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Have mathematicians become "less savvy" since the invention of the abacus or calculator? The invention of logarithms or analysis? In some ways, the answer is tr
by dvt 1mo ago
Have mathematicians become "less savvy" since the invention of the abacus or calculator? The invention of logarithms or analysis? In some ways, the answer is trivially positive. In fact, number crunching was, for most of human history, a key element of being a maths researcher.
However, when we look at the claim with a more critical eye, it becomes obvious that this view is myopic. In fact, current progress is in fact indebted to the invention various tools, which has led us to grand theories and hypotheses: things the Ancient Greeks could only dream about.
Is coding about writing assembly? Is it about writing boilerplate? About writing endless if-then statements? I would argue that it is not: it's about coming up with ideas, building products, finding customers, iterating, producing code that's easy to read, easy to understand, easy to extend.
Coding (at least the kind LLMs do) was never really the hard part, and I'd like to know specific examples of savvyness the author is losing. They've made me more critical of code and able to create better patterns, simply because I can iterate so quickly.
- grebc 1mo agoI’d argue you’ve got a very VC focused view of coding.
- pintert3 1mo agoI think he means the savviness in the art of programming the ideas. The skill and art involved in finding interesting and efficient ways to effect ideas and solutions to problems. It is(or was) fun for a good number of us who joined before AI changed the game. Now its dismissed tending to a waste of time, hence the supposed loss in savviness over time.
- me2too 1mo agoAuthor here. You described it perfectly. That's precisely the idea I wanted to describe in the article
- adamddev1 1mo ago> Have mathematicians become "less savvy" since the invention of the abacus or calculator? The invention of logarithms or analysis? This is not a fair analogy. Those things are like compilers, languages, and type-checkers. They are deterministic, carefully proven, hand-crafted tools, that allow people to go safely to a higher level of abstraction and still make things in a deterministic way. The jump into the fuzzy world of LLMs is a completely different thing. It's different than the jump from assembly to a higher-level language.
- dvt 1mo agoNot sure how much frontier math you follow, but probabilistic arguments are extremely popular (particularly in, weirdly enough, number theory), especially for fiddling with the bounds on things, or getting closer to full coverage of various theorems. So this idea that doing math is some kind of fully deterministic & mechanistic process is a bit misleading.
- adamddev1 1mo agoRight, programmers also use randomly generated info from property based testing for example? But I was referencing the analogy to the abacus, calculator, logarithms, analysis, and higher level languages.
- luke5441 1mo agoIs that kind of argument something like where you count the number of cranks claiming P=NP and the number of cranks claiming P!=NP and then if you get 95% papers claiming P!=NP that one wins?
- dvt 1mo agoWhat? Not at all. I'm referring to things like discussing distributions of certain things or probabilities of things as we go towards infinity, etc. These are proper papers, not surveys.
- luke5441 1mo agoBut if a LLM writes such a paper, how do you know there aren't any issues in it that cause wrong probabilities/distributions?
- dvt 1mo agoYou don't, that's why you review it (just how you would handle a real human submitting a paper). The main issue with LLM papers is that they tend to be very dense/circuitous or—because LLMs don't truly understand what they're doing—have the wrong focus. An LLM might spend pages on a trivial result, but quickly gloss over a truly remarkable finding. Terry Tao talks about this challenge in some of his blog posts and interviews, it's pretty interesting.
- _the_inflator 1mo agoDid you study math? I did and I cannot relate to your comparison. Mathematics isn’t about calculating numbers but formulas and proves. I have to put it politely: until the advent of AI no machine ever “calculated” a formula for me, because I didn’t have to calculate anything. It is like driving a Tesla and laughing about the manufacturer when he mentions how hard it is to get the product right, because you have an easy ride. I can relate to the article’s AI depression sometimes. Whatever comes to your mind, AI makes it happen in a couple of minutes in most cases no matter what you imagined. You invest days and the AI just build it is a couple of minutes way better than you and your 10 teams together did before. So much hard work and sacrifice - and now? Poof - there it is. It is nice but also depressing. And not being challenged is the actual problem.
- coldtea 1mo ago>Have mathematicians become "less savvy" since the invention of the abacus or calculator? The abacus and calculator doesn't do high order thinking or prove theorems for you. Math as a field aren't about manually adding numbers together or doing simple algebra formulas, and wheren't that even 2000 years ago. Those calculators are to math what something like an IDE or a helper library is to programming. The analogy would be with theorem provers, and even better, with the exact same tool as in the programming case: LLM doing the proofs. If mathematicians had LLMs and theorem provers do their job, they'd certainly have gotten "less savvy". And if they let them write their coursework, starting from university, they'd might never even become savvy enough in the first place.