> 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/do it – what are we so afraid of?

Heh, I don't know about that.

I got into motorcycles because of how dangerous they are. When I was just learning dirt riding I specifically picked out an old barely used logging road to do so. It's 2 hours from the nearest town, about 40 miles long winding road with a sheer drop on either side.

Getting there is tiring in of itself. Every time I started it, I was already fatigued from the ride out and I just go straight in without a break. But there's very little room of error. There's no cellular service, traffic is almost non existent. I don't tell my family when I got out there or where I am exactly. If I overcook a corner, loose focus for more then a second, fail to spot where the road's been eroded out, make just one little fatigued induced mistake... that's it. There's no getting out. There's no help coming. They won't even have my body to bury.

Finding the strength to crank the throttle wide open and hold it open right until the last millisecond before disaster is hard as hell when every instinct is screaming to slow down.

But in many ways, it's easier then trying to make friends or ask a someone out on a date. If and when I do make that fatal mistake, I don't have live with the knowledge that I screwed up a relationship or have to live with the regret what may or may not have not have been. Or worse; disappointing those who's opinion has weight.

Dying is easy. Living with the consequences is hard.

I really despise all the "why you should care about math" takes.

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.

But somehow mathematics is the one field which needs to justify its own existence? Mathematics needs to bend itself over and "be relevant" so that people will actually learn about it? Why? Why not ask the same of any other subject.

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.)

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.

It was never "hard", 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.

Ultimately I would study comp Sci- people would teach me the right way to program, and 40 years later it'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.

School is important, but finding something you enjoy, where "work" feels like "fun" is the truely "gifted child".

>You know they will never use it in adulthood, outside of certain career choices.

If somebody says stuff like this, then they do not understand math, imo.

Im a little bit sad whenever somebody argues for math by using "no phone available at the moment" argument.

Math is insanely powerful world modeling tool.

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.

Since math modeling is everywhere in "modeling" industries like engineerings, financial-ish jobs and other

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.

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't nearly as hard as it was being made out to be.

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.

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.

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'm interested in learning mostly because of how many people I've heard talking about how it's so challenging. May I find a worthy opponent.

Edit: This is relevant to HN when talking about C and C++. People talk about these languages as if they'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't have full mastery over the language, but you don'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'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.

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.

I’ve found this super useful for avoiding “habit destruction” during major life events/travel/moving.

I like the idea that "If you can master these topics, imagine what other topics you could master if you put your mind to it" — again, for the empowerment.

It's not about a thing being hard. Walking is hard to a paraplegic. It's about overcoming a thing and feeling good about it (instead of external rewards, like a piece of candy or good grades).

The real problem with school is that it replaces empowerment with gamification externalized rewards. You're not learning calc for the sake of understanding the world, you're doing it for a line item on a checklist. That doesn't come with empowerment.

With the mere framing of "you can do [hard thing] to prove you can do hard things" is a bad framing because it could be anything — from doing calc, to bungee jumping, to drinking a gallon of milk (please don't). This framing doesn't actually lead to empowerment (and then self-improvement).

There are infinitely many hard things. It is hard to learn Japanese. We don't require that every high school student attain basic proficiency in it though.

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'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 arbitrary 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.

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.

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.

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't be impressed with a taken calculus course (thousands of students take calculus every year) or even a math BSc, and those who can'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/programming/etc contests. That'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's important to note that passing a calculus course includes not only watching lectures or reading a textbook but also extensive problem solving. Typically "hard" college math courses are about memorization of abstract concepts, and taking any of them doesn't really prove you can do hard things (I'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'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 '96 in Florida. I also didn't go to college.

I've been a professional web developer since 2005 and a development manager (who still codes) since 2017. I don't understand the first thing about Calculus or even logarithms. I'm sure if I did, I'd probably be a better developer. I've had employees try to explain to me fairly basic log notation and my eyes just glaze over. It's never impacted my abilities, nor the respect and admiration I get from them as a well-experienced and knowledgable developer, but I can't help but feel ignorant.

