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Why teach calculus in the age of AI
- trod1234 1y agoAnyone have a mirrored link? Looks like the site is timing out now.
- q2dg 1y agoMaybe the question isn't "why" but "how"
- cubefox 1y agoBy letting the pupils do the "homework" under teacher supervision.
- 0xTJ 1y agoIt is shocking to me that people would seriously discuss not teaching calculus just because LLM tools exist. Computational math engines didn't make understanding how you solve an integral obsolete, but they can make certain tasks faster and less error-prone. This feels like a "tech bro" idea from someone who has never touched a SEM field (STEM minus the T).
- deadbabe 1y agoHow many people remember how to solve an integral?
- justonceokay 1y agoNot remembering U substitution of the top of your head is different than not being exposed to it. I remind you that Int(x^3 * 5x^2 + 7) == x^4/4 + 5x^3/3 +7x + C. Just from that alone I bet a lot of memories of integration slot back into your head, and you would know where to look up the parts you forgot. You can’t “brush up” on something you never learned
- rangerelf 1y agoIt doesn't matter if you can't solve a randomly-appearing-in-your-newsreel integral; it matters that you have the background knowledge of what an integral is, that there are rules to solving it, and you can read up on the rules and understand them. For the [current] layperson, each of those things I mentioned I might as well be speaking in Martian.
- 0xTJ 1y agoIt's not necessarily just about remembering every rule and trick you can use to simplify and solve integrals. Calculus is fundamental to understanding problems, from basic exercises in a first-year undergraduate physics course to entire fields. You'll (probably) never apply the ability out the kinetic energy vs. time of a ball rolling down a hill, but these exercises build understanding of the tools. Derivatives are everywhere in a fundamental electric circuits course, you need to have an intuitive understanding of basic calculus. The relationship between current through and voltage across ideal inductors and capacitors are directly described in the language of calculus, even if you're not "using" the calculus substitutions you learned each time you analyse a circuit. And good luck getting through a couple weeks of an introductory quantum mechanics course without using calculus as a fundamental building block. You can solve many of these problems with computers, but it's not going to build intuition on how to approach future problems. (I don't mean this as a joke or picking an arbitrary complicated-sounding topic; this is a core course in some engineering programs.) Many engineering problems have nice closed-form equations (at least to get approximations). Obtaining those equations often involves calculus, and someone has to do that in the first place. (I'm giving examples from the lens of my education, but each field of science, engineering, and mathematics will have their own context, and will vary from little-to-no calculus to being all-calculus.)
- dvrj101 1y agoif you actually spent good amount of time in mathematics during academia, you have developed neural networks for logical reasoning and problem solving but they get activated in life situations giving an edge compared to others. https://dibeos.net/wp-content/uploads/2025/08/what_happens_to_your_brain_when_you_study_advanced_math.pdf https://dibeos.net/wp-content/uploads/2025/08/what_happens_t...
- lokrian 1y agoThe question I keep wondering about is why teach anything, or what exactly is worth teaching.
- deadbabe 1y agoHow to use an LLM
- pavel_lishin 1y agoReading Pump Six will provide a partial answer.
- wrs 1y agoAnything where you care about getting the right answer?
- rangerelf 1y agoBecause, nature in its infinite wisdom, gets rid of what's not used. You don't use your muscles? They atrophy. You don't make an effort to travel without a gps regularily, to force your brain to remember your way around naturally? Your spatial memory atrophies and becomes useless [here: https://www.nature.com/articles/s41598-020-62877-0 https://www.nature.com/articles/s41598-020-62877-0 ] People don't need to learn math anymore, hence, no more calculus lessons? People are literally becoming idiots who can't calculate simple change at the cash register without pulling out their calculators. It's exercise. It keeps the brain itself from atrophying. It stops you from becoming a "wetware LLM" that's just parroting whatever echo of a thought (natural or otherwise) goes through it.
