Proof you can do hard things

I <i>really</i> despise all the &quot;why you should care about math&quot; takes.<p>The question is never asked about any other school subject and only mathematics has to justify itself that way. I had to learn about categories of plants and animals, interpret 20th century literature, learn about events from a thousand years ago, I did presentations on the demographics of European countries, how certain chemicals react and much, much more. I never used any of that knowledge for anything, certainly not in my career or in university.<p>But somehow <i>mathematics</i> is the one field which needs to justify its own existence? Mathematics needs to bend itself over and &quot;be relevant&quot; so that people will actually learn about it? Why? Why not ask the same of any other subject.<p>Justifying mathematics is easy, especially such a universally applicable subject as calculus. But I see no reason why it should have to justify itself in any way.

This resonates a lot with me. At school I coasted, ignored all home work, never studied, and was a consistent C. I was continually told I could fo better by putting in some work (an objective viewpoint I agreed with.)<p>But i had better things to do. I started programming in grade 7, from a book, with a Apple 2 (circa 1982). There were no forums, no Internet just me and a thin booket that came with the computer, plus later, the odd magazine.<p>It was never &quot;hard&quot;, but it was fun. It taught me how to build things, how to approach problems, how to throw something away and make things better. How to imagine.<p>Ultimately I would study comp Sci- people would teach me the right way to program, and 40 years later it&#x27;s still my career. As I predicted at the time (somewhat obnoxiously to my then teachers, sorry Mrs Hodge), I had better things to do than raise my Geography score from a C to an A.<p>School is important, but finding something you enjoy, where &quot;work&quot; feels like &quot;fun&quot; is the truely &quot;gifted child&quot;.

&gt;You know they will never use it in adulthood, outside of certain career choices.<p>If somebody says stuff like this, then they do not understand math, imo.<p>Im a little bit sad whenever somebody argues for math by using &quot;no phone available at the moment&quot; argument.<p>Math is insanely powerful world modeling tool.<p>Starting from calculating right amount of fence for your garden, to estimation of 500km route arrival time while taking traffic statistics into the account, to data science, ML, whatever more complex.<p>Since math modeling is everywhere in &quot;modeling&quot; industries like engineerings, financial-ish jobs and other<p>Then you basically not only get better tools to operate (model) in real world, day2day life, but also it opens you doors to highly paid careers.<p>But the goal is not to have fancy jobs, but being able to do real world modeling.

I hate the framing of problems or domains as hard, since it kept me from pursuing them further for many years. And the years later when I tried my hand at those problems, I found that it wasn&#x27;t nearly as hard as it was being made out to be.<p>Historically many problems have also been hard until people figure them out, and then they stop being considered hard problems. In recent years this has been mostly true of AI-related topics.<p>A lot of people have achieved mastery over really hard problems and synthesized their learnings over countless hours, making the information much more easily accessible for future generations.<p>If you keep hearing someone talk about how some field is hard you should take that as an opportunity to challenge yourself rather than shy away from it. One field that has recently interested me is organic chemistry, which I&#x27;m interested in learning mostly because of how many people I&#x27;ve heard talking about how it&#x27;s so challenging. May I find a worthy opponent.<p>Edit: This is relevant to HN when talking about C and C++. People talk about these languages as if they&#x27;re some magical beasts, but in reality you can get really far with them by treating it as a serious endeavor. People will talk about how they don&#x27;t have full mastery over the language, but you don&#x27;t need anything close to that in order to be effective. If you know how to program in other languages you can pick up C++ just as easily and start being effective very quickly. No mastery required. It&#x27;s not that hard.

Self-image really is important, especially on the dimension of self-efficacy. There are compounding effects in both the positive and negative direction though.<p>I’ve used this same idea to dig myself out of ruts. When things are fucked up I’ll start paying attention to small things and deliberately “defer” progress on a few bigger things that are harder to do and more costly to fail. Each small win helps build momentum into the next-biggest challenge.<p>I’ve found this super useful for avoiding “habit destruction” during major life events&#x2F;travel&#x2F;moving.