I need to go back to the basics and work my way up; I've lost a lot of it. Where do I start? Kahn Academy?

> You know they will never use it in adulthood, outside of certain career choices.

Just going to register my dislike of this particular trope. Mostly because "certain career choices" is doing a huge amount of work. "Certain career choices" 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.

People use calculus in the sciences, of course, but also in business, the arts, music, politics, and beyond.

We learn calculus when we're young as a part of expanding ourselves, casting the widest possible net to find that intersection of what we're good and and what we'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.

But I would highly recommend against taking the attitude that "you'll probably never use it." That's counter-productive. And the people who "don't use things" are boring...

> But I recently realized there is a very good reason to take Calculus. It’s to prove you can do hard things.

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.

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 "policitians" (in the negative sense), sycophants and self-promoters. On the other hand, learning hard scientific/mathematical stuff nurtures the personality trait of "no bullshitting" and developing less tolerance for claims that clearly cannot be abided by.

Thus: I really like learning hard things, but this personality trait is in my opinion often a career killer.

From that perspective, going through any kind of struggle (and building willpower/discipline) would be a good enough proxy for learning calculus.

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 actually learned/understood. 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.

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!

I disagree with the OP’s claim so fundamentally — they might as well claim that schools/education focus on literacy for the same reasons.

I agree in principle that your personal story is made of the rough things you've overcome, and it'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've come up with for ourselves. Then and only then does doing it the hardest way possible seem not just worthy of our time, but essential to our personal growth.

I'd argue that as long as someone reaches that attitude toward something that they choose, they have lived a good life. And that something doesn't need to be a high school math class. The hard thing could be trying to become a chef when you'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.

[edit: removed a critique. I had misinterpreted the words "errant period" to allude to something other than punctuation. My mistake.]

It'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.

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 "hard parts." Those are the answers I tend to give today when somebody asks me, "why take calculus?" Demystifying it doesn't even have to be a wholly practical explanation, like deriving acceleration from velocity.

Segregating out the "hard stuff" doesn'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.

The formulas to do integrals aren't important but the concept of integrals is.

Honestly I think we should try to focus on differential equations instead but maybe it's necessary to do calculus first.

Don't do hard things that are unrelated to your actual goal; they're in unlimited supply, and you could be doing hard things that are relevant instead.

This essay wouldn't have impressed me in middle school; I don't know why it's on our front page.

> ... teenager asks why they need to learn calculus

> But if we avoid hard things

I don'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.

And my answer to that question is you probably shouldn'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're more likely to grasp them when you're driven by curiosity.

To me what's more important than Calculus being hard, and I think that's especially true for maths more broadly is that it's beautiful and one of the fundamental ways how we can make sense of the world. Everyone benefits from doing some maths.

I studied maths in uni and while I've not used it much, even as a programmer, I still enjoy doing it. My dad never had much schooling but now that he's retired he actually picked up a few of my books and slowly worked through high school to now undergraduate courses. He'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 hard.”

There's some nice seeds of ideas here, but it's all a bit lost in

(a) brevity - it's a deep topic so the post length can't do it much justice &

(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/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/gender/accent/height/hair/appearance, normative mental health characteristics. It's not because of their secret extracurricular study: that's in direct contradiction of the message behind the trope.

"My goal with our kids is to avoid lying to them as much as possible." ← 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'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.

True when you happened to find just one of the soon best paying new activities. Catching butterflies would have worked out less awesome probably.

> 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.)

That was me 100%. I passed elementary school with flying colors without ever doing any homework or actively participating in class (I had better things do to: reading comics and building LEGO contraptions) and simply continued this approach in highschool, with much, much less success. But neither did I care nor did I have any time for studying or doing homework - I taught myself programming in Batch and BASIC in the 90ies from the MS-DOS manpages, and later, when we had access to the internet, Delfi, Visual Basic and C++. I had finished a small tool with a few 100 users when I was 13, and I had to take care of them and fix bugs. There simply wasn't time left for any school work. University was just a natural extension of this childhood interest into adulthood. It didn't feel like school at all, and there I quickly discovered that math (well, computer science math at least) is actually pretty easy, and all you need is practice.

