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2.12 Mathematical coincidences

List of mathematical coincidences

3 Mathematical tools

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4 Quotes

Referring to the axiomatic method, where certain properties of an (otherwise unknown) structure are assumed and consequences thereof are then logically derived, Bertrand Russell said:

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

This may explain why John Von Neumann once said:

In mathematics you don't understand things. You just get used to them.

About the beauty of Mathematics, Bertrand Russell said in Study of Mathematics:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

Elucidating the symmetry between the creative and logical aspects of mathematics, W.S. Anglin observed, in Mathematics and History:

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.

5 Mathematics is not...

Mathematics is not numerology. Although numerology uses modular arithmetic to boil names and dates down to single digit numbers, numerology arbitrarily assigns emotions or traits to numbers without bothering to prove the assignments in a logical manner. Mathematics is concerned with proving or disproving ideas in a logical manner, but numerology is not. The interactions between the arbitrarily assigned emotions of the numbers are intuitively estimated rather than calculated in a thoroughgoing manner.

Mathematics is not accountancy. Although arithmetic computation is crucial to the work of accountants, they are mainly concerned with proving that the computations are true and correct through a system of doublechecks. The proving or disproving of hypotheses is very important to mathematicians, but not so much to accountants. Advances in abstract mathematics are irrelevant to accountancy if the discoveries can't be applied to improving the efficiency of concrete bookkeeping.

Mathematics is not physics, despite the number of historical and philosophical relations between the two.

6 Bibliography

Courant, R. and H. Robbins, What Is Mathematics? ( 1941);
Davis, Philip J. and Hersh, Reuben, The Mathematical Experience. Birkhäuser, Boston, Mass., 1980. A gentle introduction to the world of mathematics.
Gullberg, Jan, Mathematics--From the Birth of Numbers. W.W. Norton, 1996. An encyclopedic overview of mathematics presented in clear, simple language.
Hazewinkel, Michiel (ed.), Encyclopaedia of Mathematics. Kluwer Academic Publishers 2000. A translated and expanded version of a Soviet math encyclopedia, in ten (expensive) volumes, the most complete and authoritative work available. Also in paperback and on CD-ROM.
Kline, M., Mathematical Thought from Ancient to Modern Times ( 1973);

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Mathematics and architectureMathematics and architecture have always enjoyed a close association with each other, not only in the sense that the latter is informed by the former, but also in that both share the search for order and beauty, the former in nature and the latter in buil	Mathematics educationMathematics education the practices and methods of teaching mathematics, is always a hotly debated subject in modern society. Euclidean geometry There is no royal road to geometry a famous quote by Euclid to Ptolemy or by Menaechmus to Alexander the Great	Mathematics and GodA number of famous mathematicians have made connections between mathematics and God often likening God to a mathematician. The Greek study of mathematics was closely related to that of religion. Plato is quoted as saying "God ever geometrizes" and Pythago
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Mathematics Association of America

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