Joel Spolsky and Clive Thompson discuss the past, present, and future of coding

You need more statistics than calculus to understand the current state of neural nets in Machine Learning, but you if you don't at least know the chain-rule, you're just using library code and not understanding even a basic perceptron.

And from a personal perspective: I've used so much trigonometry in my career (plenty of graphics work) that I'm not sure where I'd be without the time spent on trig and geometric reasoning in school.

I mean, I agree with their basic thesis that stats is important because of ML and the increasing practicality in using statistics and AI to solve problems. But I don't thin what they'd discard is well thought out in terms of what is going on. Nor is it meant to be, it's just a casual interview.

    > I could probably be convinced to jump on that bandwagon [dump calc, replace with stats]

Math curriculums would do better to focus more on getting "the foundations" right. Starting with algebra, geometry, trigonometry and real analysis (calculus), and pursuing it rigorously for college-bound students. There should be a focus on mastery rather than covering a wide variety of stuff quickly.

Too many students get to college with a mathematical foundation that looks like Swiss cheese-- with many holes in basic skills: like fractions, exponents, trig (yes, even if they took calc in high school).

I'd wager it's been a while since Joel was in a school and the course offerings across the board are likely quite different than he remembers.

Well, Joel obviously wasn't taught statistics then, because you need calculus to learn it properly.

And trig is such a fundamental math needed for linear algebra and vector calculus that it shouldn't be dropped either.

Even for discrete math you need to understand ideas like convergence, otherwise probability is filled with paradoxes.

"Pick a number!"

"Any number?"

"Well, numbers that are big are less likely to be picked."

"How much less likely do they need to be in order for your question to have a sensible answer?"

"Let's talk about convergence"

You also need algebra and trig. How else would you know what an inner product is without trig? Or that correlation is just an inner product? You need some linear algebra as well to understand cross products and inner products, otherwise they will be these magical things.

Many ideas in discrete math should be understood as the discrete versions of ideas in continuous math, with the continuous math ideas often being more natural and easy to understand. Sometimes one of the best ways to estimate an infinite sum is via an integral that is much easier to solve. A lot of complicated sums seem magical until you see that they are just the discrete versions of integrals -- sometimes path integrals -- with various weights that come from measures on the spaces of interest. So if your interest is blind computation, you don't need a lot of discrete math at all, you just need to learn what the symbols mean and how to look recipes up in books. But if your focus is on understanding what you are doing, then there is not a magic barrier between discrete and continuous math, most discrete math can be viewed as a discretization of continuous ideas, and in some cases ideas in continuous math can be better understood as limiting cases of a discrete result.

The sad thing is that this is all stuff you will get in a good gymnasium in Europe but you may need to wait until college to get it in the U.S. Absolutely no reason why a teenager can't learn calculus, limits, trig, probability and statistics, as well as basic ideas in group theory. Really algebra, geometry and trig you should get in elementary school so that you can get calculus, probability and statistics, basics of differential equations and some topology in high school. Then you can take specialized courses in algorithms if you are into CS or say PDEs if you are into engineering -- this is all stuff that should be taught in high school.

College tracked teenagers in Europe often learn that and more, and not just in math centered gymnasiums, but the price of that is tracking, otherwise you have to go as the slowest learner who has no interest in a specific major in college.

My acquaintance (having recently graduated college for maths) was explaining that in the real world, statistics and probability have far more use in the regular world. From my perspective perspective as a programmer, I confirmed that I'd used statistics far more often than trigonometry but with one notable exception: game engine programming.

Never have I felt more amateur in my understanding of mathematics during my programming career than when I had to (re)learn about matrix math, dot products, quaternions, Euler transformations, and other concepts I hadn't touched or even heard of in years. Maybe those concepts are less applicable as general math education now that everything's a pre-built framework with its own IDE.

Statistics without any calc is basically applying ad hoc tests without understanding what they are actually testing. This is the kind of statistics we should be getting rid of, not expanding.

I can't imagine I'd want to do physics or mechanical engineering without calculus or trigonometry. And computer graphics would be a lot harder without trigonometry.

And for statistics and probability... how can you have a Central Limit Theorem if you don't even know what a limit is? ;-)

Being able to deal with continuous functions is certainly useful for statistics and probability.

Neither would be better than trig and calculus. Nobody remembers the formulas and rules unless they use them regularly, and a course that is heavy on proofs would be too hard for most students.

In my view there might be a third way, which is to let the teaching of prob & stats revolve around simulation, rather than by algebraic derivation (proofs) or memorization. What can you learn from a giant bag of random numbers? What if that bag is divided down the middle and given to two groups of students? What can you deduce, when you know something about a set, but not everything about it? Can you make random numbers produce outcomes that are sometimes as convincing as the outcome of an experiment?

And so on. Even to this day, if I think that I've used the correct statistical formula, I test my recollection by feeding simulated data through it.

This kind of exploration could also gently lead students into... coding.

"I know it’s kind of a cliché but it comes back to worse is better. If you spend the time to build the perfect framework that’s going to do what you want and that’s going to carry you from release 1.0 through release 5.0 and everything’s going to be great; well guess what: release 1.0 is going to take you three years to ship and your competitor is going to ship their 1.0 in six months and now you’re out of the game. You never shipped your 1.0 because someone else ate your lunch."

Fowler writes for enterprises which have large, long-lived systems.

However you could spend forever rewriting and refactoring. What is the value in that?

But you (and I, and thousands of others) still use the site and probably didn't even notice or care about any of that. This is one of the largest, most heavily concentrated technical audiences on the internet, and even though those are the exact people you think would be most discerning about it, obviously nobody truly cares about how much isn't being done "properly". People will argue all day in the comments here about the right way to do things, but since they're here they clearly don't think it's important when deciding what they use themselves.

It's the same for everyone else, with every other site and product. As long as it works, the reality is that almost nobody cares how much of a mess anything is internally.

Sending a video about "Secrets of Mastering Excel" is less like to humiliate your colleague than sending them a link to "You suck at excel"

The current stupidity of the hiring process, the inane whiteboarding, the take-home tests and all that, is all down to him.