…it ought to be remembered that there is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things. Because the innovator has for enemies all those who have done well under the old conditions, and lukewarm defenders in those who may do well under the new.

Macbeth: How does your patient, doctor?
Doctor: Not so sick, my lord,
As she is troubled with thick-coming fancies,
That keep her from her rest.
Macbeth: Cure her of that.
Canst thou not minister to a mind diseased,
Pluck from the memory a rooted sorrow,
Raze out the written troubles of the brain,
And with some sweet oblivious antidote
Cleanse the stuffed bosom of that perilous stuff
Which weighs upon the heart?
Doctor: Therein the patient
Must minister to himself.
Macbeth: Throw physic to the dogs; I'll none of it.

A political law or a scientific truth may be perilous to the morals or the faith of individuals; but it cannot on this ground be resisted by the Church. … A discovery may be made in science which will shake the faith of thousands; yet religion cannot regret it or object to it. The difference in this respect between a true and a false religion is, that one judges all things by the standard of their truth, the other by the touchstone of its own interests. A false religion fears the progress of all truth; a true religion seeks and recognises truth wherever it can be found.

I should regard them [the Elves interested in technical devices] as no more wicked or foolish (but in much the same peril) as Catholics engaged in certain kinds of physical research (e.g. those producing, if only as by-products, poisonous gases and explosives): things not necessarily evil, but which, things being as they are, and the nature and motives of the economic masters who provide all the means for their work being as they are, are pretty certain to serve evil ends. For which they will not necessarily be to blame, even if aware of them.

If the just cure of a disease be full of peril, let the physician resort to palliation.

Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state.

Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.

Society increasingly has neglected the substructure of biology, to its own peril.

The Universe forces those who live in it to understand it. Those creatures who find everyday experience a muddled jumble of events with no predictability, no regularity, are in grave peril. The Universe belongs to those who, at least to some degree, have figured it out.