Some of my favourite quotes

Computer Science

A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine — Alan Turing

If we want a machine to be intelligent, it can’t also be infallible. — Alan Turing

But in regarding computers merely as our slaves for getting things done, we may be missing the point. — Leslie Valiant

Computational Complexity

If pigs could whistle then donkeys could fly — Richard Karp

the efficiency of an algorithm is to a considerable extent much more important than the technology used to execute it. — Sanjeev Arora and Boaz Barak

Complexity theory is an important subject that grew out of computer science, the heroes of it were Alan Turing and Alonzo Church and its quantum version, Charlie Bennett … — Leonard Susskind

Which computational problems can be solved in polynomial-time and which cannot? Though seemingly technical, this question has wide-ranging implications and brings us to the heart of both theoretical computer science and modern physics. — Stephen Jordan

By any objective standard, the theory of computational complexity ranks as one of the greatest intellectual achievements of humankind — along with fire, the wheel, and computability theory. — Scott Aaronson

if aliens with infinite computational powers came to earth, they could not only beat humans at chess, but could also mathematically prove they were playing chess perfectly — Scott Aaronson

Complexity theory could be defined as the field concerned with deep, nontrivial, mathematically-sophisticated justifications for failure. — Scott Aaronson

The first lesson is that computational complexity theory is really, really, really not about computers. Computers play the same role in complexity that clocks, trains, and elevators play in relativity. They’re a great way to illustrate the point, they were probably essential for discovering the point, but they’re not the point. — Scott Aaronson

Quantum Computational Complexity

It is a fundamental goal of quantum complexity theory to understand the implications of quantum information to computational complexity. In other words, we want to understand the impact of quantum information on the way we classify the inherent difficulty of computational problems. — John Watrous

So now we’ve got this beautiful theory of quantum mechanics, and the possibly-even-more-beautiful theory of computational complexity. Clearly, with two theories this beautiful , you can’t just let them stay single – you have to set them up, see if they hit it off, etc — Scott Aaronson

the ability to decode the Hawking radiation from a black hole implies the ability to counterfeit quantum money. — Scott Aaronson

Pure Mathematics(y)

Hóper édei deîxai. (‘Quod erat demonstrandum’) — Euclid

The scientist finds his reward in what Henri Poincare calls the joy of comprehension, and not in the possibilities of application to which any discovery may lead. — Albert Einstein

Pure mathematics is, in its way, the poetry of logical ideas. — Albert Einstein

A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful. — John von Neumann

Obviousness is always the enemy of correctness. — Bertrand Russell

I have had my results for a long time, but I don’t know yet how to arrive at them. — Karl Friedrich Gauss

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. — Richard Feynman

Mathematics is the study of abstract objects, numerical, logical, or geometrical, that follow a set of several carefully chosen axioms. — Terence Tao

I was drawn to mathematics by the abstract beauty of formal manipulation, and the remarkable ability to repeatedly use simple rules to achieve non-trivial answers. — Terence Tao

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. — G. H. Hardy

A chess problem is genuine mathematics, but it is in some way ‘trivial’ mathematics. However ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. — G. H. Hardy

The ‘seriousness’ of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. — G.H. Hardy

The proof is by reductio ad absurdum, and reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. — G.H. Hardy

When the world is mad, a mathematician may find in mathematics an incomparable anodyne — G.H. Hardy

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations,’ are simply the notes of our observations. — G.H. Hardy

The mathematician’s patterns, like those of the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. — G.H. Hardy

Obvious is the most dangerous word in mathematics. — E. T. Bell

The essence of mathematics lies entirely in its freedom. — Georg Cantor

In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi. (“In mathematics the art of asking questions is more valuable than solving problems.”) — Georg Cantor

First, it is necessary to study the facts, to multiply the number of observations, and then later to search for formulas that connect them so as thus to discern the particular laws governing a certain class of phenomena. In general, it is not until after these particular laws have been established that one can expect to discover and articulate the more general laws that complete theories by bringing a multitude of apparently very diverse phenomena together under a single governing principle. — Augustin Louis Cauchy

In fact, I came to mathematics indirectly. I was really more interested in physics and philosophy and thought about those. It is a little shortened but not quite wrong to say: I thought I am not good enough for physics and I am too good for philosophy. Mathematics is in between.” — George Pólya

The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit. — Alfred North Whitehead

It is difficult to find a definition of combinatorics that is both concise and complete, unless we are satisfied with the statement Combinatorics is what combinatorialists do. — W. T. Tutte


The effort to understand the universe is one of the few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy. — Steven Weinberg

Math is to Physics as masturbation is to sex — Usually attributed to Feynman

Quantum Mechanics

The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you accept Nature as She is — absurd. — Richard Feynman

Shut up and calculate! — Usually attributed to Feynman

My own view is that quantum mechanics, like classical probability theory, should be seen as somehow “intermediate” between a continuous and discrete theory. — Scott Aaronson

