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I do not disagree with you, but this is not answering his arguments.

Math is the language of science[...]. There are many ways to learn a language, but I think they all have something in common. You have to spend a lot of time learning, reading and writing. The writing is quite important. You have to write the language to be good at it.

He's not arguing that scientists should drop writing math altogether (although you have to admit that they are spending huge amount of efforts making the computers do the calculation for them). He's addressing the more general issue of "teaching math in elementary schools". Why do we do it today? not everyone is going to be a scientist!

The thing about math is that currently to write as it is supposed to look like can only be done most conveniently on paper. Writing a math formula in Mathematica or Wolfram alpha requires a latex-like mini language[...].

Yeah writing math formulas on a computer is a pain. But:

- you and I come from a generation of pen and paper math solving. The idea of markup annotation of your text is still very young, but is it so far fetched to imagine that in few generations, all text will be filled with metadata and tags? LaTeX is a pain because of our current primitive keyboards and screens.

- more people should work towards improving this. Wolfram Alpha is doing good things, they're not the only ones working on this either, but we still need to bring more attention to the issue.

Also, who cares if he sells WA. Let's talk about his idea, not his persona.

  > but is it so far fetched to imagine that in few
  > generations, all text will be filled with metadata
  > and tags?

Yes, I think it is.

I like your analogy with learning a language, and I would use that analogy to say the current education system is only teaching grammar rules. Imagine sitting for hours a day for an entire school year conjugating verbs without ever reading a story, listening to a conversation, or trying to pronounce words.

There is so much more to mathematics than calculation. Proofs, number theory, and simulations can all be understood by children and are much more important to their education than long division.

Err. This what he saying, you focus more on manipulating equations in the language of maths such as algebra, calculus, and less time on remembering what's the answer to 7 * 8.

Is this really a win? For most small problems or subproblems, a person who has solved similar problems many times before can solve it mentally much more quickly than by consulting a computer.

But one produces engineers, the other produces shop assistants.

Which is which? A person who works in either role will do so more quickly by virtue of not needing to constantly consult a machine over trivial problems.

Focusing on algebra, calculus, and so forth would produce more engineers/scientists/mathematicians etc . These are things rote teaching the times table can not do. His not saying let computers do all maths, just the repetitive bits.

Symbolic Manipulation is still necessary.

I learned vectors(Mostly for games), eigenvectors far more intuitively by programming them on computer as a kid, then calculating them by hand.

I knew what adding two vectors actually represented, or what the crossproducts was, rather than just calculating it(Which the computer always did).

I get top marks in calculus, linear mathematics and most college level maths classes, but my little secret is that i'm not actually very good knowing my times tables by 'art. If someone asked me to calculate a basic times table question, it would take a few seconds to work it out manually. Yet the general public thinks that's weird, but I actually found it's quite common at this level.

I apologise for my dodgy english, it's 3am in the morning here.