The Equation that Couldn’t be Solved, Livio
The Equation that Couldn’t be Solved
How Mathematical Genius Discovered the language of symmetry
A fascinating walk through the history of mathematics, Livio introduces group theory and shows its wide ranging applications. He integrates the human stories of mathematical genius with descriptions of the theories being developed.
P8 Interesting off-topic line “…This does not mean, however, that any delegation of visiting aliens would look anything like us. Any civilization sufficiently evolved to engage in interstellar travel has likely long passed the merger of an intelligent species with its far superior computational-technology-based creatures. A computer-based super-intelligence is most likely to be microscopic in size.” Someone has been reading Kurzweil.
P163 in describing operations and permutations, I was reminded of Wolfram’s a New Kind of Science. Simple rules. Identity, cyclic permutations, transpositions, inverse
P262 discusses possible characteristics of genius. “Genius does what it must, and Talent does what it can.”
Beyond a certain IQ there is no clear correlation between intelligence and creativity. For those that do make it into the roster of creators, a certain set of personality traits proves far more important than having a certain general IQ, or a high domain-specific ability, even one at prodigy.
Creators are hard-driving, focused, dominant, independent risk-takers. Complexity – tend to be able to harbor tendencies that normally appear at the opposite extremes.
The ability to think outside the box, stimulus freedom, break out of common assumptions. Tolerance of ambiguity.