Quotes about mathematics

A collection of quotes on the topic of mathematics.

„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

„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

„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

„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

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„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

„It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning.“

— David Hilbert, Mathematical Problems

Mathematical Problems (1900)

Problem

„A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts.“

— David Hilbert, Mathematical Problems

Mathematical Problems (1900)
Context: A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

Effort, Problem

„A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.“

— David Hilbert, Mathematical Problems

Eine mathematische Theorie ist nicht eher als vollkommen anzusehen, als bis du sie so klar gemacht hast, daß du sie dem ersten Manne erklären könntest, den du auf der Straße triffst.
Mathematical Problems (1900)
Context: An old French mathematician said: A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street. This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.

„Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.“

— David Hilbert, Mathematical Problems

Mathematical Problems (1900)
Context: Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

Parting, Science

„Either mathematics is too big for the human mind, or the human mind is more than a machine.“

— Kurt Gödel logician, mathematician, and philosopher of mathematics 1906 - 1978

As quoted in Topoi : The Categorial Analysis of Logic (1979) by Robert Goldblatt, p. 13

„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

„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

„Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.“

— Nikola Tesla Serbian American inventor 1856 - 1943

"Radio Power Will Revolutionize the World" in Modern Mechanics and Inventions (July 1934)

Reality

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

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