0 like 0 dislike
0 like 0 dislike
I'm reading Needham's visual complex analysis, and on a discussion about convergence of power series for multivalued function, the author says "We have demanded the impossible of the power series, and it has responded by committing suicide!"
by
0 like 0 dislike
0 like 0 dislike
I do love Needham's prose style, if not his way of laying out his exposition, and his *needless* overuse *of* italics *bugs* the *shit* out *of* me.

My favourite sentence from what I read of *Visual Differential Geometry and Forms* was that bit where he said about there being a sure sign that Cartan's differential forms were Platonic forms. I don't have the book to hand, so I can't give the exact quote, but I liked that.
0 like 0 dislike
0 like 0 dislike
About the hairy ball theorem:

"If you look at the way the hairs lie on a dog, you will find that they have a 'parting' down the dog's back, and another along the stomach. Now topologically a dog is a sphere (assuming it keeps its mouth shut and neglecting internal organs) because all we have to do is shrink its legs and fatten it up a bit."
0 like 0 dislike
0 like 0 dislike
From *States of Matter*: “Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it will be wise to approach the subject cautiously.”
0 like 0 dislike
0 like 0 dislike
From Vakil: "Finally, if you attempt to read this without working through a significant number of exercises, I will come to your house and pummel you with [Gr-EGA] until you beg for mercy."
0 like 0 dislike
0 like 0 dislike
It is certainly possible for a collection to have nothing in it. A good example would be the collection of years after 1967 in which the Toronto Maple Leafs have won The Stanley Cup

The *empty set* is the set that has no elements, that is { }. It is commonly denoted by ∅.
0 like 0 dislike
0 like 0 dislike
"The enjoyment of one’s tools is an essential ingredient of successful work."

From The art of Computer Programming by Donald Knuth.  Not really a math book, but close enough for me.
0 like 0 dislike
0 like 0 dislike
The first sentence after the foreword of Poizat's *Stable Groups* is "I hope you know what a group is."
0 like 0 dislike
0 like 0 dislike
Lots of good ones from Arnold, such as

"Instead of the principle of maximal generality that is usual in mathematical books the author has attempted to adhere to the principle of minimal generality, according to which every idea should first be clearly understood in the simplest situation;
only then can the method developed be extended to more complicated cases.  Although it is usually simpler to prove a general fact than to prove numerous special cases of it, for a student the content of a mathematical theory is never larger than the set of examples that are thoroughly understood." - from his Lectures on PDEs
by
0 like 0 dislike
0 like 0 dislike
I forget which book this was even in, but they cited a theorem discovered by Ted Kaczynski, and the author put an asterisk next to his name. In the footnote, they just said, “Known for other works.”
0 like 0 dislike
0 like 0 dislike
Not strictly a math book but Principles of Dynamics by M.B. Glauert has this gem on page 57:

*Frictional, viscous and explosive forces are all permitted.  For example, if a cat is swung and released so that its parabolic path as a projectile would take it into a bath of water - an experiment which the reader will of course not attempt to reproduce - no contortions by the cat can prevent it from landing in the bath...*

No related questions found

33.4k questions

135k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!