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I'm always in awe of what the ancient Greeks managed to figure out with nearly no mathematical notation at all. Or Calculus in Newton's book. The techniques w

• jordigh 10y ago
  Which book, the Principia Mathematica Philosophiae Naturalis? The thing is, he worked really hard to avoid calculus because it was too new and not widely accepted. Whenever he could give an argument without calculus, he would. It is hard to read but because he's trying to write calculus in the style of Euclid. So most proofs that would involve limits or derivatives would be written in a really roundabout way in terms more familiar to people at the time used to Euclid's geometry. This style of argument survives today in relics such as the geometric proof that lim sin(x)/x = 1 as x -> 0: http://math.stackexchange.com/a/75151 http://math.stackexchange.com/a/75151 Not only supermen were able to read the Principia, as obviously it was read and its ideas spread far and wide, but perhaps modern supermen would be required in order to see the actual calculus behind the veil of Euclid that Newton had to cast it at the time. I actually do read an English translation of the Principia from time to time for bedtime reading, and it's not that impenetrable.