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Comment by ams6110 | Hacker News Reader

Just as you don't really understand how a CPU works until you've programmed in assembly, you don't really understand math if you haven't done hand-computation, at least up to a point. If your approach to any math problem is "plug it into Mathmatica" you will never be able to creatively apply basic concepts to more complicated problems and you will never have any sense of whether the answers it provides are "reasonable."

That said, tools like Mathmatica are here to stay, and the argument that we need to spend more time teaching the use of these tools as an aid to exploring and understanding fundamental concepts is probably correct.

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To expand on you're point: math (and some math-like subjects) are flat out different than driving a car.

I think the problem with your example, ams6110, is that Wolfram might retort that software developers don't need to have programed in assembly. Yes (says Wolfram), the absolute best developers in the world might be well-versed in the this, but that doesn't mean all developers should be so trained, in the way that we train everyone to do arithmatic.

To respond to this, I would say: no one would ever study Ramanujan theta functions without learning linear algebra, and no one should study linear algebra without learning arithmetic. Most other subjects must be compartmentalized, because it is impossibly difficult to derive biology from basic chemistry; some things must be accepted as given. But math is different. In math, you really can derive everything from the ground up, and doing so is immensely valuable.

You may be correct but no one starts out programming in assembly then working their way up to higher order languages.

However this is exactly how math is practiced.

Wouldn't it be better to start with higher order logic first, so students can see a value proposition then work our way down to the nitty gritty computation that no one needs to do unless they're advancing the field?

I started programming with circuits, and then machine code.

And I think you're wrong about starting with higher order logic. It's too easy to make plausible statements that are simply wrong. Learning the real nitty-gritty is essential to avoid sweeping errors.

> Just as you don't really understand how a CPU works until you've programmed in assembly, you don't really understand math if you haven't done hand-computation, at least up to a point.

Conrad Wolfram addresses this very point in the video (11:30). He says that the most valid point that hand-calculating helps understanding is that teaching processes themselves helps understanding, but that there's a better way to do that: programming. In other words, programming a math solution is better for teaching math understanding that hand solving it.

In the end, I think the idea he's trying to impart is that the core of math is not calculation at all, it just seems that way because they've been intertwined for so long. But now that we have computers to do the tedious calculations, we can work on defining and exploring what math really is: how different conceptual intuitions are related

Agreed, but only up to a point. To program it is fundamental to have a strong intuition as to what should happen, why, and how to get there. Doing that without some amount of manual computation is temerary.

Actually, I disagree. Programming is about building and using abstractions. It is not strictly necessary to understand how the abstractions are built.

Case and point, how many web developers do you know who could outline the TCP/IP protocols in great detail?

Speaking as someone who's primary problem with math in school was poor handwriting, I would have much preferred to learn via programming.

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