I like the idea that &quot;If you can master these topics, imagine what other topics you could master if you put your mind to it&quot; — again, for the empowerment.<p>It&#x27;s not about a thing being hard. Walking is hard to a paraplegic. It&#x27;s about overcoming a thing and feeling good about it (instead of external rewards, like a piece of candy or good grades).<p>The real problem with school is that it replaces empowerment with gamification externalized rewards. You&#x27;re not learning calc for the sake of understanding the world, you&#x27;re doing it for a line item on a checklist. That doesn&#x27;t come with empowerment.<p>With the mere framing of &quot;you can do [hard thing] to prove you can do hard things&quot; is a bad framing because it could be anything — from doing calc, to bungee jumping, to drinking a gallon of milk (please don&#x27;t). This framing doesn&#x27;t actually lead to empowerment (and then self-improvement).

There are infinitely many hard things. It is hard to learn Japanese. We don&#x27;t require that every high school student attain basic proficiency in it though.<p>The reason we learn calculus in high school is because it is foundational for many advanced STEM fields, and we will yield better results during university for the small percentage of students who go into those fields by forcing everyone to learn it in high school. Or, moreso, that&#x27;s a viable justification for learning it today. Had history taken a different shape maybe we would learn something else, or maybe not. But the point is that calculus is not an <i>arbitrary</i> hard thing we learn for arbitrary reasons.

I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy.<p>To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus.<p>Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple things. That math is competitive and presented as a cryptic challenge is beside the point — it is designed to make it possible for anyone to reason for themselves and solve problems. The sense of impatience and criticism around math is totally unwarranted and isn’t good for anyone.<p>I get kind of bummed when I see schools spending so much creativity and enthusiasm on art and theater. There really is no reason why science should be thought of as judgmental, difficult and painful, while putting on a play is creative, inviting and fun.

Everyone commenting so far seems to be missing the forest for the trees. Doing hard things, and the proof that comes with it, is empowering.

People (and employers) who can truly appreciate calculus wouldn&#x27;t be impressed with a taken calculus course (thousands of students take calculus every year) or even a math BSc, and those who can&#x27;t, how would they assess how hard your calculus course really was? There is no competition in a typical calculus course. Better ways of signaling the ability of doing hard things, especially for kids, in my opinion, are math&#x2F;programming&#x2F;etc contests. That&#x27;s where you have a real competition and can show what you are capable of relatively to other people who participate and want to win. Also, it&#x27;s important to note that passing a calculus course includes not only watching lectures or reading a textbook but also extensive problem solving. Typically &quot;hard&quot; college math courses are about memorization of abstract concepts, and taking any of them doesn&#x27;t really prove you can do hard things (I&#x27;m not talking about PhD where you need to make novel contributions, thats crazy hard if you want your research to be competitive). Thats my experience and perspective but I&#x27;m living in my bubble.

I lost interest in school around the 10th or 11th grade. I never took any math classes beyond what was required to graduate way back in &#x27;96 in Florida. I also didn&#x27;t go to college.<p>I&#x27;ve been a professional web developer since 2005 and a development manager (who still codes) since 2017. I don&#x27;t understand the first thing about Calculus or even logarithms. I&#x27;m sure if I did, I&#x27;d probably be a better developer. I&#x27;ve had employees try to explain to me fairly basic log notation and my eyes just glaze over. It&#x27;s never impacted my abilities, nor the respect and admiration I get from them as a well-experienced and knowledgable developer, but I can&#x27;t help but feel ignorant.<p>I need to go back to the basics and work my way up; I&#x27;ve lost a lot of it. Where do I start? Kahn Academy?

&gt; You know they will never use it in adulthood, outside of certain career choices.<p>Just going to register my dislike of this particular trope. Mostly because &quot;certain career choices&quot; is doing a huge amount of work. &quot;Certain career choices&quot; can give you access to a very high income. They can give you access to a deeper understanding of some pretty interesting stuff and put you in a position to accomplish all sorts of amazing things.<p>People use calculus in the sciences, of course, but also in business, the arts, music, politics, and beyond.<p>We learn calculus when we&#x27;re young as a part of expanding ourselves, casting the widest possible net to find that intersection of what we&#x27;re good and and what we&#x27;re excited by. And to fill our quiver with as many arrows as possible for when we hit the adult world. And, of course, to build our self-esteem by showing ourselves we can accomplish hard things.<p>But I would highly recommend against taking the attitude that &quot;you&#x27;ll probably never use it.&quot; That&#x27;s counter-productive. And the people who &quot;don&#x27;t use things&quot; are boring...

