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How Infinite Series Reveal the Unity of Mathematics | Quanta Magazine

Infinite sums are among the most underrated yet powerful concepts in mathematics, capable of linking concepts across math’s vast web.

Click to view the original at quantamagazine.org

Hasnain says:

“When I was a boy, my dad told me that math is like a tower. One thing builds on the next. Addition builds on numbers. Subtraction builds on addition. And on it goes, ascending through algebra, geometry, trigonometry and calculus, all the way up to “higher math” — an appropriate name for a soaring edifice.

But once I learned about infinite series, I could no longer see math as a tower. Nor is it a tree, as another metaphor would have it. Its different parts are not branches that split off and go their separate ways. No — math is a web. All its parts connect to and support each other. No part of math is split off from the rest. It’s a network, a bit like a nervous system — or, better yet, a brain.”

Posted on 2022-02-05T06:29:08+0000