deserves. Basically I'm talking about the sub…

No misunderstanding about NP here for sure. As I said, this is about as much of a thesis as Church Turing is about what can be computed. I have no clue about CiC, lean and whatnot.…

Right, and this is also the current status of handmade mathematics. All we know is that we did not find a proof yet with everything that has been tried. This typically means that a…

Could you give me a reference? This is not something I'm familiar with. Can you claim that this equivalence proof is not in NP, without requiring this specific encoding? I would be…

Then in that target language, found by a clever human, you could do the same type of enumeration... My whole point is that humans simply cannot process/create by themselves any tru…

This is all very interesting but it seems that we're just taking different views on what is the instance size. If it is the length of the theorem statement in some suitable encodin…

Of course it would, you would enumerate lengths too. If the lengths need to be larger than polynomially bounded then we can be sure it would never be found by a human anyway.

It doesn't require anything like that. Math proofs are of NP complexity. If you had access to a non deterministic Turing machine you could enumerate all possible proofs of a given …

Without digging too much, I don't think such an argument could be made by this paper. A non trivial lower bound on a concrete problem in a general computation framework would be a …

It might be possible to compute whether the start and end States are connected without constructing the actual path. As usual non trivial lower bounds on computation are basically …

It does though. My gmail account has a dot. For some reason someone with a similar name to mine must have for believed his address was the non dotted version of mine and to this da…

There has been a push for using Source Generators to move stuff that relies on reflection to compile time code generation. JSON serialization is (mostly) supported in this mode wit…

It can get really tricky: using reflection you could read a string from any input and create a generic type instantiation that never happens in the source code. How would the code …

There are lots of techniques that use randomness to show the existence of objects with desired properties. Some of them rely on the "first moment" (expectation) which seems to be w…

That would make a great Black Mirror episode... and a terrible dystopia if it becomes reality.

I think the basic idea is that the hash has a fairly uniform probability distribution, so knowing the prefix means you can estimate its location in a sorted list. For instance if w…