This reminds me of a powerful post I read a while ago with the charter to "Half-ass [your projects] with everything you've got!". Pre-commit to what level of quality you're looking to achieve and then strive to do just what is necessary to get there: https://mindingourway.com/half-assing-it-with-everything-you...

IME a big part of this misdirection stems from school focusing on the mechanics of math, rather than the intuition of math.

In the long run, the mechanics of math (how to do long division, or differentiate an expression, or expand a geometric series) are important only insofar as to help us model and predict and analyze the world, intuitively. However, students who do not intuitively see the power of mathematical intuition as a tool for understanding and modeling the world better, think that they are taught the mechanics of math just for the sake of "no phone/calculator/computer available" circumstances.

You've given one day-to-day example (garden fence) which requires only extremely elementary math, and then listed a bunch of stuff related to specialised career paths... which was the OP's original qualifier:

> outside of certain career choices.

As someone who did a lot of calculus in university, and definitely hit a eureka moment while integrating over vector fields that helped me conceptualise some general day-to-day stuff better in my head, would most people generally benefit from that same conceptual "grokking": of course. Would it be worth the time & effort investment for them if they're not using it in their career: no.

I'm using math(s) a lot, trigonometry, matrices, algebra… But most of my friend, family, I couldn't convince to learn math just based on the argumentation they can use it in practice.

Yes, calculating the right amount of fence is useful, but not only (as someone pointed out) you don't need a lot of math for that, people just take take a ruler on the plan, or count steps in field, going across the entire length, then estimate, and it works.

> estimation of 500km route arrival time while taking traffic statistics into the account

Who does this? How would you convince a friend to learn math in order to do this? What people do is they remember how long a 200 km route took and so they estimate the 2.5× longer path will take 2.5× more time.

We need examples of real world math applications, because such examples are scarce across the Internet.

I don't think you need calculus to calculate right amount of fence for your garden.

> Since math modeling is everywhere in "modeling" industries like engineerings, financial-ish jobs and othet

In other words, certain career choices, as the OP says.

They're not everyday things for a lot of people though.

I was in a shop this weekend where the price per 250g of coffee was displayed, but the woman in front of me only had a 175g container. Neither her, the person serving her, or the other person working in the café knew how much to charge her. It's 175/250 * £PRICE_PER_250.

In supermarkets, prices of items are displayed beside each other - a sharing bar of chocolate is £x/100g, but the multipack is £y/item, and each item is z grams. Which is better value?

Cooking - I have a recipe in a book that serves 2 people, but I'm cooking for 3. How much X do I need?

I don't get why calculus is always brought as an example. It wasn't particularly hard, the entire class had to learn it in high school. We all had it (in a slightly harder shape) in every university course (no matter how detached from what we actually needed)

I forgot all my calculus after high school, had to relearn it in uni and then I promptly forgot again.

Exactly as the article says, it was more about proving we had the capacity (proxy iq test?) to learn it.

You don't need calculus in real life and I think the focus on calculus is ridiculous when we could explore other more practical areas, like category theory (which only my lucky friends who did advanced math got to play with)

I hate the framing of problems and domains as hard because I found it so confusing when they turned out to be easy for me. It gave me a false sense of competence and superiority. Because I found calculus (and everything else in school people said was hard) easy, I thought I was just exceptionally capable and other people were incompetent and/or stupid.

I didn't find out until much later (and it still feels like much too late) that I just had an aptitude for learning the subjects traditionally taught in schools in the ways schools normally teach them. I got lucky. Everybody else was just as capable at learning some things in some ways as I was at learning school things in school ways. They just didn't have the luck that their aptitude lined up with what was measured and lauded in childhood like I did.

That meant they all got to learn how to work hard to learn things outside their areas of aptitude in school. I didn't. I didn't realize there were any such things that might matter someday.

I think learning how to learn things that are hard FOR YOU is quite possibly the most important skill in life. The sooner you master it, the better.

Framing some things as "hard" when everything is hard for some people and easy for other people undercuts the more important lesson.

