[yang140]

Thanks for sharing this post. Bret mentioned this in his "Media for thinking unthinkable" talk that Mathematical notation itself is a great tool for making mathematical structure visible. They are like user interface, it tell things that language can't express. The birth of mathematical notation is considered to be birth of modern mathematics. With dynamic media provided by computer, there should be a better way to dynamically represent mathematical structure. With that in mind, I would also recommend Evan Miller's comment's on Bret Victor's "Kill Math" article called "Don't Kill Math". Evan empathize that besides dynamic simulation, we should also embrace "theory and calculation" to see the underlying structure.

http://worrydream.com/MediaForThinkingTheUnthinkable/ http://www.evanmiller.org/dont-kill-math.html

[jordigh]

> The birth of mathematical notation is considered to be birth of modern mathematics.

What does this mean? We've had some kind of mathematical notation ever since we've had mathematics. The Babylonian tablets with Pythagorean triplets had to use some sort of notation for the actual numbers:

http://www.researchhistory.org/2012/10/24/earliest-evidence-...

https://en.wikipedia.org/wiki/Babylonian_numerals What do you consider notation and what is not notation?

[alphydan]

I think you're right that there was always notation. But perhaps he is referring to the birth of algebraic notation (the manipulation of symbols to represent unknown quantities).

Although the roots of Algebra start in the middle east around the VIIIth century, the current notation doesn't really develop until the XIIIth or XIVth [0]

[0] http://cerebro.xu.edu/math/math147/02f/algebra/algebra.html

[jordigh]

I don't know, I think that dismissing Diophantus or the Greeks as not being modern enough is a bit strange. After all, we still use the exact algorithm as Euclid for finding gcds. We simply don't state it in geometric terms like he did.

I suppose if by modern mathematics one means algebra, then it's fair to place it somewhere in the 12th century.