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Comment by billfruit | Hacker News Reader

May be the way mathematicians notate is frankly ambiguous and confusing, and recent decades of programming experience have given good insight into more expressive methods of notation.

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I think this would be a more compelling thread if people discussed particulars of ambiguity in notation and how to resolve it.

Structure and Interpretation of Classical Mechanics [1] walks through ambiguity in physics and math. The first interesting note I found was footnote 2 in the preface [2], citing the ambiguity in the statement of the chain rule.

I am ignorant about some of the insight coming from recent decades of programming and would love to hear it.

[1]: https://mitpress.mit.edu/sites/default/files/titles/content/...

[2]: https://mitpress.mit.edu/sites/default/files/titles/content/...

> recent decades of programming experience

as opposed to recent millennia of mathematical experience?

Let's not pretend math notation has remained constant for millennia.

Exactly, it has been refined over millennia.

Right, and it's important to remember that mathematics is sharply optimized for human understanding, whereas programming languages strike a careful compromise between human understanding and efficient execution by machines. I don't think anyone could seriously argue that programming languages are "more expressive" than mathematical notation, which has the powers of ambiguity and hand-drawn graphics.

You are not wrong. Replace 'efficient execution by machines' with 'efficient processing by a compiler' and you will be even more correct.

Of course it has evolved. But some landmarks of it (e.g., using single letters for "variables") have been used since 2500 years ago. Now I laugh when programmers tell me to be "civilized" and name my matrices with full words.

To be fair, the mathematical notation that is familiar to us today is just a few hundred years old.

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