I'm a pretty low-key annotator but I did write this in the margins of @stevenstrogatz's Infinite Powers.pic.twitter.com/2ze822F1a0
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It’s also interesting that Stokes Theorem very often is presented as being about cancellation on common boundaries in the interior, and the 1D fundamental theorem is basically a special case of this, but isn’t usually talked about in the same way.
Indeed, Stokes' theorem is a highly suggestive further elaboration of the same basic phenomenon of telescoping cancellation, which ultimately underpins the vast edifices of homology and cohomology, Simple ideas often reach extremely far -- which is why mathematics is possible.
Indeed! This section of the book is about Leibniz, who discovered his version of the fundamental theorem via considerations of telescoping.
I've always loved Leibniz's approach to summing a geometric series, in which he achieves his goal by seeming to abandon it; he passes from the sequence of powers to its sequence of differences, which he sums easily, via telescopic cancellation. And then he notes that he's done!
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