Quotes about mathematics

A collection of quotes on the topic of mathematics.

„I don’t think that everyone should become a mathematician, but I do believe that many students don’t give mathematics a real chance.“

— Maryam Mirzakhani Iranian mathematician 1977 - 2017

Interview with Research Fellow Maryam Mirzakhani | january 2008

Chance, Thinking

„The beauty of mathematics only shows itself to more patient followers.“

— Maryam Mirzakhani Iranian mathematician 1977 - 2017

Source: http://www.theguardian.com/science/2014/aug/13/interview-maryam-mirzakhani-fields-medal-winner-mathematician

Beauty

„Now, the velocity of wave propagation can be seen, without the aid of any mathematical analysis, to depend on the elasticity of the medium and its density; for we can see that if a medium is highly elastic the disturbance would be propagated at a great speed.“

— Albert A. Michelson American physicist 1852 - 1931

Light Waves and Their Uses Page 146.

Speed, Dependency

„That logic, as a science, is susceptible of very wide applications is admitted; but it is equally certain that its ultimate forms and processes are mathematical.“

— George Boole English mathematician, philosopher and logician 1815 - 1864

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 12; Cited in: William Stanley Jevons (1887) The Principles of Science: : A Treatise on Logic and Scientific Method. p. 155

Science

„It is upon the foundation of this general principle, that I purpose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of Mathematical Analysis,“

— George Boole English mathematician, philosopher and logician 1815 - 1864

Source: 1840s, The Mathematical Analysis of Logic, 1847, p. iii
Context: That to the existing forms of Analysis a quantitative interpretation is assigned, is the result of the circumstances by which those forms were determined, and is not to be construed into a universal condition of Analysis. It is upon the foundation of this general principle, that I purpose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of Mathematical Analysis, regardless that in its object and in its instruments it must at present stand alone.

„There cannot be a greater mistake than that of looking superciliously upon the practical applications of science. The life and soul of science is its practical application; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.“

— William Thomson British physicist and engineer 1824 - 1907

Lecture on "Electrical Units of Measurement" (3 May 1883), published in Popular Lectures Vol. I, p. 73, as quoted in The Life of Lord Kelvin (1910) by Silvanus Phillips Thompson

Time, Science, Problem, Knowledge

„The object of this paper is to give a satisfactory account of the Foundations of Mathematics in accordance with the general method of Frege, Whitehead and Russell. Following these authorities, I hold that mathematics is part of logic, and so belong to what may be called the logical school as opposed to the formalist and intuitionist schools. I have therefore taken Principia Mathematica as a basis for discussion and ammendment; and believe myself to have discovered how, by using the work of Mr Ludwig Wittgenstein, it can be rendered free from the serious objections which have caused its rejection by the majority of German authorities, who have deserted altogether its line of approach.“

— Frank P. Ramsey British mathematician, philosopher 1903 - 1930

Preface
The Foundations of Mathematics (1925)

Parting, School

„If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.“

— John Von Neumann Hungarian-American mathematician and polymath 1903 - 1957

Remark made by von Neumann as keynote speaker at the first national meeting of the Association for Computing Machinery in 1947, as mentioned by Franz L. Alt at the end of "Archaeology of computers: Reminiscences, 1945--1947", Communications of the ACM, volume 15, issue 7, July 1972, special issue: Twenty-fifth anniversary of the Association for Computing Machinery, p. 694.

People, Life

„It is interesting that the term mystic is used in this derogatory sense to mean anything we cannot segmentize and count. The odd belief prevails in our culture that a thing or experience is not real if we cannot make it mathematical, and that somehow it must be real if we can reduce it to numbers.“

— Rollo May US psychiatrist 1909 - 1994

Existence (1956) p. 39; also published in The Discovery of Being : Writings in Existential Psychology (1983), Part III : Contributions to Therapy, Ch. 6 : To Be and Not to Be, p. 94
Existence (1958)
Context: It is interesting that the term mystic is used in this derogatory sense to mean anything we cannot segmentize and count. The odd belief prevails in our culture that a thing or experience is not real if we cannot make it mathematical, and that somehow it must be real if we can reduce it to numbers. But this means making an abstraction out of it … Modern Western man thus finds himself in the strange situation, after reducing something to an abstraction, of having then to persuade himself it is real. … the only experience we let ourselves believe in as real, is that which precisely is not.