Quantum Computing

Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy. — Richard Feynman


It’s not that I’m so smart. It’s just that I spent more time on problems. — Albert Einstein

Wir müssen wissen. Wir werden wissen. (We must know. We will know.) — David Hilbert

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

The “paradox” is only a conflict between reality and your feeling of what reality “ought to be.” — Richard Feynman

I learned very early the difference between knowing the name of something and knowing something. — Richard Feynman

If you have a theory, you must try to explain what’s good and what’s bad about it equally. In science, you learn a kind of standard integrity and honesty. — Richard Feynman

So then, how do you do original research? By throwing your entire life into it. Many researchers play piano, go to clubs, sail, etc., but if they’re any good they probably think about research while they’re doing these things. I know grad students who never suffer the indignity of working late into the night. They go surfing with friends every weekend and are constantly away on road trips. At this rate, they’ll enjoy life more than I will but won’t be successful researchers. — Scott Aaronson

if challenge is what you seek, then the thing to do is to tackle difficult open problems in math and computer science (or possibly physics). Unlike the skydiver, the kayaker, or the mountain-climber, the theorem-prover makes a permanent contribution in the best case, and is down a few months and a few hundred cups of coffee in the worst case. — Scott Aaronson

If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full. — G.H. Hardy

The years between 18 and 25 are are critical years in a mathematician’s career, and the damage had been done. Ramanujan’s genius never had again a chance of full development. — G.H. Hardy

There was no gain at all when the College at Kumbakonam rejected the one great man they had possessed, and the loss was irreparable; it is the worse instance that I know of the damage that can be done by an inefficient and inelastic educational system. So little was wanted, £60 a year for five years, occasional contact with almost anyone who had real knowledge and a little imagination, for the world to have gained another of its greatest mathematicians. — G.H. Hardy

Sometimes ideas just come to me. Other times I have to sweat and almost bleed to make ideas come. It’s a mysterious process, but I hope I never find out exactly how it works. — J. K. Rowling

If I have seen farther than other men, it is because I have stood on the shoulders of giants. — Isaac Newton


They had wasted all their time memorizing stuff like that, when it could be looked up in fifteen minutes. — Richard Feynman

The reading of all good books is like a conversation with the finest people of past centuries. — Descartes

ζῷον δίπουν ἄπτερον (‘two-legged featherless animal’, he was referring to humans) — Plato


The only purpose for which power can be rightfully exercised over any member of a civilized community, against his will, is to prevent harm to others. — John Stuart Mill

He who knows only his own side of the case, knows little of that. His reasons may be good, and no one may have been able to refute them. But if he is equally unable to refute the reasons on the opposite side; if he does not so much as know what they are, he has no ground for preferring either opinion. — John Stuart Mill

Are we so certain of always finding a man made to our hands for any duty or function of social importance which falls vacant, that we lose nothing by putting a ban upon one half of mankind, and refusing beforehand to make their faculties available, however distinguished they may be? — John Stuart Mill

Whoever claims that economic competition represents “survival of the fittest” in the sense of the law of the jungle, provides the clearest possible evidence of his lack of knowledge of economic science. — George Reisman

Under communism (socialism), there is no incentive to supply people with anything they need or want, including safety. — George Reisman

Ancient Wisdom

λάθε βιώσας (‘Live hidden’) — Epicurus

μέτρον ἄριστον. (‘Moderation is best’) — Cleobulus

πάντοτε ζητεῖν τὴν ἀλήθειαν (‘ever seeking the truth’) — Diogenes Laertius

τί εὔκολον; Τὸ ἄλλῳ ὑποτίθεσθαι. (‘What is easy? To advise another.’) — Thales

τὸ γὰρ ἡδύ, ἐὰν πολύ, οὐ τί γε ἡδύ. (‘A sweet thing tasted too often is no longer sweet.’) — unattributed


Amicus Plato, sed magis amica veritas (‘Plato is my friend, but truth is a better friend. ‘) — Aristotle

cogito ergo sum (‘I think, therefore I am.’) — René Descartes

Τί ἐστιν ἀλήθεια; (‘What is truth?’) — John 18:38

Philosophy is too important to be left to the philosophers. — John Wheeler

Quantum states are a bunch of linear operators, that is what they are. — John Watrous


Dream is not that which you see while sleeping, it is something that does not let you sleep. ― A.P.J. Abdul Kalam

More weirder stuff

The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore, all progress depends on the unreasonable man. — George Bernard Shaw

Of course it’s complicated. If it wasn’t, I probably wouldn’t be interested — Jon Ellis

There are people who have been ignored and kicked around a few times, the ones the crowd will tell you to stay away from. Seek those people out, and find them; they are the ones who will change the world. — R.M. Drake

There is nothing deep or technical about it, it is just complicated [about a proof]. — John Watrous