G. H. Hardy Quotes

Mathematics is one of the essential emanations of the human spirit, a thing to be valued in and for itself, like art or poetry.

I think that great programming is not all that dissimilar to great art. Once you start thinking in concepts of programming it makes you a better person...as does learning a foreign language, as does learning math, as does learning how to read.

And as to the faculties of the mind, setting aside the arts grounded upon words, and especially that skill of proceeding upon generall, and infallible rules, called Science; which very few have, and but in few things; as being not a native faculty, born within us; nor attained, (as Prudence,) while we look after somewhat else.

Problems may be solved in the study which have baffled all those who have sought a solution by the aid of their senses. To carry the art, however, to its highest pitch, it is necessary that the reasoner should be able to use all the facts which have come to his knowledge; and this in itself implies, as you will readily see, a possession of all knowledge, which, even in these days of free education and encyclopaedias, is a somewhat rare accomplishment.

If all art aspires to the condition of music, all the sciences aspire to the condition of mathematics.

-But rational thoughts lead only to rational thoughts, whereas irrational thoughts lead to new experiences.

We [may] answer the question: "Why is snow white?" by saying, "For the same reason that soap-suds or whipped eggs are white"-in other words, instead of giving the reason for a fact, we give another example of the same fact. This offering a similar instance, instead of a reason, has often been criticised as one of the forms of logical depravity in men. But manifestly it is not a perverse act of thought, but only an incomplete one. Furnishing parallel cases is the necessary first step towards abstracting the reason imbedded in them all.

The art of reasoning becomes of first importance. In this line antiquity has left us the finest models for imitation; I should consider the speeches of Livy, Sallust, and Tacitus, as pre-eminent specimens of logic, taste, and that sententious brevity which, using not a word to spare, leaves not a moment for inattention to the hearer. Amplification is the vice of modern oratory.

I think it's important to reason from first principles rather than by analogy. The normal way we conduct our lives is we reason by analogy. [With analogy] we are doing this because it's like something else that was done, or it is like what other people are doing. [With first principles] you boil things down to the most fundamental truths…and then reason up from there.

Mathematics is really an art, not a science.

Art arises from sources other than logic." (p.32)

Logic is the art of thinking well: the mind, like the body, requires to be trained before it can use its powers in the most advantageous way.

To me programming is more than an important practical art. It is also a gigantic undertaking in the foundations of knowledge.

Wilderness areas are first of all a series of sanctuaries for the primitive arts of wilderness travel, especially canoeing and packing.

But the nature of our civilized minds is so detached from the senses, even in the vulgar, by abstractions corresponding to all theabstract terms our languages abound in, and so refined by the art of writing, and as it were spiritualized by the use of numbers, because even the vulgar know how to count and reckon, that it is naturally beyond our power to form the vast image of this mistress called "Sympathetic Nature.

Intuition is the art, peculiar to the human mind, of working out the correct answer from data that is, in itself, incomplete or even, perhaps, misleading.

I had inherited what my father called the art of the advocate, or the irritating habit of looking for the flaw in any argument.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.

... mathematics is the science of skillful operations with concepts and rules invented just for this purpose.

We have art so that we shall not die of reality.

What if there were no hypothetical questions?

[The decay of Logic results from an] untroubled assumption that the particular is real and the universal is not.

Nobody is made anything by hearing of rules, or laying them up in his memory; practice must settle the habit of doing, without reflecting on the rule; and you may as well hope to make a good painter, or musician, extempore, by a lecture and instruction in the arts of music and painting, as a coherent thinker, or a strict reasoner, by a set of rules, showing him wherein right reasoning consists.

The capacity to reason is a special sort of capacity because it can lead us to places that we did not expect to go.

The best result of mathematics is to be able to do without it.