Mathematician Quotes

Mathematics is an aspect of culture as well as a collection of algorithms.

By slow degrees, the minds of men were cut adrift from their old scholastic moorings and sent forth on the wide sea of scientific inquiry, to discover new islands and continents of truth.

Florian Cajori
Florian Cajori
The importance of infinite processes for the practical exigencies of technical life can hardly be overemphasized. Practically all applications of arithmetic to geometry, mechanics, physics and even statistics involve these processes directly and indirectly.

It is all too easy to notice the statistical sea that supports our thoughts and actions. If that sea loses its buoyancy, it may take a long time to regain the lost support.

In early times of Christianity, even those who used animal food themselves came to think of the vegetarian as one who lived a higher life, and approached more nearly to Christian perfection.

George Salmon
George Salmon
Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known.

The triplet of specifications - the product-market scope, the growth vector and the competitive advantage - describes the firm's product-market path in the external environment.

It seems certain that there is a limit to the amount of living mathematics that humanity can sustain at any time. As new mathematical specialties arise, old ones will have to be neglected.

Mathematics is the science of the connection of magnitudes. Magnitude is anything that can be put equal or unequal to another thing. Two things are equal when in every assertion each may be replaced by the other.

Hermann Grassmann
Hermann Grassmann
Most often it is the case that people know that something big can be manipulated with it [i. e., the screw], but not how and in what way it is connected to time, and that untold time, and finally such force of machines, wheels, and shafts is necessary as cannot be produced nor be had.

Jacob Leupold
Jacob Leupold
'My dear friend, that must be a delusion, what can a circle have to do with the number of people alive at a given time?'

W. W. Rouse Ball
W. W. Rouse Ball
Statistical methods of analysis are intended to aid the interpretation of data that are subject to appreciable haphazard variability.

Proof, being the highest level of reproduction activity, has an important interiorization aspect: as Yuri Manin stresses in his book Provable and Unprovable, a proof becomes such only after it is accepted (as the result of a highly rigorous process)... Manin describes the act of acceptance as a social act; however, the importance of its personal, psychological component can hardly be overestimated.

I wonder what an astronomy would look like which has been rigorously demonstrated in every respect. It seems as if one can get to the truth only through a series of hypotheses, and that one has to reject each previous one to espouse the next and to abandon it again.

Johann Heinrich Lambert
Johann Heinrich Lambert
Even in the realm of things which do not claim actuality, and do not even claim possibility, there exist beyond dispute sets which are infinite.

Bernard Bolzano
Bernard Bolzano
We use Reason for improving the Sciences; whereas we ought to use the Sciences for improving our Reason.

My thesis, paradoxically, and a little provocatively, but nonetheless genuinely, is simply this : PROBABILITY DOES NOT EXIST. The abandonment of superstitious beliefs about theexistence of Phlogiston, the Cosmic Ether, Absolute Space and Time,..., or Fairies and Witches, was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our true probabilistic beliefs.

Man is what he is, because a spiritual element has entered into, and taken possession of, animal consciousness. This spiritual element is not, according to Christian teaching, divine: but it is capable of entering into relations with God. It can perceive Him: in thought, it can reason as to His nature and actions: in will and feeling, it can serve and love Him, or disobey and fear Him. Such activity shows itself in what we call the working of conscience.

Ernest Barnes
Ernest Barnes
It is widely believed that in our quantum world physical facts about occurrences in space time must be grounded in the wave function. There are several long recognized and much discussed difficulties with this view.

The characteristic which distinguishes the present-day professional statistician, is his interest and skill in the measurement of the fallibility of conclusions.

I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses.

One cannot guess the real difficulties of a problem before having solved it.

For that my opinion doth differ from some of the ancient writers in natural Phylosophy, it is possible that it may be ytterly dislyked of and condemned to be of no trueth.

When I saw that Moses' version of the Genesis of the world did not fit sufficiently in many ways with Aristotle and the rest of the philosophers, I began to have doubts about the truth of all philosophers and started to investigate the secrets of nature.

Gerardus Mercator
Gerardus Mercator
If we arrive at an equation containing on each side the same term but with different coefficients, we must take equals from equals until we get one term equal to another term. But, if there are on one or on both sides negative terms, the deficiencies must be added on both bides until all the terms on both sides are positive. Then we must take equals from equals until one term is left on each side.