- yoyohello13 1y agoWhy learn anything? I for one want my brain to be completely empty, devoid of any thought or knowledge. Then I can simply pay OpenAI to think for me. Honestly, the trend toward anti-intellectualism in the world is very disturbing to me, and it seems AI is enabling this kind of contempt for knowledge even more.
- somenameforme 1y agoIt's not anti-intellectualism so much as people forgetting the reason we learn in the first place. It's one of the biggest downsides of going from a world where education was largely optional to one where people are largely shoved onto a treadmill from birth to college. So many people never stop think about why we do the things that we are simply expected to do, instead of doing other things.
- cultofmetatron 1y agoyou literally cant do regression analysis without calculus.
- deleted 1y ago[deleted]
- 9rx 1y agoNot teaching calculus does not imply not learning calculus.
- tptacek 1y agoNo? You literally can't derive regression procedures without it, but you don't need to. You can just do least-squares.
- srean 1y agoAlong the happy path yes. But when things break and you have to understand why, or you have to fix it, or even describe the problem in some detail that someone else is able to guide you to fix it, it sure helps to have an idea of how it works.
- y-curious 1y agoLike, on the backend? You can't run code without electricity, but FAANG doesn't teach that in their onboarding
- muldvarp 1y agoI genuinely wonder what even is worth learning in the age of AI. It just feels like learning stuff doesn't really matter anymore. Unless you're an expert in some field, a novice with access to an LLM will usually produce better results than you.
- HPsquared 1y agoYou still need a decent mental model and mathematical fluency to critically assess the outputs.
- muldvarp 1y agoCurrently. Although producing something yourself (especially if you're not an expert) doesn't guarantee high-quality output either.
- softwaredoug 1y agoThe most important skill with using AI is critical thinking. And that's really only honed by learning and questioning a lot of subjects. I don't use Calculus in my day job, but it was still valuable for me to learn to hone my ability to think
- florbnit 1y ago> And that's really only honed by learning and questioning a lot of subjects. Sounds like a job for AI.
- bregma 1y agoWhere will the experts come from in the future if no one learns and we just accept whatever the Markov chain generates for us from the Bayesian database of old information?
- tapoxi 1y agoGood question, but that isn't incentivized by capital. We're in an era of massive student loans and unaffordable housing. Unless there's a clear and direct incentive to learn, people will take the easiest path. Life is tough enough as-is.
- jameskilton 1y agoArticle has been hugged so commenting more along the comments here. Pharmacy school teaches Calculus. Why would that be? Do you need to run derivatives and integrals to fill prescriptions? No. Teaching maths, particularly calculus, teaches people how to 1) not make mistakes and 2) catch your own mistakes quickly. Vitally important skills for someone filling out live-saving medicine.
- jacobolus 1y agoThe point of learning mathematics is not to "not make mistakes". More strongly: the misconception that mathematics or mathematics education is about getting "right answers" as quickly and accurately as possible is a disaster for learning. A calculus class should ideally be making someone think much harder than that. Calculus is about understanding the relationships involved with continuous quantities and modeling the way things move and change. It is a basic prerequisite for understanding biochemistry and statistics, essential background for understanding pharmaceuticals.
- tptacek 1y agoI'm pretty sure this is a retcon. There are subject-matter-specific reasons PharmD's learn calculus. They don't use it day-to-day, but lots of STEM curricula (a) don't make sense without calculus and (b) don't lead to jobs where you're integrating by parts every day.
- 9rx 1y ago> Teaching maths, particularly calculus, teaches people how to 1) not make mistakes and 2) catch your own mistakes quickly. Vitally important skills for someone filling out live-saving medicine. Learning calculus achieves the same effect, though. It is not the teaching that is important (although some may find it useful).
- pharrington 1y agoYou literally need calculus to understand dosage response curves.
