Quotes of All Topics . Occasions . Authors
Natural religion itself, seems to decay very much. Many will have human souls to be material: others make God himself a corporeal being.
And there must be simple substances, because there are compounds; for the compound is nothing but a collection or aggregatum of simples.
A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
The wish to hurt, the momentary intoxication with pain, is the loophole through which the pervert climbs into the minds of ordinary men.
The life of a mathematician is dominated by an insatiable curiosity, a desire bordering on passion to solve the problems he is studying.
Only dead mathematics can be taught where the attitude of competition prevails: living mathematics must always be a communal possession.
There is nothing like a naturalistic orientation to dispel all these morbid thoughts of "sin" and "free will" and "moral responsibility.
Familiar things happen, and mankind does not bother about them. It requires a very unusual mind to undertake the analysis of the obvious.
The diameter of the earth is greater than the diameter of the moon and the diameter of the sun is greater than the diameter of the earth.
As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.
If you want to be a real seeker of truth, you need to, at least once in your lifetime, doubt in, as much as it's possible, in everything.
We make an idol of truth itself; for truth apart from charity is not God, but His image and idol, which we must neither love nor worship.
ALGEBRA is a general Method of Computation by certain Signs and Symbols which have been contrived for this Purpose, and found convenient.
There is a certain way of searching for the truth in mathematics that Plato is said first to have discovered. Theon called this analysis.
The aim of scientific work is truth. While we internally recognise something as true, we judge, and while we utter judgements, we assert.
Science is built up of facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.
Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination.
No one who achieves success does so without acknowledging the help of others. The wise and confident acknowledge this help with gratitude.
The difference between ancients and moderns is that the ancients asked what have we experienced, and moderns asked what can we experience.
The paradox is now fully established that the utmost abstractions are the true weapons with which to control our thought of concrete fact.
Philosophy is the product of wonder. The effort after the general characterization of the world around us is the romance of human thought.
We should seek the truth without hesitation; and, if we refuse it, we show that we value the esteem of men more than the search for truth.
What a difficult thing it is to ask someone's advice on a matter without coloring his judgment by the way in which we present our problem.
There are vices which have no hold upon us, but in connection with others; and which, when you cut down the trunk, fall like the branches.
Eloquence is a painting of thought; and thus those who, after having painted it, add something more, make a picture instead of a portrait.
To love is to take delight in happiness of another, or, what amounts to the same thing, it is to account another's happiness as one's own.
Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.
The Creator, the fountain of all wisdom, the approver of perpetual order, the eternal and superessential spring of geometry and harmonics.
The referee said it was not acceptable, but the Press considered they could not refuse to publish a book by a professor of the university.
The Best of the artist's art, which will one day be in a Museum wall, the Painting that sets the artist apart of all other artist artists.
What good your beautiful proof on the transcendence of Pi: Why investigate such problems, given that irrational numbers do not even exist?
All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.
Any use of a human being in which less is demanded of him and less is attributed to him than his full status is a degradation and a waste.
I read once that the true mark of a pro - at anything - is that he understands, loves, and is good at even the drudgery of his profession.
The importance of an individual thinker owes something to chance. For it depends upon the fate of his ideas in the minds of his successors.
The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'.
The world is satisfied with words. Few appreciate the things beneath. [Fr., Le monde se paye de paroles; peu approfondissement les choses.]
Mathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life.
They [formulae 1.10 - 1.12 of Ramanujan] must be true because, if they were not true, no one would have had the imagination to invent them.
Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.
People (or students) do not have shortcomings, only uniquenesses. The goal of a good teacher is to turn these uniquenesses into advantages.
Whether our work is art or science or the daily work of society, it is only the form in which we explore our experience which is different.
If the earth should cease to attract its waters to itself all the waters of the sea would be raised and would flow to the body of the moon.
A marveilous newtrality have these things mathematicall, and also a strange participation between things supernaturall and things naturall.
I recall once saying that when I had given the same lecture several times I couldn't help feeling that they really ought to know it by now.
To some extent, people who are insane are nonconformists, and society and their family wish they would live what appear to be useful lives.
It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection.
One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden.
The task of a university is the creation of the future, so far as rational thought and civilized modes of appreciation can affect the issue.