Math notation is out of date

(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at: lawrence@krubner.com, or follow me on Twitter.

gnaritas writes some very insightful stuff about math notation:

Which is often the problem, it looks specific, but it really isn’t; it’s full of implicit assumptions about what the reader should know. It’s not executable, because it’s a language designed for being written by hand rather than executed by a computer.

However, the teaching of math would greatly benefit from an explicit executable form that makes no assumptions, i.e. a programming language. Gerry Sussman makes this case, he’s pretty convincing.

…I heard Sussman say at a conference, which he makes clear in http://en.wikipedia.org/wiki/SICM. Though I saw him a good 8 years after the book, so I’m sure he’d grown some new opinions.

He is of the opinion that if you can’t write the algorithm, you don’t understand it; forcing students to write the algorithm aids in teaching them a real understanding. He spent quite a bit of time complaining about the vagueness of mathematical notation due to its implicit assumptions for the purposes of teaching and the superiority of executable code for the task.

On a side note, the speech was aimed at both engineers and programmers and the audience was a mix of both. He did a wow demo with a circuit on the overview, calculating all the voltages and resistances on the fly from chosen starting values that made all the programmers smile really big and all the engineers jaws drop. Everyone was impressed because he flew through it, but the programmers much less so because what he did was just how a programmer thinks, albeit it very fast. He was demonstrating to the engineers the benefits of thinking like a programmer. As he is both and teaches both, he clearly connected some dots that they generally don’t.

Post external references

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    http://news.ycombinator.com/item?id=4889528
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