- aoki 1y ago
- TYPE_FASTER 1y agoI was lucky to have a high school math teacher who derived calculus with us. Understanding calculus made understanding physics so much easier. Being able to solve some physics problems using calculus seemed like magic. Of course, I've never had to use any of that knowledge since, but I'm glad I went through the process to acquire it.
- nathan_compton 1y agoI think its nuts anyone even bothers to teach physics without calculus.
- sn9 1y agoI'd rather they be exposed to physics without calculus than never be exposed to it at all. Calculus is an elective course in most schools.
- nathan_compton 1y agoCalculus should be taught to 10 year olds and it should be mandatory. I can't believe how much people in US are afraid of math.
- fooker 1y agoExactly. There’s nothing about the basics that can’t be grasped early. Sure you won’t be solving weird indefinite integrals or differential equations, but the concepts should be delivered early.
- sn9 1y agoWith sites like Math Academy, anyone who can afford the monthly fee will be able to learn not just calculus, but linear algebra and discrete math and probability as well at whatever age they want so long as they're willing to put in the work. I'm extremely optimistic about the future of mathematical literacy beyond the requirements for high school graduation.
- tonetegeatinst 1y agoI mean I think the bigger issue is that, at least for me, unless I am regularly using a skill I learn I forget most if not all of it. I trig, and calc 1 yet I hardly remember how to solve most problems because its not something I use regularly. Same with subnetting or remembering certain programming languages. I literally don't use these things 99% of the time and so I forget them. Sure I understand some of the basics and I could probably pick it back up way faster than someone who knows nothing but I am human.
- yoyohello13 1y agoI was recently studying some basics of quantum computing and had to re-learn a bunch of linear algebra. I thought I had forgotten everything, but when I sat down to review the material I picked it up very quickly (much faster than when I was in undergrad). It was like riding a bike. I think we think we forget, but the knowledge is actually dormant and much easier to get back. So I don't think forgotten knowledge is wasted, it's still valuable.
- alphazard 1y agoI wouldn't recommend a traditional calculus course to anyone. There's no reason to do derivatives or integrals by hand, and that's most of the course. The practical applications of running differences and running sums can be taught to people with minimal programming experience and without algebra. I've never done an integral by hand as part of any productive activity. Monte carlo integration and loops for multiply-and-add have proven incredibly useful. Why not teach those directly?
- fxwin 1y agonot to anyone? really?
- drivebyhooting 1y agoMany times you can speed up your code and boost accuracy by using higher order methods. What you describe, if I understand it rightly, is 0th order.
- tptacek 1y agoI'm early into Calc II right now (MathAcademy's equivalent of it), having started 6 months ago at a D-student's level of Algebra II, and I'm curious what the "right" calculus to learn would be. It's pretty clear to me as I work through problem sets that I'm never going to do any of this hand-computation in reality, in the same way that nobody computes eigenvectors by finding the roots of a characteristic equation. It's still fine by me, for 2 reasons: (1) because I'm doing this to replace the New York Times Crossword with something productive, and it's great for that, and (2) because every time I get annoyed at like messy trig derivatives with double-angle substitutions and stuff, I instead pivot to learning how to solve it with Sage Math, and so I get better at that instead. But if there's a smarter sequence, I'm super interested!
