### iPad Notebook export for Significant Figures: The Lives and Work of Great Mathematicians

Sunday, April 29th, 2018Some quick quotes from

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Significant Figures: The Lives and Work of Great Mathematicians Stewart, Ian

Citation (MLA): Stewart, Ian. Significant Figures: The Lives and Work of Great Mathematicians. Basic Books, 2017. Kindle file.

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that I really liked

Each short quote below is preceded by the words “Highlight” & indication of the location in the book.

9 The Heat Operator • Joseph Fourier

Highlight(orange) – Page 91 · Location 1439

The precise form of the equation led Fourier to a simple solution, in a special case. If the initial temperature distribution is a sine curve, with a maximum temperature in the middle which tails away towards the ends, then as time passes the temperature has the same profile, but this decays exponentially towards zero.

10 Invisible Scaffolding • Carl Friedrich Gauss

Highlight(orange) – Page 98 · Location 1536

When Gauss was eight, his schoolteacher Büttner set the class an arithmetic problem. It’s often stated that this was to add the numbers from 1 to 100, but that’s probably a simplification.

14 The Laws of Thought • George Boole

Highlight(orange) – Page 146 · Location 2255

The quadratic is then the square (px + qy) 2 of a linear form. A coordinate change is a geometric distortion, and it carries the original lines to the corresponding ones for the new variables. If the two lines coincide for the original variables, they therefore coincide for the new ones. So the discriminants must be related in such a manner that if one vanishes, so does the other. Invariance is the formal expression of this relationship.

21 The Formula Man • Srinivasa Ramanujan

Highlight(orange) – Page 223 · Location 3480

For the first three years of his life, he scarcely said a word, and his mother feared he was dumb. Aged five, he didn’t like his teacher and didn’t want to go to school. He preferred to think about things for himself, asking annoying questions such as ‘How far apart are clouds?’ Ramanujan’s mathematical talents surfaced early, and by the age of 11 he had outstripped two college students who lodged at his home.

23 The Machine Stops • Alan Turing

Highlight(orange) – Page 251 · Location 3929

After the war Turing moved to London, and worked on the design of one of the first computers, ACE (Automatic Computing Engine) at the National Physical Laboratory. Early in 1946 he gave a presentation on the design of a stored-program computer –far more detailed than the American mathematician John von Neumann’s slightly earlier design for EDVAC (Electronic Discrete Variable Automatic Computer). The ACE project was slowed down by official secrecy about Bletchley Park, so Turing went back to Cambridge for a year,

Highlight(orange) – Page 252 · Location 3940

He worked on phyllotaxis, the remarkable tendency of plant structures to involve Fibonacci numbers 2, 3, 5, 8, 13, and so on, each being the sum of the previous two.

24 Father of Fractals • Benoit Mandelbrot

Highlight(orange) – Page 261 · Location 4084

In general, if the rank-n item has frequency proportional to nc, for some constant c, we speak of a cth power law.

Highlight(orange) – Page 261 · Location 4085

Classical statistics pays little attention to power-law distributions, focusing instead on the normal distribution (or bell curve), for a variety of reasons, some good. But nature often seems to use power-law distributions instead.

Highlight(orange) – Page 265 · Location 4147

Julia, and another mathematician Pierre Fatou, had analysed the strange behaviour of complex functions under iteration. That is, start with some number, apply the function to that to get a second number, then apply the function to that to get a third number, and so on, indefinitely. They focused on the simplest nontrivial case: quadratic functions of the form f( z) = z2 + c for a complex constant c.