Just earlier today I wanted to check if exp(inx) is an orthonormal basis on L^2((0, 1)) or if it needs normalization. This is an extremely trivial one though. Less trivially I had an issue where a paper claimed that a certain white noise, a random series which diverges in a certain Hilbert space, is actually convergent in some L^infinity type space. I had tried to use a Sobolev embedding but that was too crude so it didn't work. o1 correctly realized that you have to use the decay of the L^infinity norm of the eigenbasis, a technique which I had used before but just didn't think of in the moment. It also gave me the eigenbasis and checked that everything works (again, standard but takes a while to find in YOUR setting). I wasn't sure about the normalization so again I asked it to calculate the integral.
This kind of adaptation to your specific setting instead of just spitting out memorized answers in commonn settings is what makes o1 useful for me. Now again, it is often wrong, but if I am completely clueless I like to watch it attempt things and I can get inspiration from that. That's much more useful than seeing a confident wrong answer like 4o would give it.
This kind of adaptation to your specific setting instead of just spitting out memorized answers in commonn settings is what makes o1 useful for me. Now again, it is often wrong, but if I am completely clueless I like to watch it attempt things and I can get inspiration from that. That's much more useful than seeing a confident wrong answer like 4o would give it.