- jacobolus 1y agoFor a more conceptual introduction leaning on using computers, whose goal was getting STEM students up to speed to understand the context of work in their various fields, you might enjoy https://www.science.smith.edu/~callahan/intromine.html https://www.science.smith.edu/~callahan/intromine.html For something more traditional, take a look at textbooks by Piskunov, Courant, or Apostol. Spivak's Calculus has excellent problems if you are looking for something more abstract and rigorous (probably better after a first course). https://archive.org/details/n.-piskunov-differential-and-integral-calculus-mir-1969 https://archive.org/details/n.-piskunov-differential-and-int... ; https://archive.org/details/ost-math-courant-differentialintegralcalculusvoli https://archive.org/details/ost-math-courant-differentialint... ; https://archive.org/details/calculus-tom-m.-apostol-calculus-volume-1-2nd-edition-proper.-1-john-wiley-sons-inc.-1991/%28Calculus%29%20Tom%20M.%20Apostol%20-%20Calculus%2C%20Volume%201%2C%202nd%20Edition%20%28PROPER%29.%201-John%20Wiley%20%26%20Sons%2C%20Inc.%20%281991%29/ https://archive.org/details/calculus-tom-m.-apostol-calculus... ; https://archive.org/details/introductory-calculus-book-collection/Spivak%2C%20Michael%20-%20Calculus-Publish%20or%20Perish%2C%20Inc.%20%282008%29%281%29/page/n7/mode/2up https://archive.org/details/introductory-calculus-book-colle... Finally, if you want a strategy for those tricky integrals, per se, take a look at Schoenfeld's "Integration: Getting it All Together", https://files.eric.ed.gov/fulltext/ED214787.pdf https://files.eric.ed.gov/fulltext/ED214787.pdf ; some results of teaching the solution of integrals by this method were presented in https://www.jstor.org/stable/2320344 https://www.jstor.org/stable/2320344
- kylemaxwell 1y agoThe question makes as much sense to me as "why teach literature in the age of typewriters?" Not that the analogies are perfect, but the idea that it's not worth learning something because a related technology has advanced significantly is a non sequitur. There may be good reasons to learn or not to learn calculus, or literary theory, or anything else, but the existence of some related technology isn't it. I'd go so far as to suggest that perhaps calculus is even more important for some folks to learn in the age of AI (e.g. applications in neural networks), and we don't know who those folks will be in advance.
- rs186 1y agoIs AI even relevant here? Mathematica can do calculus and linear algebra better than most if not all college graduates since decades ago, but colleges are still teaching those courses. That should explain enough.
- rightbyte 1y agoI used Wolfram Alfa like 15 something years ago to explain book exercise solutions step by step in some algebra and differential equation courses.
- j45 1y agoCalculus is critical. One of the few moments in university was learning how so much was actually Calculus. Whether it was physics, chemistry, etc, the formulas I was given ften had a calculus version. It helped me open up to taking math and stats courses I never would have as a comp sci student, which in turn gave me a different perspective than just taking cs courses alone.
- Onavo 1y ago...how do you plan to do gradient descent if not without calculus? Seems like OP is trying to lock an entire generation into proprietary tooling.
- ryandv 1y ago[flagged]
- inetknght 1y ago> 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.
- ryandv 1y agoSo 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?
- inetknght 1y ago> are you bullish or bearish on "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.
- loudmax 1y agoI'd never recommend someone not learn calculus, but the average non-technical high school or college student would probably benefit more from learning statistics instead. Learning calculus is very valuable to a relatively small number of people. We should absolutely make calculus available to any student, regardless in advances in AI. But a lot more people, particularly non-technical or non-math type people, would benefit more from experience with statistics than calculus. Statistics, combined with an introduction to simple programming, should be part of the basic high-school curriculum.
- sn9 1y agoBoth statistics and calculus are usually electives, not requirements.
- lispisok 1y agoStats without calculus is like physics without calculus. Sure you can teach high schoolers to memorize displacement and velocity equations without calc but actual derivation and understanding requires calc.
- quantumcotton 1y agoMath is like language. You can have a translation book and sure it'll work if needed. But being fluent teaches you about an entire new world. Math teaches you how to think internally in an interesting way like algorithms of thought. Physics teaches you how the world works reading it is one thing. Understanding the language is where the beauty lies
- corimaith 1y agoAs somebody who aced calculus, what I was effectively doing was just being a human calculator mindlessly applying memorized differentiation and integration rules to get desired result. No real thinking or problem solving, which begs the question of why bother really teaching kids to be machines when machines can do such task. I would imagine the difficulty others had was more due to the way the topic was approached/framed rather than their executive ability to do predetermined tasks.