“Despite the vociferous claims of the Platonists and Neoplatonists, Plato was not a mathematician. To Plato and his followers mathematics was largely a means to an end… they viewed the technical aspects of mathematics as a mere device for sharpening one's wits, or at most a course of training peparatory to handling the larger issues of philosophy. This is reflected in the very name "mathematics,"… a course of studies or… a curriculum. …in the Dialogues… such topics as harmony, triangular numbers, figurate numbers… which we view today as more or less irrelevant, if not trivial, were taken up at length. …the guiding motive behind the… Pythagoreans and Platonists was… metaphysical …which for the nonprofessional have all the earmarks of the occult.”

— Tobias Dantzig

...We also discover in the Pythagorean speculations more than a mere germ of... the scientific attitude.
The Bequest of the Greeks (1955)

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Tobias Dantzig25

American mathematician 1884–1956

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

“Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited. …The two topics”

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Context: Increasingly... the application of mathematics to the real world involves discrete mathematics... the nature of the discrete is often most clearly revealed through the continuous models of both calculus and probability. Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited.... The two topics, discrete and continuous mathematics, are both ill served by being rigidly separated.

“For to pass by those Ancients, the wonderful Pythagoras, the sagacious Democritus, the divine Plato, the most subtle and very learned Aristotle, Men whom every Age has hitherto acknowledged as deservedly honored, as the greatest Philosophers, the Ring-leaders of Arts; in whose Judgments how much these Studies [mathematics] were esteemed, is abundantly proclaimed in History and confirmed by their famous Monuments, which are everywhere interspersed and bespangled with Mathematical Reasonings and Examples, as with so many Stars; and consequently anyone not in some Degree conversant in these Studies will in vain expect to understand, or unlock their hidden Meanings, without the Help of a Mathematical Key: For who can play well on Aristotle’s Instrument but with a Mathematical Quill; or not be altogether deaf to the Lessons of natural Philosophy, while ignorant of Geometry? Who void of (Geometry shall I say, or) Arithmetic can comprehend Plato’s 218 Socrates lisping with Children concerning Square Numbers; or can conceive Plato himself treating not only of the Universe, but the Polity of Commonwealths regulated by the Laws of Geometry, and formed according to a Mathematical Plan?”

Isaac Barrow (1630–1677) English Christian theologian, and mathematician

Source: Mathematical Lectures (1734), pp. 26-27

“The elementary particles in Plato's Timaeus are finally not substance but mathematical forms. "All things are numbers" is a sentence attributed to Pythagoras.”

Werner Heisenberg (1901–1976) German theoretical physicist

Physics and Philosophy (1958)
Context: But the resemblance of the modern views to those of Plato and the Pythagoreans can be carried somewhat further. The elementary particles in Plato's Timaeus are finally not substance but mathematical forms. "All things are numbers" is a sentence attributed to Pythagoras. The only mathematical forms available at that time were such geometric forms as the regular solids or the triangles which form their surface. In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical forms but of a much more complicated nature.

“It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, “Economics is what economists do,” and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.”

Kenneth E. Boulding (1910–1993) British-American economist

Source: 1970s, Economics As a Science, 1970, p. 97

“I must tell you that mathematicians are not scientists, they are artists…. Apart from the most elementary mathematics, like arithmetic or high school algebra, the symbols, formulas and words of mathematics have no meaning at all. The entire structure of pure mathematics is a monstrous swindle, simply a game, a reckless prank. You may well ask: "Are there no renegades to reveal the truth?" Yes, of course. But the facts are so incredible that no one takes them seriously. So the secret is in no danger.”

Theodore Kaczynski (1942) American domestic terrorist, mathematician and anarchist

The Net: The Unabomber, LSD and the Internet https://www.youtube.com/watch?v=xLqrVCi3l6E <br class="br">Interviews

“Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 495

“At the present time it is of course quite customary for physicists to trespass on chemical ground, for mathematicians to do excellent work in physics, and for physicists to develop new mathematical procedures… Trespassing is one of the most successful techniques in science.”

Wolfgang Köhler (1887–1967) German-American psychologist and phenomenologist

Source: Dynamics in Psychology, 1940, p. 116

“To the average mathematician who merely wants to know that his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency.”

Paul Cohen (1934–2007) American mathematician

p. 11 of "Comments on the foundations of set theory." https://books.google.com/books?id=TVi2AwAAQBAJ&pg=PA11 In Axiomatic set theory, pp. 9-15. Providence (RI). American Mathematical Society, 1971.

“Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.”

Edsger W. Dijkstra (1930–2002) Dutch computer scientist

1970s, How do we tell truths that might hurt? (1975)

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