I've seen the enthusiasm for any subject wither away when a child or teen is told a particular subject is hard, whether that be math, a programming language, or learning a musical instrument. I was this way. In their totality, yes, the subject is hard. But what they aren't taught about any difficult subject matter is that they are achievable by breaking them up into a series of small, easier to understand concepts. Their practical utility grows as the number of these small steps are achieved. And as they are achieved, mini demonstrations of their use should be performed so the student understands the importance and gets exited to continue.

Example 1: "I learned five notes in shape 1 of the minor pentatonic scale. That took a bit of practice, but now I'm able to play a bunch of cool licks. Neat! If I continue this path, who knows what other cool licks I can pull off!".

Example 2: "I learned how to import libraries. My lesson had me register a twillio account. I imported the twillio library into my python script. And I copied some code that'll instruct the library to send me a text message. I don't quite understand these python concepts, but wow, this is really cool; I just got a text message from my computer program. The fact that libraries can give me abilities like these is neat. I can already imagine how I can build some basic automation to leverage them. Who knows what else I can accomplish if I discover more libraries and understand python better to actually build something automated!"

Rightly on Wrongly some areas of study have the reputation/stigma of being difficult attached to them.

Back when I was a high school student math (not just calculus - but the entire subject of mathematics) had this reputation as being a "hard" subject as a result scores of my fellow students just decided math is to difficult I'm not going to engage with this.

I suspect this is related to a fear of failure or kids being afraid of "looking dumb" in front of their friends - There was a definite "if I don't try then it doesn't matter if I can't do it." attitude, so they just switched off in those particular classes.

A lot of these attitudes carry forward into adulthood. I'm almost 40 and amongst my generation programming has a similar reputation. People I grew up with think if you can read or write code you are some kind of mystical wizard with powers beyond the understanding of mere mortals.

I see it today at my day job - I work as an engineer (the non software kind). I've seen my coworkers completely baulk at computer code I hear all the same things I heard back in high school. "This is too hard, I can't learn this stuff, I'm not going to bother attempting to understand it".

Fluid Dynamics was a hard subject (in my opinion), Solid Mechanics was challenging a dozen lines of python code is not on the same level.

> People will talk about how they don't have full mastery over the language, but you don't need anything close to that in order to be effective.

My daily work is 80% C# and 20% Python (to make internal Blender tools for our artists). And I'm really bad at Python. I don't know any of itertools. I don't know zip() besides its name. I don't even use lambda.

The result? My bad code can be easily understood by some of more tech-savvy artists.

  for x,y in zip(['a', 'b', 'c'], ['1', '2', '3']):

     print(x + y)

  >>'a1'

  >>'b2'

  >>'c3'

> I hate the framing of problems or domains as hard

The easiness or difficulty of a domain or discipline is always in relation to some individual context; and that context includes variables that the learner controls. To the impatient, disinterested or undisciplined, I imagine calculus, learning the kanji, or playing the oboe all seem hard. But to the extent I can marshal patience, curiosity and discipline, the difficult domain becomes just a series of small steps integrated over time. I’m a musician and when a student complains about how hard a piece is, I ask if they can play the first note, then the second. If so, then it’s not hard. Because the process to acquire the whole thing is right there. Yes there are interpretive elements and techniques to be acquired along the way. But nothing is hard unless you are in a great hurry or you don’t really want to do the thing.

It is useful to use the words hard and easy. As you mention, changing perspective around these concepts is the crux.

Hard problems or domains are unknowns. Working towards solving hard problems involves thinking through unknowns, which may or may not lead to understanding. An aversion to hard problems is an aversion to the unknown.

>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.

lol, typical HN answer. Mathematics is not "easy", it is a niche; some people are good at, some are average, some are bad. Expecting every person to be able to do math is folly. People will fail. People already fail at memorizing math concepts and literally just applying said concept by plugging the numbers around. Some people just don't "get" it, I know I don't "get" probability, but is pretty good at other branches of math like group theory and calculus. To some people, deriving derivatives is basically black magic, but to me it's pretty intuitive.

