>Don't. Calculus is going to become as obsolete and antiquated as studying Euclid's Elements
Yeah, as antiquated and obsolete that we basically have every high school student do it in the United States. You know, the class we call GEOMETRY. Because you do know, that high school geometry classes are just basically using cleaned up and modernized texts based on Euclid's Elements, right?
Sounds good. More people will study Calculus than ever before. Good plan.
Why are you not pasting the full sentence and blatantly strawmanning by taking my words out of context?
> high school geometry classes are just basically using cleaned up and modernized texts based on Euclid's Elements, right?
So you are admitting then that Euclid is too antiquated and required "clean up" and "modernization" to be presented to modern American audiences? Do those "cleaned up and modernized texts" still have you do compass and straightedge proofs? What about instruction in the use of an abacus?
Fuck modern mathematical algebraic notation too, let's expend paragraphs of ancient Greek to describe a mathematical object that would be one line in modern notation.
Your argument was utterly absurd on its own, no strawmanning was needed. Your followup here is also absurd and shows your complete lack of understanding of mathematics and its history.
> Calculus is going to become as obsolete and antiquated as studying Euclid's Elements and doing your own compass and straightedge constructions, or using an abacus.
What do you think is going to replace calculus? Until something better comes along, calculus is among the best introduction to higher theories of mathematics.
> LLMs have made obsolete the study and practice of...
It sounds like you're trying to say that Calculus will be replaced by LLMs. In fact it's the reverse: LLMs can get better by studying calculus and the higher math things that calculus enables.
> There is no reason to suppose mathematics is any different. You don't break out your pen and paper to compute change at the checkout aisle at the grocer's; you don't even have to punch numbers into a calculator, or indeed be numerate at all - just scan the barcode
Buddy, barcodes can be wrong. If you don't know how to do math yourself, you won't know when a sweet potato gets confused with a differently-priced yam. Or your new tablet with 5 year warranty gets scanned as a server CPU with 1 year warranty; then when your tablet dies at 4 years 11 months, your warranty was never activated, and your tablet is reported stolen.
> Look forward to the future described in Stephenson's Anathem where cutting-edge spacefaring nuclear technology is wielded by the literally illiterate
You may be right on that. But, in that world, the "literally illiterate" people will always be outshone by people who actually know how things work.
So are you bullish or bearish on the prospect of LLMs replacing programmers? The industry is breathless with hype and media pieces on how traditional programming is obsolete; do your criticisms of my position also apply, were software engineering, rather than calculus, its subject?
"bullish" and "bearish" are words that are useless in this context. Use them for stock markets where those words belong.
> LLMs replacing programmers? The industry is breathless with hype and media pieces on how traditional programming is obsolete
I believe LLMs fill a small (over-hyped) niche currently, but that niche will grow over time. I don't believe LLMs will, within our lifetimes, fill the specialized roles of high intelligence. It certainly will (and in many cases already does) fill the roles that don't require lots of thinking and intelligence.
Could LLMs replace programmers? Definitely, right now. Could LLMs replace developers? Currently, it could replace some of the worst developers, and help but not replace some of the better developers. Could it replace engineers? Definitely not right now, and probably not for the next several decades.
Is that a bad thing? To a lot of people, it is, especially in short term measured by job losses. But in the long run I believe LLMs are transformative in nature. Programming and development will be transformed to use LLMs as the tools that they are. Anyone who doesn't adapt to using an LLM will end up being a loser in their industry or be required to retrain to another role. That's generally good for the economy as a whole even if it's not great for the individual person.
You could manually do a lot of things that a CNC mill can do. Or you can learn how to use a CNC mill. Or you could pay someone else to use their CNC mill. But a CNC mill is not a great thing to use for cutting raw lumber or assembling furniture. You "could" use a CNC mill for it, but it'd be extremely inefficient. You could use it to manufacture furniter pieces, but it's not going to assemble them. LLMs are kind've the same thing for computers.
> do your criticisms of my position also apply, were software engineering, rather than calculus, its subject?
I think yes. Software Engineering (as an Engineering discipline) is used where it matters (eg, regulated aviation, safety, etc). It's not used much (if at all) for basic websites or even most games. But when it is used for these things, it's a much better product. That will pretty much always be true even with LLMs guiding the developer (not engineer).
For your example I replied to: I don't know much about nuclear reactors. But I know more than, say, 80% of the general population. I know enough to know that they can be dangerous but some designs are less-dangerous than others. Could I build a reactor myself? Probably, while the average person wouldn't even know where to start. I wouldn't do it without a lot more knowledge though because anything I come up with would be miles behind current state of the art in safety and procedure. I probably could identify nuclear fuel ores, but I have no idea how to refine it safely. I don't really care to learn that, it's not my passion. But I also know that refining it is dangerous if not done "properly" and so I wouldn't even want it as a hobby.
Contrast that with robotics. Robotics can certainly be dangerous, but not nearly as dangerous as refining nuclear fuel. I know how robotics work, and how to work with them with some modicum of safety, and so I do that as a hobby. That doesn't mean I would encourage anyone to come along and just use an LLM to build robots because they'd be missing out on sooooooo many fundamentally important concepts and would have to rely on the LLM to tell them what's dangerous or what's not and how to implement safety features and procedures.
> What do you think is going to replace calculus? Until something better comes along, calculus is among the best introduction to higher theories of mathematics.
> Programming and development will be transformed to use LLMs as the tools that they are. Anyone who doesn't adapt to using an LLM will end up being a loser in their industry or be required to retrain to another role [...]
Mathematics will be transformed to use LLMs as the tools that they are. Any mathematician who doesn't adapt to using an LLM will end up being a loser in academia or be required to retrain to another role.
The study of calculus will be replaced by tooling that carries out the mechanics of differentiation, integration, finding extrema, etc, making such education obsolete.
> You could manually do a lot of things that a CNC mill can do. Or you can learn how to use a CNC mill. Or you could pay someone else to use their CNC mill. But a CNC mill is not a great thing to use for cutting raw lumber or assembling furniture. You "could" use a CNC mill for it, but it'd be extremely inefficient. You could use it to manufacture furniter pieces, but it's not going to assemble them. LLMs are kind've the same thing for computers.
You could manually do a lot of things that a calculator, CAS, or LLM can do. Or you can learn how to use a CAS system or LLM, or pay someone to use their cloud service. But an LLM is not a great thing to use for deciding research programs or assembling a proof. You could use an LLM for it, but it'd be extremely inefficient. You could use it to formalize certain lemmata or minor results, but it's not going to compose them together into a larger theorem.
> Could LLMs replace programmers? Definitely, right now. Could LLMs replace developers? Currently, it could replace some of the worst developers, and help but not replace some of the better developers. Could it replace engineers? Definitely not right now, and probably not for the next several decades.
Could LLMs replace arithmeticians or calculators (in the original sense of the word, as a human occupation)? Definitely, right now. Could it replace mathematicians? Definitely not right now, and probably not for the next several decades.
You distinguish between Software Engineers(tm) and lowly developers; I point out that you can draw the same distinction between mathematicians and lowly arithmeticians or "calculators" (in the original sense of the term as a human occupation), or between calculus and analysis.
Leave the solution of this particular integral or the differentiation of this particular function, the mechanics of calculus, to the LLMs and the machines. Mathematicians need not concern themselves with such trivialities, and will prove results for all continuous functions in arbitrary metric spaces, or something similarly general and insightful.
> The study of calculus will be replaced by tooling that carries out the mechanics of differentiation, integration, finding extrema, etc, making such education obsolete.
What makes you think this time is different? We've had tools for those things for decades now.
