Quotes, Quoting, and Quotations
Some thoughts and comments on various topics
John Bartlett wrote one of the most famous collections of quotations. His book, Bartlett’s Familiar Quotations, was published in 1855 and is still published today, or is available on-line.
Today I thought I would share some quotes about mathematics, theory, and science.
I hope you enjoy them and like some of them. My favorite is
Only math nerds would call finite.
When a professor insists computer science is X but not Y, have compassion for his graduate students.
Computers are useless. They can only give you answers.
All parts should go together without forcing. You must remember that the parts you are reassembling were disassembled by you. Therefore, if you can’t get them together again, there must be a reason. By all means, do not use a hammer.
—IBM Manual, 1925
The biggest difference between time and space is that you can’t reuse time.
Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.
—John von Neumann
The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can’t even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions.
The infinite we shall do right away. The finite may take a little longer.
Complete disorder is impossible.
A set is a Many that allows itself to be thought of as a One.
The Riemann Hypothesis is the most basic connection between addition and multiplication that there is, so I think of it in the simplest terms as something really basic that we don’t understand about the link between addition and multiplication.
If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?
Try a hard problem. You may not solve it, but you will prove something else.
If you don’t work on important problems, it’s not likely that you’ll do important work.
A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one.
A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.
It isn’t that they can’t see the solution. It is that they can’t see the problem.
I have yet to see any problem, however complicated, which, when you looked at it in the right way, did not become still more complicated.
The open secret of real success is to throw your whole personality at a problem.
“Obvious” is the most dangerous word in mathematics.
In mathematics the art of proposing a question must be held of higher value than solving it.
We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.
The essence of mathematics is not to make simple things complicated, but to make complicated things simple.
For every complex problem there is an answer that is clear, simple, and wrong.
Proof is an idol before whom the pure mathematician tortures himself.
What are your favorites?