Mathematical Quotes

500+ Sourced quotes

Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.

Carl Friedrich Gauss

The science we are after is not about mathematicals either none of them, you see, is separable.

There is no certainty in sciences where one of the mathematical sciences cannot be applied, or which are not in relation with these mathematics.

Leonardo da Vinci

Physics is mathematical not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover.

Bertrand Russell

Although I'm regarded as a dangerous radical by particle physicists for proposing that there may be loss of quantum coherence, I'm definitely a conservative compared to Roger. I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation. I think Roger [Penrose] is a Platonist at heart but he must answer for himself.

Stephen Hawking

First Shakespeare sonnets seem meaningless; first Bach fugues, a bore; first differential equations, sheer torture. But training changes the nature of our spiritual experiences. In due course, contact with an obscurely beautiful poem, an elaborate piece of counterpoint or of mathematical reasoning, causes us to feel direct intuitions of beauty and significance. It is the same in the moral world.

I design to speak of the Physical, Metaphysical and Mathematical — of the Material and Spiritual Universe: — of its Essence, its Origin, its Creation, its Present Condition and its Destiny.

Edgar Allan Poe

I became more and more convinced that even nature could be understood as a relatively simple mathematical structure.

Albert Einstein

Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.

Leonardo da Vinci

But we have higher mathematics, haven't we? This gives me freedom from my senses. The language of mathematics is even more inborn and universal than the language of music; a mathematical formula is crystal clear and independent of all sense organs. I therefore built a mathematical laboratory, set myself in it as if I were sitting in a car, and moved along with a beam of light.

Albert Einstein

You propound a complicated mathematical problem: give me a slate and half an hour's time, and I can produce a wrong answer.

George Bernard Shaw

Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment.

Albert Einstein

I doubt not but it will be easily granted, that the knowledge we have of mathematical truths is not only certain, but real knowledge; and not the bare empty vision of vain, insignificant chimeras of the brain.

The conception of tensors is possible owing to the circumstance that the transition from one co-ordinate system to another expresses itself as a linear transformation in the differentials. One here uses the exceedingly fruitful mathematical device of making a problem "linear" by reverting to infinitely small quantities.

Bertrand Russell

As a proposition of linguistics: "Energy" is the name of the mathematical expression in question...As a propo sition of psychology: our senses are such that we notice what is roughly the mathematical expression in question, and we are led nearer and nearer to it as we refine upon our crude perceptions by scientific observation.

Bertrand Russell

Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

The smallest natural point is larger than all mathematical points, and this is proved because the natural point has continuity, and any thing that is continuous is infinitely divisible; but the mathematical point is indivisible because it has no size.

Leonardo da Vinci

Einstein's relativity work is a magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king... its exponents are brilliant men but they are metaphysicists rather than scientists.

All mathematicians would... be intuitive if they had clear sight, for they do not reason incorrectly from principles known to them; and intuitive minds would be mathematical if they could turn their eyes to the principles of mathematics to which they are unused.

The human story does not always unfold like a mathematical calculation on the principle that two and two make four. Sometimes in life they make five or minus three; and sometimes the blackboard topples down in the middle of the sum and leaves the class in disorder and the pedagogue with a black eye.

Winston Churchill

Einstein is the only figure in the physical sciences with a stature that can be compared with Newton. Newton is reported to have said "If I have seen further than other men, it is because I stood on the shoulders of giants." This remark is even more true of Einstein who stood on the shoulders of Newton. Both Newton and Einstein put forward a theory of mechanics and a theory of gravity but Einstein was able to base General Relativity on the mathematical theory of curved spaces that had been constructed by Riemann while Newton had to develop his own mathematical machinery. It is therefore appropriate to acclaim Newton as the greatest figure in mathematical physics and the Principia is his greatest achievement.

Stephen Hawking

One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?

Stephen Hawking

Our design, not respecting arts, but philosophy, and our subject, not manual, but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this — from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena...

The world looks like a multiplication-table, or a mathematical equation, which, turn it how you will, balances itself.

Ralph Waldo Emerson

First you must have faith in an eternal world independent of you; then you must have faith in your ability to perceive it, and finally you must try to explain it by means of concepts or mathematical constructions. But don't always accept traditional concepts without reexamining them. Even overthrow my relativity theory, if you find a better one.... You must believe that the world was created as a unified whole which is comprehensible to man. Of course, it's going to take an infinitely long time to investigate this unified creation. But to me that is the highest and most sacred duty—unifying physics. Simplicity is the criterion of the universe.

Albert Einstein