Theorem Quotes
-
the theorem of incompleteness . . . [shows] there is nothing on this level of existence that can fully explain this level of existence.
-
Green's theorem is true. It's us that are false.
-
The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance.
-
Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can’t be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere – no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what’s also amazing is that we own all of them. No one can patent a mathematical formula, it’s ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It’s too precious to be given away to the “initiated few.” It belongs to all of us.
-
In just shutting your eyes and following fundamental theorem of calculus, we are led into a grievous error.
-
A theorem is a proposition which is a strict logical consequence of certain definitions and other proposition.
-
It gives me the same pleasure when someone else proves a good theorem as when I do it myself.
-
A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem.
-
Never call yourself a philosopher, nor talk a great deal among the unlearned about theorems, but act conformably to them. Thus, at an entertainment, don't talk how persons ought to eat, but eat as you ought. For remember that in this manner Socrates also universally avoided all ostentation.
-
Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?
-
The Babylonians had known about Pythagoras’s theorem centuries before Pythagoras was born.
-
Too much knowledge could be a bad thing. I was lead to the Szemerédi theorem by proving a result, about squares, that Euler had already proven, and I relied on an "obvious" fact, about arithmetical progressions, that was unproved at the time. But that lead me to try and prove that formerly unproved statement- about arithmetical progressions-and that ultimately lead to the Szemerédi Theorem.
