[To a man expecting a scientific proof of the impossibility of flying saucers] I might have said to him: “Listen, I mean that from my knowledge of the world that I see around me, I think that it is much more likely that the reports of flying saucers are the results of the known irrational characteristics of terrestrial intelligence than of the unknown rational efforts of extra-terrestrial intelligence.” It is just more likely, that is all. It is a good guess. And we always try to guess the most likely explanation, keeping in the back of the mind the fact that if it does not work we must discuss the other possibilities.

Dilbert: Evolution must be true because it is a logical conclusion of the scientific method.
Dogbert: But science is based on the irrational belief that because we cannot perceive reality all at once, things called “time” and “cause and effect” exist.
Dilbert: That’s what I was taught and that’s what I believe.
Dogbert: Sounds cultish.

Sir Robert Chiltern: You think science cannot grapple with the problem of women?
Mrs. Cheveley: Science can never grapple with the irrational. That is why it has no future before it in this world.

Disinterestedness is as great a puzzle and paradox as ever. Indeed, strictly speaking, it is a species of irrationality, or insanity, as regards the individual’s self; a contradiction of the most essential nature of a sentient being, which is to move to pleasure and from pain.

Hellenic science is a victory of rationalism, which appears greater, not smaller, when one is made to realize that it had been won in spite of the irrational beliefs of the Greek people; all in all, it was a triumph of reason in the face of unreason. Some knowledge of Greek superstitions is needed not only for a proper appreciation of that triumph but also for the justification of occasional failures, such as the many Platonic aberrations.

If it is true as Whewell says, that the essence of the triumphs of Science and its progress consists in that it enables us to consider evident and necessary, views which our ancestors held to be unintelligible and were unable to comprehend, then the extension of the number concept to include the irrational, and we will at once add, the imaginary, is the greatest forward step which pure mathematics has ever taken.

In the school of political projectors, I was but ill entertained, the professors appearing, in my judgment, wholly out of their senses; which is a scene that never fails to make me melancholy. These unhappy people were proposing schemes for persuading monarchs to choose favourites upon the score of their wisdom, capacity, and virtue; of teaching ministers to consult the public good; of rewarding merit, great abilities, and eminent services; of instructing princes to know their true interest, by placing it on the same foundation with that of their people; of choosing for employment persons qualified to exercise them; with many other wild impossible chimeras, that never entered before into the heart of man to conceive, and confirmed in me the old observation, that there is nothing so extravagant and irrational which some philosophers have not maintained for truth.

It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.

It is well known that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled. And so the guilty man, who fortuitously touched on and revealed this aspect of living things, was taken to the place where he began and there is for ever beaten by the waves.

No irrational exaggeration of the claims of Mathematics can ever deprive that part of philosophy of the property of being the natural basis of all logical education, through its simplicity, abstractness, generality, and freedom from disturbance by human passion. There, and there alone, we find in full development the art of reasoning, all the resources of which, from the most spontaneous to the most sublime, are continually applied with far more variety and fruitfulness than elsewhere;… The more abstract portion of mathematics may in fact be regarded as an immense repository of logical resources, ready for use in scientific deduction and co-ordination.

Objections … inspired Kronecker and others to attack Weierstrass’ “sequential” definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth—whatever that may be, if anything—precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals.

Piphobia is an irrational fear.

Science discovery is an irrational act. It’s an intuition which turns out to be reality at the end of it. I see no difference between a scientist developing a marvellous discovery and an artist making a painting

Science keeps religion from sinking into the valley of crippling irrationalism and paralyzing obscurantism. Religion prevents science from falling into the marsh of obsolete materialism and moral nihilism.

Scientists become as irrational and panicky as any other group when their basic tenets are questioned.

True and constant vigour of body is the effect of health, which is much better preserved with watery, herbaceous, frugal, and tender food, than with vinous, abundant, hard, and gross flesh (che col cameo vinoso ed unto abundante e duro). And in a sound body, a clear intelligence, and desire to suppress the mischievous inclinations (voglie dannose), and to conquer the irrational passions, produces true worth.