Entropy

• Entropy is an anthropomorphic concept. --- Eugene Wigner


• A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts. --- Albert Einstein


• Every mathematician knows it is impossible to understand an elementary course in thermodynamics. --- V Arnold


• You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage. --- John von Neumann, in a response to Claude Shannon


• Glib, unqualified statements to the effect that "entropy measures randomness" are in my opinion totally meaningless, and present a serious barrier to any real understanding of these problems. --- Edwin T Jaynes

Life, the Universe, and Everything

• How many ... does it take to change a light blub?
  • Scientists --- Ten. One to change the light bulb, and nine to coauthor the paper.
  • Graduate students --- One. But, it takes eight years.
  • Mathematicians --- None. It is left to the reader as an exercise.


• What is essential in the life of man of my kind lies in what he thinks and how he thinks, and not in what he does or suffers. --- Albert Einstein


• Your real job security as a scientist is the recognition and approval of your peers around the world. --- P J Feibelman


• If that earns me the right to get back to my wife, well then ... then that's my mission. --- Captain Miller, Saving Private Ryan


• It's not a lie, if you believe it. --- George, Seinfeld


• You should take what you do seriously, but not take yourself seriously. --- Anonymous


• My rule is, when you are unhappy, think about it. But when you're happy, don't. Why spoil it? You're probably happy for some ridiculous reason and you'd just spoil it to know it. --- Richard Feynman

Mathematics

• The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face the blackboard and to turn his back on the class. He writes a, he says b, he means c; but it should be d. --- G Polya


• I protest against the use of infinite magnitude as something accomplished, which is never permissible in mathematics. Infinity is merely a figure of speech, the true meaning being a limit. --- C F Gauss


• A serious threat to the very life of science is implied in the assertion that mathematics is nothing but a system of conclusions drawn from definitions and postulates that must be consistent but otherwise may be created by the free will of the mathematician. --- Richard Courant


• The constructive intuition of the mathematician brings to mathematics a non-deductive and irrational element which makes it comparable to music and art. --- Richard Courant

Probability

• Probability theory is nothing but common sense reduced to calculation. --- Laplace


• Bayes' theorem is precisely the mother of all adaptive procedures. --- E T Jaynes

Research, Science

• If you do not work on an important problem, it's unlikely you'll do important work. It's perfectly obvious. ... The average scientist, so far as I can make out, spends almost all his time working on problems which he believes will not be important and he also doesn't believe that they will lead to important problems. --- Richard Hamming


• That is the characteristic of great scientists; they have courage. They will go forward under incredible circumstances; they think and continue to think. --- Richard Hamming


• Academia places a young person under a kind of cumpulsion to produce impressive quantities of scientific publications - a temptation to superficiality, which only strong characters can resist. --- Albert Einstein


• When there is a hard problem, one has to work a long time and has to be persistent. In order to be persistent, you have got to be convinved that it's worthwhile working so hard, that you're going to get somewhere. And that takes a certain kind of fooling yourself. --- Richard Feynman


• Science at any moment does not claim to have explanations of everything. --- Harold Jeffreys


• One of the difficulties of scientific research is that it is impossible to make progress without clear understanding, yet this understanding can come only from the work itself; every completed piece of research represents a victory over this contradiction. --- A B Migdal


• It's not that I'm so smart, it's just that I stay with problems longer. --- Albert Einstein


• Nature has not troubled to make the discovery of its laws easy for us. --- Albert Einstein


• Do not believe anything but doubt only what is worth doubting. --- G Polya


• Look around when you have got your first mushroom or made your first discovery; they grow in clusters. --- G Polya


• If you find a problem interesting, don't worry too much about whether it has been solved in the existing literature. You will have a lot more fun with it if you don't know, and you will learn a lot, even if what you come up with turns out not to be publishable. --- A J Leggett


• Basic research is like shooting an arrow into the air and where it lands, painting a target. --- Homer Adkins


• I don't mind your thinking slowly; I mind your publishing faster than you think. --- Wolfgang Pauli

Teaching, Writing

• I believe altogether that love is a better teacher than a sense of duty. --- Albert Einstein


• Teachers and authors of textbooks should not forget that the intelligent student and the intelligent reader are not satisfied by verifying that the steps of a reasoning are correct but also want to know the motive and the purpose of various steps. --- G Polya


• We solve a problem for the first time by that (perhaps dull to some) direct calculation applying our systematic rules. After seeing the solution, we may contemplate it and see a clever trick that would have led us to the answer much more quickly. Then, of course, we have the opportunity for gamesmanship by showing others only the clever trick, scorning to mention the base means by which we first found the answer. But while this may give a boost to our ego, it does not help anyone else. ... For a teacher, therefore, maturity is largely a matter of overcoming the urge to gamesmanship. --- Edwin T Jaynes


• The first rule of style is to have something to say. The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then the other, not both at the same time. --- G Polya


• I hoped that maybe someday I'd write something that Feynman would admire. And then I thought, no, even better, I hope that someday I will write something that I will admire. --- Leonard Mlodinow


• Any fool may write a most valuable book by chance, if he will only tell us what he heard and saw with veracity. --- Thomas Gray