&gt; But I recently realized there is a very good reason to take Calculus. It’s to prove you can do hard things.<p>While I do like mathematics (thus I clearly have no negative feelings about learning calculus), this argument is dubious: the longer I live, the more I realize that the capability to learn complicated scientific stuff (including mathematics) hardly does transfer to other areas of life.<p>Just consider this: if such skills transferred so well, one would expect that those people who make a steep career in companies have learned lots of insanely hard stuff, often hard mathematical and scientific stuff. The reality is that the people who have such a steep career are rather great &quot;policitians&quot; (in the negative sense), sycophants and self-promoters. On the other hand, learning hard scientific&#x2F;mathematical stuff nurtures the personality trait of &quot;no bullshitting&quot; and developing less tolerance for claims that clearly cannot be abided by.<p>Thus: I really like learning hard things, but this personality trait is in my opinion often a career killer.

From that perspective, going through <i>any</i> kind of struggle (and building willpower&#x2F;discipline) would be a good enough proxy for learning calculus.<p>It’s a little sad that the best value that the OP can impute for learning calculus is masochism — I cannot imagine saying that for anything in the school curriculum that I <i>actually learned&#x2F;understood</i>. I wonder (in good faith) whether the OP actually even absorbed calculus at all… (i.e. can they solve calculus problems even today, for example?) — if not, they’re not the person who should be making authoritative comments on the usefulness of calculus.<p>Calculus (Taylor approximations, perturbation modeling, error propagation, significant figures in measurement precision, gradient descent, etc — just off the top of my head) is so deeply embedded in my thinking, that it strongly shapes how I think and amplifies my effectiveness!<p>I disagree with the OP’s claim so fundamentally — they might as well claim that schools&#x2F;education focus on literacy for the same reasons.

I agree in principle that your personal story is made of the rough things you&#x27;ve overcome, and it&#x27;s refreshing to hear it stated in a positive way (calculus) as opposed to the usual negative way (abuse, alcoholism, etc). It misses something, though: Many people will slack endlessly on doing the hard thing until it appears to us to be a challenge we&#x27;ve come up with <i>for ourselves</i>. Then and only then does doing it the hardest way possible seem not just worthy of our time, but essential to our personal growth.<p>I&#x27;d argue that as long as someone reaches that attitude toward <i>something</i> that <i>they choose</i>, they have lived a good life. And that something doesn&#x27;t need to be a high school math class. The hard thing could be trying to become a chef when you&#x27;re 50, or deciding to write your next app in Assembly knowing none at all, or surviving a month in the woods, or going to a foreign country with the intention of learning the language. It has to be hard to make it worthwhile, but it has to be your own to make it valuable as an accomplishment to you, as opposed to something imposed on you which you merely endured. I think this is why a lot of people come out of incredibly hard ordeals in the military with much less personal sense of self-worth than they were sold they would get going in.<p>[edit: removed a critique. I had misinterpreted the words &quot;errant period&quot; to allude to something other than punctuation. My mistake.]

It&#x27;s a bit sad that calculus remains the stereotypical example of difficulty in most curriculums. Throughout childhood, I remember it seeming like some sort of complex, inscrutable, untouchable phantom hanging in the distance at the far end of the high school math course progression.<p>If somebody had told me that calculus is how you transition between dimensions, or that techniques of integration would enable me to generate 3D shapes from 2D lines, I think I would have been much more motivated to progress rapidly in math, and much less discouraged when I hit the &quot;hard parts.&quot; Those are the answers I tend to give today when somebody asks me, &quot;why take calculus?&quot; Demystifying it doesn&#x27;t even have to be a wholly practical explanation, like deriving acceleration from velocity.<p>Segregating out the &quot;hard stuff&quot; doesn&#x27;t even necessarily lead to great learning outcomes, either. At my high school, and it seems many others, the honors kids were put on the track leading to calculus while everyone else ended up in a dedicated statistics class. The honors kids were expected to pick up statistics through supplementary assignments in their laboratory science classes, and this same approach carried over into lower-division undergrad. As an adult, I feel like that approach has only given me cause to go back and seek out a firmer grounding in statistics.

You take calculus to understand the nature of change over time, which is the foundation of physics.<p>The formulas to do integrals aren&#x27;t important but the concept of integrals is.<p>Honestly I think we should try to focus on differential equations instead but maybe it&#x27;s necessary to do calculus first.

Don&#x27;t do hard things that are unrelated to your actual goal; they&#x27;re in unlimited supply, and you could be doing hard things that are relevant instead.<p>This essay wouldn&#x27;t have impressed me in middle school; I don&#x27;t know why it&#x27;s on our front page.

