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https://qntm.org/perso

I saw it as a sort of science-fiction - imagine living in a world where the smartest intellectuals all struggled to solve basic exercises about graph theory. Really imagine living …

For learning the theory behind quantum computing, I usually recommend Watrous's lecture notes [1] - they start out by immediately giving a helpful analogy to ordinary probabilistic…

Are you also uncomfortable with the idea of flipping 256 unbiased coins independently?

There is no general procedure for computing upper bounds on busy beaver numbers (this can be proven). We haven't even come close to enumerating all of the interesting six-state Tur…

I've only skimmed the paper, but this looks very nice: the construction is very simple (aside from the precise choices of the parameters), just the analysis to show that it works i…

The consistency of ZFC is (presumably) a theorem of second order PA, and ZFC is unable to prove it (unless ZFC is inconsistent).

Unfortunately no, ZFC isn't good enough to capture arithmetical truth. The problem is that there are nonstandard models of ZFC where every single model of second-order PA within is…

Speaking as someone from the math community: 90% of the time, when we get a request like this, there is some form of mental illness involved. We aren't psychologists, so we tend to…

"For instance, global pharmaceutical companies are advancing both disease research and the frontier of quantum-enabled drug discovery. And in automotive and aerospace, companies ar…

The (actual) article has a fairly detailed literature review in the introduction, and makes it pretty clear that the main idea was sort-of known already if you squint - but it look…

Think about it: with 20% tariffs, we will now have the option to work 14 hour shifts for 60c a day!

If the discrete logarithm problem is NP-hard, then I will eat my hat. The discrete logarithm problem can be solved by Shor's algorithm on a quantum computer, placing it in the comp…

There are plenty of mathematicians - mostly set theorists - who are actively working on finding new axioms of mathematics to resolve questions which can't be resolved by ZFC. Proje…

The error rate of human mathematical work is not zero, but it does go down exponentially with the amount of time that the mathematician spends carefully thinking about the problem.…

When you get good enough at mathematics, you can tell if your proofs are correct or not without asking a TA to grade them for you. Most mathematicians reach this level before they …

I always recommend Watrous's lecture notes: https://cs.uwaterloo.ca/~watrous/QC-notes/QC-notes.pdf I prefer his explanation to most other explanations because he starts, right away…

MIT's PRIMES program does exactly this - they give advanced high school students a mentor who picks out a problem, gets them up to speed on what is known, and then they work on the…

If the Hanoi pieces alternate in color, there is another very easy algorithm: always avoid putting two pieces of the same color directly on top of each other. I noticed this by acc…

Have you tried to read any of the literature on the Risch algorithm? If you haven't, you might want to get started by taking a look at the paper "Integration in Finite Terms" by Ro…

Reminds me of "Scheduling Algorithms for Procrastinators" [1] [1] https://www3.cs.stonybrook.edu/~bender/newpub/2007-BenderClT...

Watrous's notes get straight to the point, with a good analogy to ordinary probability theory: https://cs.uwaterloo.ca/~watrous/QC-notes/QC-notes.pdf