Quotable Mathematics

"A model is a good model if it: 1. Is elegant 2. Contains few arbitrary or adjustable elements 3. Agrees with and explains all existing...

"If we refused to use complex numbers out of stubbornness disguised as some kind of bogus philosophical objection, a solution to a whol...

"The dialectician is concerned only with proceeding from propositions which are as acceptable as possible. These are propositions which...

  "[…] in order to observe, our mind has need of some theory or other. If in contemplating phenomena we did not immediately connect the...

"Hypothesis, however, is an inference based on knowledge which is insufficient to prove its high probability." (Frederick L Barry,...

"Events are independent when the happening of any one of them does neither increase nor abate the probability of the rest." (Thoma...

"The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which ...

"For each of the elements into which we have divided the amount of fluid matter, its  shape will be altered during the time dt, and als...

"For a linear operator, the change of the basis of the underlying linear space corresponds to a similarity transformation of the matric...

"Freedom of expression is the matrix, the indispensable condition, of nearly every other form of freedom." (Benjamin N Cardozo, Pa...