mcontrac

Cool method but I hate that "digital twin" is really catching on in terms of nomenclature. See it constantly in comp neuro papers nowadays

Beautiful writing. In my highest impression of (pure) math I've always thought of it as an art. We would think of AI-generated classical music as a waste, at least philosophically speaking--the point of writing music is to experience its creation. Unfortunately the public would not think the same of AI-generated math because it would be considered "relevant" to scientific matters. But the same is true. The point of doing math at the highest level is simply to experience doing it.

The trouble is that if you want math to be standardized/able to be described in a sort of "objective" manner (what mathematicians call a proof), you'd like to start out with a set of axioms that are not themselves provable in the traditional sense but from which everything else can be proven. If you leave out infinity, it turns out that your set of axioms isn't really powerful enough to do anything, much less the kind of math that physicists require to describe the universe. If you keep it in, your set of axioms is SO powerful that you end up proving things that don't seem compatible with the physical world. There is no objective solution to this problem. The mathematical community chose the latter because, well, it helped us prove cooler and more sophisticated stuff. Some of that stuff is a beautiful way to describe the physical world (try googling something like representation theory), while other things make us question our intuition about it (i.e. string theory).

What people might not be understanding is that mathematics is inherently built... ZFC was pored over for years and eventually the community concluded it was a good system to (a) preserve most, if not all, of the mathematics that had already been done and (b) build more mathematics.

You can have gripes over whether or not pure math is compatible with the physical world but we're not exactly close to solving that problem... if we were, then physicists would have a much easier time lol

Find it funny that PromptArmor needed to reach out 3 times in a row to get a nearly month-late response that the issue "was resolved"

Math is particularly nice in that whole papers can be discussed/compressed into a single conversation, unlike, a scientific experiment which requires many figures and controls to confirm or deny one's hypothesis. It's why teatime culture is so great in academic math departments worldwide. I'd listen in at my undergrad institution and usually a single conversation between two professors at teatime could be written up into a paper if they really wanted to. During undergrad I was mentored by one of Bill's students, and he'd often comment that Bill's glib throwaways would usually be very profound if you thought through it carefully.

I think the author is really just getting at the fact that humans are by nature intelligent and by nature tend to think of similar ideas. So you can either unknowingly complete a project which is inevitably in some sense a replication of another project, or you can do the research first and realize it's partially a replication which is a bit disheartening. I think the solution might lie in realizing that completing a project for the sake of your own learning might be the most important factor. (This is easier said than done is when you are trying to complete novel academic research or when you are trying to make a profit off of your unique project.) But those, too, are more than forgiving to research that seem only to slightly tweak something that already exists.