Mathematics, Numbers and More…

“It is not of the essence of mathematics to be conversant with the ideas of number and quantity. Whether as a general habit of mind it would be desirable to apply symbolic processes to moral argument, is another question.” (George Boole, “An Investigation of the Laws of Thought”, 1854)

“The purely formal sciences, logic and mathematics, deal with such relations which are independent of the definite content, or the substance of the objects, or at least can be. In particular, mathematics involves those relations of objects to each other that involve the concept of size, measure, number.” (Hermann Hankel, “Theorie der Complexen Zahlensysteme”, 1867)

“Mathematics is the science of the functional laws and transformations which enable us to convert figured extension and rated motion into number.” (George Holmes Howison, “The Departments of Mathematics, and their Mutual Relations”, Journal of Speculative Philosophy Vol. 5, No. 2, 1871)

“It may be surprising to see emotional sensibility invoked apropos of mathematical demonstrations which, it would seem, can interest only the intellect. This would be to forget the feeling of mathematical beauty, of the harmony of numbers and forms, of geometric elegance. This is a true esthetic feeling that all real mathematicians know, and surely it belongs to emotional sensibility.” (Henri Poincaré, 1913)

“Mathematics is the science of number and space. It starts from a group of self-evident truths and by infallible deduction arrives at incontestable conclusions […] the facts of mathematics are absolute, unalterable, and eternal truths.” (E Russell Stabler, “An Interpretation and Comparison of Three Schools of Thought in the Foundations of Mathematics”, The Mathematics Teacher, Vol 26, 1935)

“The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.” (Sir D’Arcy W Thompson, “On Growth and Form”, 1951)

“Mathematics, springing from the soil of basic human experience with numbers and data and space and motion, builds up a far-flung architectural structure composed of theorems which reveal insights into the reasons behind appearances and of concepts which relate totally disparate concrete ideas.” (Saunders MacLane, “Of Course and Courses”The American Mathematical Monthly, Vol 61, No 3, 1954)

“Just as mathematics aims to study such entities as numbers, functions, spaces, etc., the subject matter of metamathematics is mathematics itself.” (Frank C DeSua, “Mathematics: A Non-Technical Exposition”, American Scientist, 3 Jul 1954)