Sense

„The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.“

— Ronald Fisher English statistician, evolutionary biologist, geneticist, and eugenicist 1890 - 1962

Discussion to ‘Statistics in agricultural research’ by J.Wishart, Journal of the Royal Statistical Society, Supplement, 1, 26-61, 1934.
1930s

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„He has made contributions to many areas of science; among them are agronomy, anthropology, astronomy, bacteriology, botany, economics, forestry, meteorology, psychology, public health, and-above all-genetics, in which he is recognized as one of the leaders. Out of this varied scientific research and his skill in mathematics, he has evolved systematic principles for the interpretation of empirical data; and he has founded a science of experimental design. On the foundations he has laid down, there has been erected a structure of statistical techniques that are used whenever people attempt to learn about nature from experiment and observation.“

— Ronald Fisher English statistician, evolutionary biologist, geneticist, and eugenicist 1890 - 1962

W. Allen Wallis (1952) at the University of Chicago while honoring Fisher with the Honorary degree of Doctor of Science; cited in: George E. P. Box (1976) " Science and Statistics http://www-sop.inria.fr/members/Ian.Jermyn/philosophy/writings/Boxonmaths.pdf" Journal of the American Statistical Association, Vol. 71, No. 356. (Dec., 1976), pp. 791-799.

Science, Nature, Health, Learning

„[B]ecause that which is finite is always bounded with reference to something… it is necessary that there should be no end… [N]umber also appears to be infinite, and mathematical magnitudes, and that which is beyond the heavens. And since that which is beyond is infinite, body also appears to be infinite, and it would seem that there are infinite worlds; for why is there rather void here than there? …If also there is a vacuum, and an infinite place, it is necessary that there should be an infinite body: for in things which have a perpetual subsistence, capacity differs nothing from being. The speculation of the infinite is, however, attended with doubt: for many impossibilities happen both to those who do not admit that it has a subsistence, and to those who do. …It is …especially the province of a natural philosopher to consider if there be a sensible infinite magnitude.“

— Aristotle, book Physics

Book III, Ch. V, p. 156.
Physics

Appearance, Nature, World

„Mathematics is the gate and key of the sciences. … Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy.“

— Roger Bacon, book Opus Majus

cited in: Morris Kline (1969) Mathematics and the physical world. p. 1
Opus Majus, c. 1267

Science, Knowledge, World, Men

„I am persuaded that it [The Method of Mechanical Theorems] will be of no little service to mathematics; for I apprehend that some, either of my contemporaries or of my successors, will, by means of the method when once established, be able to discover other theorems in addition, which have not yet occurred to me.“

— Archimedes, book The Method of Mechanical Theorems

The Method of Mechanical Theorems

„Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori, and it will be your task to find out the false deduction in each case.“

— Carl Gustav Jacob Jacobi German mathematician 1804 - 1851

Vorlesungen über analytische Mechanik [Lectures on Analytical Mechanics] (1847/48; edited by Helmut Pulte in 1996).

Falseness

„The employment of mathematical symbols is perfectly natural when the relations between magnitudes are under discussion; and even if they are not rigorously necessary, it would hardly be reasonable to reject them, because they are not equally familiar to all readers and because they have sometimes been wrongly used, if they are able to facilitate the exposition of problems, to render it more concise, to open the way to more extended developments, and to avoid the digressions of vague argumentation.“

— Antoine Augustin Cournot, Researches into the Mathematical Principles of the Theory of Wealth

Source: Researches into the Mathematical Principles of the Theory of Wealth, 1897, pp. 3-4; Cited in: Moritz (1914, 199)

Problem, Nature, Way

„If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions. …Hence the question of whether axioms are a priori becomes pointless since they are arbitrary.“

— Hans Reichenbach American philosopher 1891 - 1953

The Philosophy of Space and Time (1928, tr. 1957)

Falseness, Question, Idea

„We had principles in mathematics that were granted to be absolute in mathematics for over 800 years, but new science has gotten rid of those absolutism, gotten — forward other different logics of looking at mathematics, and sort of turned the way we look at it as a science altogether after 800 years.“

— Mahmoud Ahmadinejad 6th President of the Islamic Republic of Iran 1956

Columbia University speech, 24 September 2007
[24 September 2007, http://www.azstarnet.com/sn/hourlyupdate/202820.php, "Iran's president at Columbia University - a transcript", azstarnet.com, 2007-09-25]
2007

Science, Way

„The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!“

— David Hilbert, Mathematical Problems

Mathematical Problems (1900)

Science, Knowledge, Nature

„He is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world.“

— Aryabhata Indian mathematician-astronomer 476 - 550

Bhaskara I, quoted in: J J O'Connor and E F Robertson "Aryabhata the Elder".

Science, World, Knowledge, Learning

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“

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