&gt; ... teenager asks why they need to learn calculus<p>&gt; But if we avoid hard things<p>I don&#x27;t see how you can justify the former by arguing the latter. These two are orthogonal. If I were that teenager, I think what I really would want to ask is that why it has to be calculus instead of some other things that is also hard but with obvious real world application like writing a small 3D game engine.<p>And my answer to that question is you probably shouldn&#x27;t if your were in an ideal education system. You would be taught what interesting interactions you could have with the physical world, and be induced to discover calculus or some other math tools that helps you understand how the interactions really work and demonstrates you really need such tools. You&#x27;re more likely to grasp them when you&#x27;re driven by curiosity.

To me what&#x27;s more important than Calculus being hard, and I think that&#x27;s especially true for maths more broadly is that it&#x27;s beautiful and one of the fundamental ways how we can make sense of the world. Everyone benefits from doing some maths.<p>I studied maths in uni and while I&#x27;ve not used it much, even as a programmer, I still enjoy doing it. My dad never had much schooling but now that he&#x27;s retired he actually picked up a few of my books and slowly worked through high school to now undergraduate courses. He&#x27;s having a lot of fun with it.

Not to distract everyone from complaining about calculus, but this reminded me of something I heard from a person with a Ph.D. in astrophysics from Caltech. They were not working in astrophysics, but they said the degree was still quite valuable to them. Whenever they had trouble learning something, rather than feel stupid, they reminded themselves: “I have a Ph.D. in astrophysics from Caltech, so I am definitely not stupid. This is just <i>hard</i>.”

There&#x27;s some nice seeds of ideas here, but it&#x27;s all a bit lost in<p>(a) brevity - it&#x27;s a deep topic so the post length can&#x27;t do it much justice &amp;<p>(b) naïvety - their extremely oversimplified explainer for the “C students hire A students” trope is that the C students are actually secret A students in other areas. This assumes a utopian world where academic-style assessment of study&#x2F;effort maps to career progression. C students do well for a range of reasons including-but-not-limited-to: charisma, nepotism, unconscious-bias-hiring on the basis of race&#x2F;gender&#x2F;accent&#x2F;height&#x2F;hair&#x2F;appearance, normative mental health characteristics. It&#x27;s not because of their secret extracurricular study: that&#x27;s in direct contradiction of the message behind the trope.

&quot;My goal with our kids is to avoid lying to them as much as possible.&quot; ← Thank you. Why is that so difficult for parents to do?

I took calculus in High School just so I could make a comment here saying I did so. It almost cost me my diploma as I didn&#x27;t want to do the homework. I paid attention in class though and learned just enough to pass the exams.

Some things which are hard for someone might be easy for someone else. Usually academic things like calculus are seen as hard, but there are many hard things in day to day life, like selling anything to unwilling buyer, handling a rude customer with calm and much more. They too are hard and calculus guys can not do them well.

Learn calculus because it is beautiful.<p>Newton had discovered the law of gravitation, but didn’t publish it for a long time because he couldn’t justify how the gravitational effect of a sphere could be the same as if all its mass was concentrated at a point in the center. He had to invent calculus to prove it. Isn’t that amazing?<p>I know the author is using calculus as an example of a hard thing, but if someone is genuinely following their curiosity, then things do not seem hard. Personally I wouldn’t want to work on hard things just to prove to myself that I can do hard things. I’m happy being lazy.

I think there is an similar argument for Greek and Latin in grammar schools. And the same for ancient Chinese in Chinese schools. Partly for cultural immersion and partly for brain gymnastics.<p>Math, and proof based Math such as Number Theory and Analysis is definitely in the same league if not for a career in academics.

&gt;But I recently realized there is a very good reason to take Calculus. It’s to prove you can do hard things<p>Doing hard things proves you can do hard things. Where does calculus enter into it?<p>&gt;The more hard things you push yourself to do, the more competent you will see yourself to be<p>&quot;The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.&quot;<p>&gt;Most C students are not doing other hard things instead of school. They’re just goofing off, so they end up working for the A student.<p>This is ridiculous. Author goes on to imply these (&quot;most C students&quot;) are on social media and using drugs. I&#x27;d put any money on them being much more likely to have been raised by the type of parent who believes their kid needs a reason to want to learn calculus.<p>Oh, and what is &quot;hard&quot; by the way? Is it doing something you&#x27;re not good at until you&#x27;re good at it? Does it need to be valuable from my perspective or that of my parent? Should it take a certain amount of time to become &quot;good&quot; at it? When am I good at it? Can it be a hobby I enjoy even while it&#x27;s difficult, or must it be a chore? What if I&#x27;m forced to overcome some hurdle in my life for example growing up with a foolish parent with warped worldviews?

