Mathematical Quotes

500+ Sourced quotes

Mathematical equations and literary phrases are useful but they are no substitute for the spatial eloquence of the map.

Arthur H. Robinson

Mathematical problems in physics have their place in teaching; but physics should not be made a means of teaching mathematics.

John Trowbridge

We cannot convey mathematics to the great mass of people unless we first dwell upon the utility of the subject and imagine what would happen to the world if every trace of mathematics and of mathematical knowledge should cease to exist.

David Eugene Smith

It is important to remember that the physical interpretation of the mathematical notions occurring in a physical theory must be compatible with the equations of the theory.

Andrzej Trautman

I shall mix together results which may prove to be of scientific importance and results that are probably no more than mathematical curiosities. The plan is to set down anything that seems worthy of note, even though we cannot see that it has any ultimate importance in nature.

Arthur Eddington

Without the power of observation, without judgment, without sagacity, all mathematical knowledge is useless.

Justus von Liebig

Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it.

Nowhere is intellectual beauty so deeply felt and fastidiously appreciated in its various grades and qualities as in mathematics, and only the informal appreciation of mathematical value can distinguish what is mathematics from a welter of formally similar, yet altogether trivial statements and operations.

Michael Polanyi

These last few days I've felt Godless. I've felt cleaner, less muddled, less blind. I still believe in a God. But he's so remote, so cold, so mathematical. I see that we have to live as if there is no God. Prayer and worship and singing hymns-all silly and useless.

As mathematicians navigate their way across the mathematical terrain, it as though all paths will necessarily lead at some point to the same awesome vista of the Riemann Hypothesis.

Marcus du Sautoy

In my own professional work I have touched on a variety of different fields. I've done work in mathematical linguistics, for example, without any professional credentials in mathematics; in this subject I am completely self-taught, and not very well taught.

Whether mathematical simplicity is God's affair or our, the fact remains that this feature more than any other remains the mainspring of progress in the physical sciences.

The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.

A geometrical theory in physical interpretation can never be validated with mathematical certainty... ; like any other theory of empirical science, it can acquire only a more or less high degree of confirmation.

Carl Gustav Hempel

Only he who knows what mathematics is, and what its function in our present civilization, can give sound advice for the improvement of our mathematical teaching.

So long as men strive to transcend their native powers, to rid themselves of prejudice and preconception, to observe phenomena in a dry light, the effort is scientific, whether at the moment it attains mathematical accuracy or not.

Abraham Flexner

It is a curious circumstance that a science so profoundly mathematical as the theory of probability should have originated in the games of chance which occupy the thoughtless and the profligate.

Robert Simpson Woodward

For vacuum rightly conceived of is merely a mathematical quantity extended in the three dimensions, existing per se without heat and cold, soft and hard, rare and dense, and without any natural quality, merely occupying space, as the philosophers maintained before Aristotle, not only within the heavens, but beyond.

A mathematical congress of today reminds one of the Tower of Babel, for few men can follow profitably the discussions of sections other than their own, and even there they are sometimes made to feel like strangers.

It is impossible to study the properties of a single mathematical trajectory. The physicist knows only bundles of trajectories, corresponding to slightly different initial conditions.

Léon Brillouin

It would be difficult to find a greater distance between any two terms than that which separates "matter" in the Greek-medieval tradition and the technical signification, suitably expressed in mathematical symbols, that the word bears in science today.

There are crystals as big as cathedral pillars, delicate as mildew and sharp as needles; plain, blue, green like nothing in the world, of fiery colours or black; mathematical, perfect, like the contrivances of queer and bewildered sages; or recalling livers, hearts, gigantic human organs and animal fluids.

Conclusions based upon analogies may fill up a portion of the vast chasm which separates the certain results of a mathematical natural philosophy from conjectures verging on the extreme, and therefore obscure and barren confines of all scientific development of mind.

Alexander von Humboldt

The spider's web is a glorious mathematical problem.

Jean Henri Fabre

History has never regarded itself as a science of statistics. It was the Science of Vital Energy in relation with time; and of late this radiating center of life has been steadily tending, — together with every form of physical and mechanical energy, — toward mathematical expression.