csheehan10

To achieve this you would need to show that 3SAT is solvable in 2^{n^c} time for every c>0, not just a single c<1.

In this case they have c = 1-0.5(\log \log n)/(\log n) which is approaching 1 for large n.

It's NP-complete problems if "subexponential" means O(2^{n^{\epsilon}}) for every \epsilon>0.

If subexponential just means 2^{o(n)}, (as it is here, O(2^{n/\sqrt{\log n}})), then no. E.g. if the cost of the reduction took you from n to \sqrt{\log n}n, then you'd be back to exponential time. The Subexponential Reduction Family is the class of problems that preserve subexponential time in the second sense.

The twin primes conjecture says that there are infinitely many primes p such that p+2 is also prime. The best existing result says that there exists some k < = 246 such that p, p+k are both prime infinitely often. This paper reduces the upper bound on k to 240, and is also the first improvement since 2014.

I am a PhD student in mathematical statistics. The people I have spoken too think this is very exciting and cool. There is also a sense of unease about what this will mean in terms of being a mathematician, and what effects it will have on our future employment.

I am also a little worried about what it means for your training as a junior PhD. Often you would try and solve a problem your advisor thinks is doable that they assign to you as a learning exercise. It may be more and more difficult to find problems that a junior PhD can solve but that AI can not. Tim Gowers has written about that here: https://gowers.wordpress.com/2026/05/08/a-recent-experience-...

"The Organismic and Evolutionary Biology department will shrink its class size by roughly 75 percent to three new Ph.D. students, according to two professors. Molecular and Cellular Biology will reduce its figure to four new students, and Chemistry and Chemical Biology will go down to four or five admits, one of the professors added."

Do you really think that is the purpose of those departments?

The military wing of Hamas has stopped accepting cryptocurrency donations in order to ensure "the safety of donors and prevent them any harm".

No, we only need one massive paradigm shift per century, and then there are plenty of new productive areas again.

I find it very unconvincing that parents needing to get to work on time necessitates starting school so early. In Ireland (a country with very poor public transport) in the 2010s I started secondary school at 8.45am. This usually meant getting up about 7.45am, and being dropped to school by parents about 8.30am, so they'd have plenty of time to make it to work by 9. In what universe is making teenagers arrive in by 7am justified?