The plan here is to collect some quotes that I have heard or read somewhere. They will not be categorized according to subject now, maybe in the future I may do so.

The first principle is that you must not fool yourself — and you are the easiest person to fool.
Richard Feynman

What one fool can do, another can do better.
Richard Feynman

The set of things that I don’t know is dense in any topology.
Fabio Vlacci in a complex analysis lecture at ICTP

Once you have said a thing, it is very difficult to say it in another way.

We must know, we shall know.
David Hilbert

Now we move quickly and painfully, or painlessly depending on who you are, and derive the Schrödinger equation.
Douglas Hofstadter while speaking at a Mathematics Collouquim in the University of Vienna, 2017.

Every math talk should include at least one joke and one proof, preferably distinct.
Henry Cohn while speaking at a Summer School for PhD students of the University of Vienna, Obergurgl, September 2017.

Someday somebody will be able to write a paper with a great title 'The best packing is the best, or 'not...', it won't make sense unless someone knows which is which.
Henry Cohn explaining about results of Best in sphere packing, Obergurgl, September 2017.

If you are going to read only one thing about information theory then this is it; also you should read at least one thing about information theory in your life.
Henry Cohn, Obergurgl, September 2017.

The world of math is path connected.
Mathias Kreck while lecturing about Poincare Conjecture, Obergurgl, September 2017.

God created the world in four dimensions, well 11 if you are a string theorist. But it's 4+7.
Mathias Kreck while lecturing about Poincare Conjecture, Obergurgl, September 2017.

The name is what it is. But it's wrong.
Mathias Kreck on positive definite kernels, Obergurgl, September 2017.

Mathematics is the universal language that no one speaks.
Pierre Loius Lions, Vienna, September 2017.

I have a lot of knowledge in my computer.
Vivien Ripoll referring to the files saved on his computer, while at lunch in Vienna, 2017.

If you are dying it's supposed to be a full time job, but Ramanujan sent a letter three months before his death to Hardy.
George Andrews speaking about Ramanujan, Hagenberg, 2017.

The airline ticket pricing policy was very fortunate, if you spend three weeks in Europe then the price was $\epsilon$, if you spent less than three weeks then it was $\dfrac{1}{\epsilon}$.
George Andrews while speaking about how he discovered Ramanujan's Lost Notebook, Hagenberg, 2017.

I became the leading expert on mock theta functions, in the sense that no one else knew about it at that time.
George Andrews speaking about Ramanujan, Hagenberg, 2017.

Please think of this 4 as a 5.
George Andrews pointing out a typo in one of his slides, Hagenberg, 2017.

Harold Potter came, then some magic happened.
Michael Schlosser referring to a result by H. Potter, mathematician, Vienna, 2017.