&gt; But I recently realized there is a very good reason to take Calculus. It’s to prove you can do hard things.<p>This doesn&#x27;t explain why Calculus over any other number of hard things.

I raised the same questions as Nat, but I think he hasn&#x27;t really discovered why we were asking that. The reason why I was looking for a good reason to study calculus is because I was lazy, and if I&#x27;m lazy enough then I can change the definition of what &quot;hard&quot; means. For instance, I could convince myself that if my could teach calculus, and him being just another dude, then surely I could learn calculus.<p>I would also be cautious about setting yourself up for a hard life. The takeaway resonates well with the HN crowd, myself included, because we like challenging ourselves. There&#x27;s a lot of people out there who are simply looking to satisfice their lives, and you&#x27;ll need another way to motivate them to learn calculus.

The reason to learn calculus is because, as soon as you grasp it, you will start to see it everywhere.

Calculus is important, because (among other things) the proper definition of limits teaches you how to manipulate logic quantifiers.<p>In any case, IMHO best advice to young people - try to learn hardest things you can. Later, there will be less time, less energy and more distractions.

Feels like many other comments here are trivial objections for the sake of sounding contrarian. Or even, humble bragging about how easy math was to the commenter. I found the article to be a great, new (to me), and widely applicable perspective on the matter.

I always felt like linking education to direct use of the knowledge is missing the point. It is irrelevant whether or not you&#x27;ll need the knowlege you learned in school or at uni. What matters is your learnability, and that&#x27;s the muscle you train with education. Learning smth just to use it to get paid for it is the lowest form of learning; the whole point is to acquire ability to learn whatever quickly so that you can become proficient in whatever is needed in the future, which in turn gives you an edge in the talent pool. In that sense the central point of the article is 100% valid - it&#x27;s all about track record

Learning difficult concepts is only one aspect of developing perseverance - which is probably the greater ability to master. Others are finishing what you start, developing habits to complete undesirable tasks (like regular exercise or doing the dishes) and overcoming fear.<p>The latter is something you see creep in as you get older and it&#x27;s something that&#x27;s always attracted me to hobbies that require you to keep your nerve like skiing, scuba diving and flying planes. There&#x27;s nothing like having to land a plane solo with a bit of a crosswind to give you confidence in yourself.

As Hilbert put it, “Every boy in the streets of our mathematical Gottingen understands more about four-dimensional geometry than Einstein. Yet, despite that, Einstein did the work and not the mathematicians.&quot;

What&#x27;s it really mean to be hard?<p>Some things are vaguely impossible, like finding a solution to fluid mechanics, or finding a theory that combines quantum mechanics and general relativity.<p>Others are proven to be impossible under some conditions like the halting problem.<p>Others still require access to some amount of resources, or some amount of leverage, like buying a $100M yacht.<p>Lots of these hard things are quite unlikely for me to be able to do.<p>I think most people refer to the resource one? And that some people have more access to resources than they think, and the scales of resources needed are smaller than assumed?

It’s really interesting how we shy away from some “hard” things, even though there is literally nothing at stake that could prevent us from doing them. Nothing life-threatening, no (or minimal) risk of physical or psychological damage, no social exclusion, no irreversable decisions about the future to make. Why can’t we just try&#x2F;do it – what are we so afraid of?<p>Many people (especially those in a lucky environment) can just try to draw realistically (which is actually not that hard, given a good teacher&#x2F;instruction), study a “hard” topic in philosophy, get good at playing a “hard” song on an instrument or even learn how to prove mathematical statements or how to model and analyze complex systems. We can <i>just</i> try, there is nothing at stake except our time and energy.<p>When something is really interesting to me, I try not to stop myself from pursuing it just because it is considered “hard”. I have many mental issues (executive dysfunction, bad memory, etc.) but I am also stubborn and curious enough to try anything, again and again if I have to, which I never regretted. It doesn’t hurt and it can be so much fun with a humble and relaxed attitude and especially if I don’t try to compare myself to others, which might be one of the main things that is holding most of us back.

Same reason you should be able to do pullups or deadlift twice your body weight. To paraphrase Socrates: no one should live their life without learning what they are capable of.

