Is programming the new math?

Sorry to even mention this and get your blood pressure up. (Didn't mean to scratch a sore spot by simply criticizing an educational system that I certainly paid my dues in.)

And BTW, in addition to your other unsupported inferences (ironic given the subject matter), I wouldn't confuse not taking further math classes with stopping one's mathematical education. If you insist on reading things that don't exist in someone's words, how do your proofs turn out well? You must be constantly assuming things which aren't given, and even changing "equals" to "not equals" in a problem to turn it to one you have a textbook solution for.

[Edit: Ahh... Not to sound at all stalker-y, but I looked at your public account info to understand your perspective better. I see that not only you studied at UChicago — which probably means Spivak's Calculus and learning epsilon-delta proofs might be a matter of pride with you — you work at a financial market. My comment does contain a criticism of the status quo, which you may have strong ideological feelings about and therefore respond with a bit less rationality than otherwise. And... maybe I did come across as calling a subset of people here 'tools'.]

Let's examine the post in light of C-H. I'm not super familiar with Python, but I believe it is dynamically (that is to say, singleton) typed. This might not correspond exactly to Python, but let's assume there is an any type, product types (for forming tuples in function arguments) corresponding logically to conjunction and function types corresponding logically to implication. Any well-formed expression (e.g. 0) has any type, so any is true as a proposition. Thus, all types are inhabited and all propositions are true. By proof irrelevence, the logical content of any Python program is equal to the constant function 0. In other words, they have no proof content. Thus, I claim the students here are not doing math via programming in the techincal sense of C-H.

I stand by my original claim that they are not doing math by programming in a looser sense, either. I studied computer science, spent a dozen years working as a programmer and now I'm studying math in graduate school.

> I think programming is much closer to math than this comment gives it credit for.

I might have said something like this before I started doing serious math.

You make a mistake by thinking that programming and math are the same, except that programs get "checked" by computer. That's like claiming that video games are more physically demanding than sports because the rules are enforced perfectly.

Math is about understanding why something is true. A program that uses or applies a mathematical idea rarely (never?) contains a proof of that idea's correctness. For a mathematician, testing is insufficient evidence for truth. Proofs are universal and they generally apply to an infinite number of cases. There is a deep qualitative difference between conceptually understanding why something is true and checking a finite number of cases, or even implementing a procedure to check those cases. You can try to belittle mathematical methods by calling them hand waving or imprecise, but programmers are not even trying to do what they do.

It was an assumption based on your words (epsilon delta proofs and whatever else we did were tedious) and my experiences with people who dislike classes of proof-based math. No projecting here--I enjoyed my analysis class. We a fair number of epsilon-delta proofs.

My issue with your initial response was that you were implicitly blaming the class for being boring and causing you to lose your enthusiasm for math. My point is that its not their job to foster your enthusiasm, especially at that level.

Now of course, we should always be re-evaluating how subjects are taught to make sure information is being conveyed as best as possible. But we have to resist the temptation to immediately blame a student's failing (by any measure) on the teacher being inadequate in some way. If we start the conversation on that note then the space of potential solutions becomes severely restricted.

I am what you might call an autodidact. When I observe an institution isn't sufficiently good, I pivot and fulfill my requirements elsewhere, for example by reading a book or meeting passionate people informally. I do not believe that this autodidacticism is great efficiency-wise, but often it's unfortunately better than alternatives.

When evaluating the earlier poster's anecdote of teaching 180 adults, of course it's very unlikely that she/he had the terrible luck to draw 180 (or even 100) genetic freaks who were born with terrible attitudes. (And even if she/he did, just wait a semester and problem solved!) Far more likely to me: at least one major institution failed them along the way. So it is clearly useful to identify which ones failed — especially if it's the one you're in, as that's the one you have most control over. (Teachers in particular have a position of power in the classroom.)

(The power of institutional analysis is you can completely replace the people in them, and they'll still function essentially the same.)

More important — if you realize that your approach is clearly unsuccessful, I think you need to stop, reevaluate and probably pivot. Be open to shattering your worldview. Rather than plod on stubbornly in a direction you know leads to abject failure, because most people around you are willing to fail miserably in the same way. (Or because "But it's not in my job description!") I do not intend to be such an extreme romanticist of failure. In fact, today I happened to institute post-mortems at work, to identify our little failures. Not to blame, but to improve.

It is important for teachers to have good attitudes, and it's disheartening to meet those ironically unwilling to learn. But I've met wonderful teachers.