Knowledge is of two kinds. We know a subject ourselves or we know where we can find information upon it -- Samuel Johnson, Boswell’s Life of Johnson (1775) (From the beginning of the Subject Index of Higham's monograph, ASNA)

Cogito, Ergo Sum.  -- Descartes

When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false. -- Carl Friedrich Gauss

The total number of Dirichlet's publications is not large; jewels are not weighed on a grocery scale -- Carl Friedrich Gauss

 

(From MIT Professors)

By geometry, [pause] Well, just by looking at it actually.

Trivial: go home and stare at it for 3 hours until you’re convinced.

After working at it long enough to understand it, you should agree that it’s trivial.

The margin of this blackboard is too small for the proof of this theorem.

Pure math is divided into analysis, algebra, and topology. Never mind what they are, they’re not important (This one is from Mattuck!)

I have a feeling I must be a windbag, since my notes for this lecture consist of 4 lines, and [in 44 minutes] I’ve only covered 2.

How many people don’t know \omega is the cube-root of unity? That’s a lie; I just told you.

You’ll use it in the next problem set. If that isn’t applied mathematics I don’t know what is.

Some of you said 0, which is a reasonable answer, but not right.

I didn’t do it last time, but I stated that you could read it in your book, and that’s the same thing.

Aha! Your have Mattuck syndrome! You fall asleep at unpredictable moments. (Obviously from Mattuck!)

So, so, so…what am I trying to say?

It looks like the hypothesis has nothing to do with the solution. That makes a good theorem.

You can’t argue with me there. Well, you could, but it would be pointless, because this is the right answer.

I erased the theorem. It makes it easier to prove.

Well, let’s just defer that. Maybe we’ll defer that off to infinity.

So, tan theta is… [thinks] Well, let’s just say theta is whatever it is.

At certain critical values of \beta , something terrible is going to happen.

This is one of those things which you probably already understand but won’t after I’m finished explaining it.

 After scribbling all over one board, and mumbling a few disjointed, incoherent, sentences: That was a proof, by the way.

The sum of the heights of eight Canadians is close enough to infinity…

So far, I have prefaced every lecture by saying that this one is trivial. You may be asking yourself, 'is every lecture trivial?' Fortunately, or unfortunately, no.

While discussing multivariable max/min problems: It’s obvious that there’s a maximum... It’s obvious to me, anyway, and I’m giving the lecture.

There is a point I want to make. [pause] That was my point.

(Looking at a stack of problem sets being returned — each set about 50 pages long) I’m glad I’m not taking this class… it looks like a lot of work!

No hardcore math people here…? Then I can get away with this.

Don’t worry, I can’t pass the exams either.

 

[Miscellaneous--Most of these are picked from books I've read]

One may wish mournfully for faster silicon, but the only absolutely fatal disease to a scientist is a deficiency of thinking. [Boyd, Cheb and Four Spec 2nd ed, p.41]

We all owe it.
It is our duty to repay it.
And repaying it is the way we pass the debt on to our descendants. (Kahan, in his honorary doctoral speech, U of Waterloo)

The analysis was very complicated---a member of the National Academy of Sciences once described it to me, laughing, as ``the most complicated damn thing I've ever seen''---but the final answer fits on one line. [Boyd, op. cit., p.xii]

[Iserles, An Intro to Num Anal Diff Eq's]
Mathematics is not learnt from crib-sheets and brief compendia but by careful study of definitions, theorems and - most importantly, pehrhaps - proofs, by elucidating the intuition behind ideas and grasping the interconnectedness between what might seem disparate concepts at first glance. There are no shortcuts and no cherry-tasting knowledge capsules to help you along your path...

If we need it, we explain it. However, every book has to start from somewhere.

It is not unusual for students to attend a lecture course, study material, absorb it, pass an exam with flying colours and yet, a year or two later, a concept is perhaps not entirely forgotten but resides so deep in the recesses of memory that it cannot be used here and now.

A virtuous reader consults another textbook or perhaps her lecture notes. A less virtuous reader usually means to do so - not just yet - in the meantime plunges ahead with a decreased level of comprehension.

This appendix has been written in recognition of poverty and scarcity of virtue.

While trying to read a mathematical textbook, nothing can be worse than gradually losing the thread, progressively understanding less and less. This can happen either because the reader fails to understand the actual material - and the fault may well rest with the author - or when she encounters unfamilar mathematical constructs.

If in this volume you occasionally come across a mathematical concept and, for the life of you, simply cannot recall exactly what it means (or perhaps are not sure of the finer details of its definition), do glance in this appendix - you may find it here! However, if these glances become a habit, rather than an exception, perhaps you had better use a proper textbook!

There are two sections to this appendix, one on linear algebra and the second on analysis. Neither is complete - they both endeavour to answer possible queries arising from this book, rather than providing a potted summary of a subject.

There is nothing on basic calculus [here]. Unless you are familiar with calculus then, I am afraid, you are trying to dance the samba before you can walk.

Mathematics is replete with diverse concepts bearing the identical sobriquet 'stability' and a careful mathematician should always verify whether a casual reference to 'stability' has to do with stable ultrafilters in logic, with stable fluid flow or, perhaps, with (13.17).

Divide et impera---Divide and conquer. [Louis XI]

Think freely, think deeply, think differently... [Ehssan, my brother]