The only things in life that are hard are the things you don’t want to do.

There will come a time when you have enough money, enough of everything, and deeper questions will arise. What is the meaning of existence? Why is there anything instead of nothing?<p>You will see that math plays a very fundamental role in our reality, and once you start seeing it in such a manner it may begin to interest you.

One of the dumbest things I’ve ever heard a math teacher tell me&#x2F;the class is “you’ll probably never use this outside of this classroom”! And I’ve heard this story before, so it seems slightly common?<p>I entered college without a rock solid foundation in mathematics and it made things much more difficult.

&quot;If you do weightlifting then sleep deprivation from a newborn is easy&quot;<p>Right. Tell that to my partner, who has been nursing our newborn every two hours for the last 5 months. There is no way to wake up 2-4 times every night for months and not be tired.<p>Weight lifting would be zero help with that.

I don&#x27;t know anything about Calculus. My time is school was mostly spending a year in class studying to take a single test so that the school got more government money. But I will say that when a bunch of people online carry on about how hard something is, it makes me want to try it. Usually it turns out that what ever they were saying was hard or impossible is difficult and time consuming but not impossible. The hardest part is getting over how other people have built something up as impossible.<p>But perhaps my FU-mode is stronger than other peoples. Someone on here said I&#x27;d never work for a FAANG company, so I guess that&#x27;s something I&#x27;ll have to do just because. Not impossible.

There’s a difference of having to do and wanting to do hard things.<p>Most people pass a class because they have to for their degree.<p>Most people raise a child while being sleep deprived because they frankly have to.<p>When people want to do something, they don’t need to prove to themselves that they can do hard things because difficulty hardly matters to one with their mind set on something. For example anyone who decides to run a marathon one day.<p>Instead for the things you have to do, one could reframe the “have to” with a “get to”. Gratitude is empowering. Not everyone gets to go to college. Not everyone gets the opportunity of being a parent. Etc.

I thought &quot;doing hard things&quot; would be something like a running Marathon, studying or working while having toddlers, learning to be a pro coder as an adult, taking care of your close ones while they are sick.. But it was about doing basic math.<p>Proving to yourself or anyone else that &quot;you can do hard things&quot; since you did more or less math in school&#x2F;collage&#x2F;university will leave you trainwreck at the first real hard thing that bumps your way.<p>And why some people don&#x27;t do the math? I guess, because they are told its boring and&#x2F;or hard, but they should do it anyway. And people don&#x27;t like to be told what to do.

I am not good in calculus and that&#x27;s something I wish I did pick up when it came to it.<p>The harder thing was keeping the pressure up to pass the tests and in total, pass a course, while dealing with the severe discomforting exhaustion of coming in early in the morning for classes, having to understand rather complex abstract notions. I still cannot think when tired or even inebriated. But going through that was really to get that good pencil pushing job reserved for college graduates, no? :D<p>Instead, in the end, I like what I do and if the spirit moves me or need it for something, I would sharpen those calculus skills.

Funny, First semester of calculus I got a C i think, second semester, I failed. I thought about going back to community college and taking a calc class just to see if I can actually pass it. No reason other then that<p>I suspect I could have passed it with better teaching. I hated that I had to memorize things, which felt tedious, not hard in a good way. If you dont memorize cos,sin,tan stuff you can&#x27;t take tests fast enough. The class was just how good can you memorize things. I also hated the proofs, pages of proof. No idea why, and the teacher didn&#x27;t speak english well or communicate well in general

So you proved to yourself that you can do hard things, what then? You don&#x27;t need to continue proving the same, doesn&#x27;t then that stop being a fuel for motivation? That&#x27;s what happened to me at least.

It&#x27;s not the point, but a lot of people are going on and on about the lack of need for calculus as a programmer. If you even touch how any machine learning works it&#x27;s all basic calculus and intermediate linear algebra under the hood.<p>Sure most people can get a long way without understanding anything under the hood but I think I am better developer knowing assembly and architecture. The same for ML, you can get by most of the time. You can also make a whole career not doing hard things. That&#x27;s not for everyone.

This comment is not for or against calculus.<p>Doing random hard things in order to get into college or get a white-collar job is really no different than pointless test preparation that shows you can follow instructions, and it has produced strange hierarchies such as Qing-era mandarins.<p>Much better to find something that intrinsically motivates you to do hard things that feel less hard to you. It&#x27;ll take you further. Or you can prove to the world that you are capable of a yearlong mindless grind...

