116 karma · joined October 15, 2009
We do live in that universe, under some currently believed assumptions. An NP-complete problem is an example of something where checking a solution is (thought to be) easier than finding one.
Zero-knowledge proofs make it such that checking that a computation (such as inference) has been done correctly is easier than doing the computation (even keeping some parts private). A great reference is here: https://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.pdf
Interestingly, if you ask people which they would trust for a rollup, most say ZK is the more trustworthy technology. In part just because it doesn't depend on one vendor (the enclave manufacturer).
https://www.youtube.com/playlist?list=PLj80z0cJm8QErn3akRcqv...
Speed and memory usage is improving quickly.
Many comments would be considered "fraudulent" in the same sense, in that they were not authored by a real person, but a bot, or someone writing comments as fast as possible because it is their job.
This is the exam all Berkeley math Ph.D. students must pass within three semesters of arriving to stay in the program, and the fail rate is about 50%.
You will also need reference books, advanced undergraduate and beginning graduate textbooks. Buy, download, or borrow as appropriate.
Pick a problem (start with the older ones, they are easier). Set aside 30-60 mins and try to solve it. No devices, no references at all, go to a library or a coffee shop without your devices. Dont' give up till time is over. If you cannot (usually the case), still don't look at the answer. Hit the reference books (don't look up the problem online either, it will go right to the answer and you won't learn much). Read and try to understand enough so that you can solve the problem. It is ok if you solve it this way (in the course of reading about it).
For bonus points, students studying for the exam will typically take entire old exams (available from the Berkeley website), take that to the library and just sit down for three to six hours and try to solve all the problems correctly. Then self-grade harshly. When you can do that for a recent exam (and get a good score), you will have more or less mastered undergrad math to the point that you could teach it.
Most important: you have to struggle to solve problems. Reading a solution is about as useful as watching someone else lift weights: you get minor tips on form but not any stronger.
A course is kind of like a web app with a lot of common functionality. Too bad most LMSs seem to think we want to write our course in a little text box with no version control (even newer ones like Canvas make this assumption).