Mathematician Quotes

With the exception of the geometric series, there does not exist in all of mathematics a single infinite series whose sum has been determined rigorously.

Niels Henrik Abel

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

Research programmes, besides their negative heuristic, are also characterized by their positive heuristic.

The notion that the intellect can create meaningful postulational systems at its whim is a deceptive half-truth. Only under the discipline of responsibility to the organic whole, only guided by intrinsic necessity, can the free mind achieve results of scientific value.

Herbert Robbins

If we have a certain class of objects and a certain class of relations and if the only questions which we investigate are whether ordered groups of these objects do or do not satisfy the relations, the results of the investigations are called mathematics.

Mathematics is the science of order and mathematicians seek to identify instances of order and to formulate and understand concepts that enable us to perceive order in complicated situations.

Shlomo Sternberg

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

Carl Ludwig Siegel

I Gladly avail myself of the opportunity of inscribing to you, for a second time, a work of mine on Algebra, as a sincere tribute of my respect, affection and gratitude.
I trust that I shall not be considered as derogating from the higher duties which, (in common with you), I owe to my station in the Church, if I continue to devote some portion of the leisure at my command, to the completion of an extensive Treatise, embracing the more important departments of Analysis, the execution of which I have long contemplated, and which, in its first volume I now offer to the public, under the auspices of one of my best and dearest friends.

The value of [pi] has engaged the attention of many mathematicians and calculators from the time of Archimedes to the present day, and has been computed from so many different formulae, that a complete account of its calculation would almost amount to a history of mathematics.

James Whitbread Lee Glaisher

There are a number of theorems in ordinary algebra, which, though apparently proved to be true only for symbols representing numbers, admit of a much more extended application. Such theorems depend only on the laws of combination to which the symbols are subject, and are therefore true for all symbols, whatever their nature may be, which are subject to the same laws of combination. The laws with which we have here concern are few in number, and may be stated in the following manner. Let a, b represent two operations, u, v two subjects on which they operate, then the laws are

Duncan Farquharson Gregory

When I was on the train from Liverpool to Cambridge to become a student, it occurred to me that no one at Cambridge knew I was painfully shy, so I could become an extrovert instead of an introvert.

John Horton Conway

Mathematics deals mainly with realities and stern facts, and it arms those whose life work is beset with physical difficulties. Hence it appeals especially to the leaders of the common people, and it performs a fundamental function in the education of those who aim to excel in overcoming material difficulties.

George Abram Miller

If we know anything we know it by mathematics; but those people have no concern for the true and legitimate science of things! they cling to trivialities!

Pierre Gassendi

There is a certain way of searching for the truth in mathematics that Plato is said first to have discovered; Theon named it analysis, and defined it as the assumption of that which is sought as if it were admitted and working through its consequences to what is admitted to be true. This is opposed to synthesis, which is the assuming what is admitted and working through its consequences to arrive at and to understand that which is sought.

François Viète

Logic is invincible because in order to combat logic it is necessary to use logic.

Pierre Boutroux

I think I perceive or remember something but am not sure; this would seem to give me some ground for believing it, contrary to Mr. Keynes' theory, by which the degree of belief in it which it would be rational for me to have is that given by the probability relation between the proposition in question and the things I know for certain.

Frank P. Ramsey

To history we shall adhere no farther, than is sufficient to preserve an unbroken series of methods gradually becoming more exact and extensive; the series beginning with the first rude, though perfectly just, method of James Bernoulli, and ending with Lagrange's exquisite and refined Calculus of Variations.

Robert Woodhouse

I have endeavour'd to make every thing so plain, that a very little Skill in Geometry may be sufficient to enable one to read this Book by himself. And upon this occasion I would advise all my Readers, who desire to make themselves Masters of this Subject, not to be contented with the Schemes they find here; but upon every Occasion to draw new ones of their own, in all the Variety of Circumstances they can think of. This will take up a little more Time at first; but in a little while they will find the vast Benefit of it, by the extensive Notions it will give them of the Nature of these Principles.

The group of problems which I propose to describe belong to that Cinderella of pure mathematics - the study of differential equations.

George Frederick James Temple

With even a superficial knowledge of mathematics, it is easy to recognize certain characteristic features: its abstractions, its precision, its logical rigor, the indisputable character of its conclusions, and finally, the exceptionally broad range for its applications.

Aleksandr Danilovich Aleksandrov

Where did you intend to go when you applied for your passport? [...] Did you get into any of the countries we now call Iron Curtain countries?

Richard Friederich Arens

[The George E. P. Box paper Fitting empirical data (1960) is] a mature exposition of an important branch of statistics, to which the author has made great contributions. One feature of particular interest is practical discussion of genuinely nonlinear fitting problems and their solution with the help of tact and a special, publicly available, IBM-704 program. Another is insightful comments on the role of prior distributions in statistics.

Leonard Jimmie Savage

Almost everyone has heard that "figures don't lie, but liars can figure." We need statistics, but liars give them a bad name, so to be able to tell the liars from the statisticians is crucial.

Robert Hooke (mathematician)

And how admirable and rare an ornament, O good God, is mildenesse in a divine? And how much is it to be wished in this age, that all divines were mathematicians? that is men gentle and meeke.

Bartholomaeus Pitiscus

Science is one aspect of God's presence, and scientists therefore part of the company of His heralds.

Charles Coulson