I don&#x27;t want to be overly rude, but this is nonsense. The reason to learn calculus is that it&#x27;s incredibly useful in several domains and never learning it prevents you from become a skilled practitioner in those domains which in turn reduces your future earning potential.<p>Basically: <a href="https:&#x2F;&#x2F;www.smbc-comics.com&#x2F;comic&#x2F;why-i-couldn39t-be-a-math-teacher" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.smbc-comics.com&#x2F;comic&#x2F;why-i-couldn39t-be-a-math-...</a>

It&#x27;s better to avoid waste, waste of time, waste of calories. Most of the things that most people want you to do are wasteful, pointless, better to not be done. A very valuable skill is to be able to discern bullshit, and decline it.<p>(As an aside, the idea that calculus is hard is a pedagogical failure. Calculus is easy to learn if it&#x27;s taught well. Most of our education systems actually make learning much more difficult than it is.)

I like this approach as well.<p>My current explanation for this is more along the lines of being well-rounded. By being exposed to a number of different skills and learnings throughout your education, your more likely to be able to connect the dots in other areas - and just hold better conversations with people.<p>Don&#x27;t need to ace all your classes for that, but put in the effort to try and structurally understand whatever it is you&#x27;re coming across.

My bf learnt how to do hard things soon enough (mostly against his own will I admit) and I wish I could find the strength to emulate him in a way.

I think the better way is to come out with a lot of interesting real world scenarios that require calculus or other math. Math doesn&#x27;t get created out of a vacuum. It was created for a reason. I think if we can avoid diving into abstractions too quickly and focus on specific real world problems and lead the kids step by step to the solutions , that would be more interesting.

You should do calculus because it translates to actual problem-solving. Not everything is nice and chunky in discrete - calculus allows you to model and calculate continuous kinds of problems. Even if its not the area under the curve or some infinite series thing, it&#x27;s a really good intro to modeling things in terms of adding up many small steps.

I can do hard things but loss of sleep from a newborn is still hard. This guy prob didn’t do overnight feedings for his kids

You take maths because it shapes your brain, it forces new neuron connections to be formed in the right side of your brain. Then you also have literature and arts for the left side.<p>The brain is like a muscle, if you don&#x27;t train it, it wont grow AND you will basically be STUPID. That is it.

For some small percentage of high schoolers who can learn calculus, that knowledge will be worth ~100k a year for 40 years- and worth far more than that for their bosses. We can’t tell in advance who is in that percent, so we hedge by teaching it to all of them.

Of course, one thing a solid mathematical education will also give you is an appreciation that while ‘having passed AP Calculus’ implies ‘can do hard things’, that does not mean ‘having failed to take or complete AP Calculus’ implies ‘can’t do hard things’.

Am I just hopelessly old fashioned? Or is this not most of the justification for bachelors degrees?

Attending a good college is also useful in the same way. &quot;I went to Stanford, I should be able to figure this out.&quot;

I am not convinced „doing hard things“ should be a top priority for kids. For my own kids -or actually everyone- i hope they find a passion big enough to make a living. This takes time and lots of experimenting and cannot be forced into existance. Grinding through „hard things“ can leave you with a great deal of confusion. It is so much easier to do „hard things“ if you love doing them. The problem with math is: it is very hard to learn later on in life. Maybe even as hard as drawing. Schools should really focus on reading, drawing, writing and math- everything else should come secondary.

I can do hard things that I am interested in, that is true. But I also have this theory that nothing can be proven, but I can’t prove it.

I mean, I found learning calculus to be fun and rewarding in its own right! It can be challenging at times, but also beautiful.

I don&#x27;t think this is the reason you learn calculus in school, but I do think it is a good reason to learn it.

This is similarly true for finishing a degree. Luckily, that occurred to me before finishing a degree, because that did feel futile. But finishing a degree proves that you can finish stuff. That&#x27;s valuable proof for yourself and when you need to give an impression.<p>The topic itself really doesn&#x27;t matter that much -- which is also good, because then you can freely choose it to your liking, if possible.<p>TL;DR: I think this is very helpful advice to people who question stuff.

Conversely, hard domains are the only ones where you can achieve mastery.

I liked calculus because it was hard things that you could prove.

lol. it tends to be pretty flimsy proof, especially in light of the expanded horizon.

This echoes in my soul

prove to who? i refuse to prove myself to them.