Thus, if the world economy relies on people being good at probability then I am screwed. Fortunately for me, the world economy somehow relies on people being good at writing texts on a computer to tell it what to do (programming). I personally think programming is piss easy (its the actual problem being solved that is hard, programming is just knowing how to knock a hammer) However, there are people out there that simply can't program, either because they are not interested or not capable. Perhaps they are good at something else that is not entirely marketable? Is it wrong to be that way?

Being humble is one thing, but not realizing one's gift is another.

I've found that some disciplines need calculus, others don't. I've found deeply understanding logic and binary/hex MUCH more important than calculus in my career.

Physics and gravity are behind any kind of predictable motion. But you don't need to understand those things at all to be a successful surfer. Even though surfing is entirely about physics and calculable predictions, performing the act doesn't require any detailed knowledge of either topic.

It's the same with calculus and almost everything you mentioned. People can create algorithms, make statistics calculations and financial predictions, build robots, etc. All without any knowledge of calculus of any kind.

The skills of all of those things are based on calculus like surfing is based on physics. Related, but not in the sense of practical application. Knowledge of the math that underlies the math that underlies the thing is neither required nor sufficient for actually doing the thing.

Putting on a play is a very human interactive activity. Until math lets you interact with many humans in a rich experience, it won't be put on a pedestal like drama.

I saw an article where they asked a bunch of scientists and engineers if they actually used calculus in their professions. None of them did. They used Excel and the R programming language.

It will be amusing if we find out that all the things come in discrete quanta, even space-time, which I hear hasn't been ruled out. Calculus and real numbers might not be sitting as pretty.

You probably understand logs intuitively. Don’t worry about notation, here’s the idea: sometimes we count digits, not values.

When we say someone has a 6 figure salary, we are counting how many 0’s (10s) to takes to get there.

For memory, we say something has 32 bits and can have 2^32 possible values. It’s more graspable to talk about the “address size” vs the “number of possible values”, especially for things that grow fast (like storage).

I’d suggest starting with your intuitions and slowly translating them to math.

(Without being a shill, I wrote about real world logs here, it may help: https://betterexplained.com/articles/using-logs-in-the-real-...)

Khan Academy is great, but there are also an incredible number of great youtube videos. I would watch this 3blue1brown video to see if you like his style : https://www.youtube.com/watch?v=WUvTyaaNkzM

> go back to the basics and work my way up; I've lost a lot of it. Where do I start?

You might want to check out my book "No Bullshit Guide to Math & Physics," which starts with a high school math review, and goes up to calculus. It's specifically written for adult learners (self contained + lots of practice exercises).

You can see a PDF preview here https://minireference.com/static/excerpts/noBSmathphys_v5_pr...

The concept map from the book is independently useful to check out: https://minireference.com/static/conceptmaps/math_and_physic... And you should also check out this SymPy tutorial https://minireference.com/static/tutorials/sympy_tutorial.pd... which can help you build a bridge between coding skills and math operations.

A lot of math is cumulative, i.e. built on top of the prior concepts/tools. There are some things that are effectively the start of their own branches, but a lot of them then go back into a tangle of general mathematics that's all deeply interrelated, and also a subject onto itself when you get into ways to convert problems into totally different representations to use other mathematical tools on them.

In your case, follow something like Khan academy through the normal grade school programs to pick up where you left off and work backwards on picking up any concepts you're weak on then pursue whatever threads interest you. Wolfram can also help you look up specific things or find necessary formulas if, e.g. you just need the formula for a cone or to know how to integrate sin().

> I need to go back to the basics and work my way up; I've lost a lot of it. Where do I start?

One very good place to start is Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by George F. Simmons (less than 150 pages!).

Just a meta comment: Don't think of calculus as hard in the same way learning a language or learning to paint is hard. Calculus is more of a gotcha moment. You fumble in the dark for a few focused hours (or minutes) and then you Get It. From then on it's relatively easy.

I liked Khan Academy. Got me all the way through Mechanical Engineering and I didn't start until I was 38