“In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.”

—  Hermann Weyl, Invariants

Weyl, Hermann. Invariants. Duke Math. J. 5 (1939), no. 3, 489--502. doi:10.1215/S0012-7094-39-00540-5. http://projecteuclid.org/euclid.dmj/1077491405.

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematica…" by Hermann Weyl?
Hermann Weyl photo
Hermann Weyl28
German mathematician 1885–1955

Related quotes

George Klir photo

“In mathematics, logic, linguistics, and other abstract disciplines, the systems are not assigned to objects. They are defined by an enumeration of the variables, their admissible values, and their algebraic, topological, grammatical, and other properties which, in the given case, determine the relations between the variables under consideration.”

George Klir (1932–2016) American computer scientist

Source: An approach to general systems theory (1969), p. 40.

Solomon Lefschetz photo

“It was my lot to plant the harpoon of algebraic topology into the body of the whale of algebraic geometry.”

Solomon Lefschetz (1884–1972) American mathematician

[Carl C. Gaither, Alma E. Cavazos-Gaither, Gaither's Dictionary of Scientific Quotations: A Collection of Approximately 27,000 Quotations Pertaining to Archaeology, Architecture, Astronomy, Biology, Botany, Chemistry, Cosmology, Darwinism, Engineering, Geology, Mathematics, Medicine, Nature, Nursing, Paleontology, Philosophy, Physics, Probability, Science, Statistics, Technology, Theory, Universe, and Zoology, https://books.google.com/books?id=zQaCSlEM-OEC&pg=PA29, 5 January 2012, Springer Science & Business Media, 978-1-4614-1114-7, 29]

“Ninety per cent of all the mathematics we know has been discovered (or invented), in the last hundred years… the advances made in each of some dozen directions are converging into one single discipline uniting algebra, topology and analysis.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“From Pythagoras to Boethius, when pure mathematics consisted of arithmetic and geometry while applied mathematics consisted of music and astronomy, mathematics could be characterized as the deductive study of 'such abstractions as quantities and their consequences, namely figures and so forth' (Acquinas ca. 1260). But since the emergence of abstract algebra it has become increasingly difficult to formulate a definition to cover the whole of the rich, complex and expanding domain of mathematics.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“Topology or relational mathematics, including non-metrical fields such as network and graph theory.”

Ludwig von Bertalanffy (1901–1972) austrian biologist and philosopher

General System Theory (1968), 4. Advances in General Systems Theory

Kurt Lewin photo

“The young mathematical disciple 'topology' might be of some help in making psychology a real science.”

Kurt Lewin (1890–1947) German-American psychologist

Source: 1930s, Principles of topological psychology, 1936, p. vii.

Georg Cantor photo

“In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand through a definition. However, this domain cannot itself be something variable, since otherwise each fixed support for the study would collapse. Thus this domain is a definite, actually infinite set of values. Hence each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

"Über die verschiedenen Ansichten in Bezug auf die actualunendlichen Zahlen" ["Over the different views with regard to the actual infinite numbers"] - Bihand Till Koniglen Svenska Vetenskaps Akademiens Handigar (1886)

Doron Zeilberger photo

“Computer Algebra Systems are NOT the Devil but the new MESSIAH that will take us out of the current utterly trivial phase of human-made mathematics into the much deeper semi-trivial computer-generated phase of future mathematics. Even more important, Computer Algebra Systems will turn out to be much more than just a `tool', since the methodology of computer-assisted and computer-generated research will rule in the future, and will make past mathematics seem like alchemy and astrology, or, at best, theology.”

Doron Zeilberger (1950) Israeli mathematician

Nikolai Ivanovich Lobachevsky photo

“There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.”

Nikolai Ivanovich Lobachevsky (1792–1856) Russian mathematician of Ukrainian origin

As quoted in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane, Springer (1998 [1975]), p. 225; also in Stanley Gudder, A Mathematical Journey, McGraw-Hill (1976), p. 36.

Michael Atiyah photo

“Algebra is the offer made by the devil to the mathematician. The devil says: `I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine.”

Michael Atiyah (1929–2019) British mathematician

[Michael Atiyah, Collected works. Vol. 6, The Clarendon Press Oxford University Press, Oxford Science Publications, http://www.math.tamu.edu/~rojas/atiyah20thcentury.pdf, 978-0-19-853099-2, 2160826, 2004]

Related topics