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Comment by version_five | Hacker News Reader

Off the top of my head, Euler, Gauss, Newton, Leibniz, Euclid pretty much cover an undergraduate curriculum and all the math most people would know, and those are just five people. Expanding to the fullness of the discipline and 24 families does not seem surprising at all. It's probably more about how much of a long tail of subjects the field has.

(As I said, this is off the top of my head and some obviously build on predecessors work. Descartes and to a lesser extent Fermat are also relevant here, no doubt others that made contributions the people I listed built on - Cardano?)

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You would also need Cantor and Riemann, as well as Pythagoras, Bernoulli, Al-Kashi and Al-Khawarizmi, Yang Hui maybe also Lebesgue, Cayley, etc...

There are a lot of small but inaccessible results that are necessary and left out if you only consider sheer amount.

And while the list already includes Newton and Leibniz, nobody is proving calculus without Cauchy. There's no calculus without limits -- well, not unless you consider infinitesimal calculus, but that wasn't formalized until the mid-20th century.

> nobody is proving calculus without Cauchy

Unless you are Heine?

Cauchy was also a pioneer in complex analysis, which is taught in undergrad.

Riemann and Cantor are both in Gauss’s family.

> Off the top of my head, Euler, Gauss, Newton, Leibniz, Euclid pretty much cover an undergraduate curriculum and all the math most people would know, and those are just five people.

Who just happened to be around at the right time to a certain extent. The fact that these particular people are the famous ones may be an accident of history and someone else would have come along and and produce the same results.

Newton and Leibniz (and de Fermat, etc) famously both invented/discovered calculus at the same time:

* https://en.wikipedia.org/wiki/List_of_multiple_discoveries#1...

* https://en.wikipedia.org/wiki/Multiple_discovery

At least when it comes to mathematics, and perhaps 'mechanical' discoveries/inventions; lots of folks fiddling around with boiling water over the course of history, for example:

* https://en.wikipedia.org/wiki/History_of_the_steam_engine

Other aspects of human thought may be different: I think Aristotle (and later Thomas Aquinas) were unique and we'd be in a very different place, world-view-wise, if they hadn't been around.

Hey don't forget that Archimedes also invented calculus.

I learned the expression "grandstudent" when I met a number theorist who had studied under a student of Andrew Weil.

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