The current wave of AI slop mathematics might end up driving the next generation of mathematicians away from the subject for the same reason that Mochizuki would have convinced me to quit if his proof had been accepted by the community. Luckily, my professors had the taste to immediately recognize that it was garbage.

Comments URL: https://news.ycombinator.com/item?id=49218320

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The online tutorial [2] is a good followup, especially if you want to understand Clifford gates / stabilizer states, which are important for quantum error correction.

If you have a more theoretical bent, you may enjoy learning about the ZX-calculus [3] - I found this useful for understanding how measurement-based quantum computing is supposed to work.

[1] https://cs.uwaterloo.ca/~watrous/QC-notes/QC-notes.pdf [2] https://qubit.guide/ [3] https://zxcalculus.com/

Comments URL: https://news.ycombinator.com/item?id=45574032

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(I bet the construction can be refined - it feels like there is a semidefinite programming problem lurking in the background, so there is probably a way to mindlessly optimize things with an SDP solver once the proof technique is rephrased a bit.)

https://jdh.hamkins.org/the-universal-algorithm-a-new-simple...

- It looks like the first block of stuff here is some equalities in Q[√5] which you have checked either numerically or symbolically (I haven't checked any of them in detail, but I doubt you made any mistakes here).

- The first claimed breakthrough is a representation of the fundamental unit of a Pell equation as a linear function of √5, but I'm pretty sure that this has been known for at least 200 years (maybe much more than that, I'm not an expert in history of math). I guess it's supposed to be new because you are using these other constants T, J, K instead of √5, but mathematically this is just a roundabout way of writing down the same thing, since they are all linear functions of each other.

- We then have the standard formulas for the Fibonacci numbers, rewritten in terms of T,J,K again. Once again, a roundabout way of writing down the same thing.

- Next up is an unconvincing argument for a special case of the BSD conjecture - I don't see how you checked that L(1) = 0 or that L'(1) ≠ 0 (or even that the rank of the curve isn't 2 or more). Since you are trying to verify BSD for a curve which has rank 1, this case is actually already known (the first link google gave me when I searched for this was [1]).

- Finally we have a bizarre argument trying to tie this into the Riemann hypothesis, but the only thing you actually used was that T+J = 1/2, so in fact the √5 stuff has zero relationship to the numerical coincidences you found.

I worked in number theory as a grad student, and to this day I don't understand the bizarre fixation people have on the Riemann hypothesis or the BSD conjecture. Sure, it would be cool to know if they were true, but there are lots of other interesting questions out there - why not try your hand at the sum of square roots problem [2] or resolving Kontsevich and Zagier's conjecture about determining when two periods are equal [3]? In fact, why not work on something more practical than number theory, like SAT-solving [4]?

[1] https://mathoverflow.net/questions/309086/bsd-conjecture-for... [2] https://en.wikipedia.org/wiki/Square-root_sum_problem [3] https://en.wikipedia.org/wiki/Period_(algebraic_geometry)#Op... [4] https://satcompetition.github.io/

Given what I know about the current progress towards building a useful quantum computer, this is complete nonsense. No company out there has anywhere near enough qubits with enough coherence to solve any real problem more efficiently than brute force on a classical computer. We'll get there eventually - maybe in just a few years - but anyone who tells you it is already here is a bullshit artist.

The proof they give that the hyper-Catalan series solves the Lagrange inversion problem is very good from a pedagogical point of view - I don't think I'll ever be able to forget it now that I've seen it. The only thing this paper is missing is a direct, self-contained combinatorial proof of the factorial-ratio formula they gave for the hyper-Catalan numbers - digging though the chain of equivalences proved in the references eventually got too annoying for me and I had to sit down and find a proof myself (there is a simple variation of the usual argument for counting Dyck paths [1] that does the trick).

Another thing to note is that the power series solution isn't just "a power series" - it's a hypergeometric series. There are lots of computation techniques that apply to hypergeometric series which don't apply to power series in general (see [2]).

[1] https://jlmartin.ku.edu/courses/math724-F13/count-dyck.pdf (for instance) [2] https://sites.math.rutgers.edu/~zeilberg/AeqB.pdf