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Discrete optimization, including combinatorial optimization, integer programming, constraint programming O'Connor, J. J.; Robertson, E. F. (February 1996). "Non-Euclidean geometry". MacTuror. School of Mathematics and Statistics, University of St Andrews, Scotland. Archived from the original on November 6, 2022 . Retrieved November 6, 2022. Hilbert, David (1962). The Foundations of Geometry. Open Court Publishing Company. p.1 . Retrieved March 22, 2023. The most prestigious award in mathematics is the Fields Medal, [196] [197] established in 1936 and awarded every four years (except around World War II) to up to four individuals. [198] [199] It is considered the mathematical equivalent of the Nobel Prize. [199]Stump, David J. (1997). "Reconstructing the Unity of Mathematics circa 1900". Perspectives on Science. 5 (3): 383. doi: 10.1162/posc_a_00532. S2CID 117709681. Archived from the original on November 6, 2022 . Retrieved November 6, 2022. Lim, Lisa (December 21, 2018). "Where algebra got its x from, and Xmas its X". South China Morning Post. Archived from the original on August 9, 2022 . Retrieved August 9, 2022. Kolachana, A.; Mahesh, K.; Ramasubramanian, K. (2019). "Use of series in India". Studies in Indian Mathematics and Astronomy. Sources and Studies in the History of Mathematics and Physical Sciences. Singapore: Springer. pp.438–461. doi: 10.1007/978-981-13-7326-8_20. ISBN 978-981-13-7325-1. S2CID 190176726. Main category: Mathematics awards The front side of the Fields Medal with an illustration of the Greek polymath Archimedes Curves: Ellipse". MacTutor. School of Mathematics and Statistics, University of St Andrews, Scotland. Archived from the original on October 14, 2022 . Retrieved November 20, 2022.

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Kleiner, Israel (February 2000). "From Fermat to Wiles: Fermat's Last Theorem Becomes a Theorem". Elemente der Mathematik. 55: 19–37. doi: 10.1007/PL00000079. S2CID 53319514.

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Batchelder, William H. (January 1, 2015), "Mathematical Psychology: History", in Wright, James D. (ed.), International Encyclopedia of the Social & Behavioral Sciences (Second Edition), Oxford: Elsevier, Parshall, Karen Hunger (2022). "The American Mathematical Society and Applied Mathematics from the 1920s to the 1950s: A Revisionist Account". Bulletin of the American Mathematical Society. 59 (3): 405–427. doi: 10.1090/bull/1754. S2CID 249561106. Archived from the original on November 20, 2022 . Retrieved November 20, 2022.

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Creativity and rigor are not the only psychological aspects of the activity of mathematicians. Some mathematicians can see their activity as a game, more specifically as solving puzzles. [181] This aspect of mathematical activity is emphasized in recreational mathematics. Game theory (although continuous games are also studied, most common games, such as chess and poker are discrete) Main articles: Mathematical notation, Language of mathematics, and Glossary of mathematics An explanation of the sigma (Σ) summation notation Differential geometry, the study of curves, surfaces, and their generalizations, which are defined using differentiable functions.

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Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified numbers. [41] Variables allow mathematicians to describe the operations that have to be done on the numbers represented using mathematical formulas. Takase, M. (2014). "Pure Mathematics and Applied Mathematics are Inseparably Intertwined: Observation of the Early Analysis of the Infinity". A Mathematical Approach to Research Problems of Science and Technology. Mathematics for Industry. Vol.5. Tokyo: Springer. pp.393–399. doi: 10.1007/978-4-431-55060-0_29. ISBN 978-4-431-55059-4 . Retrieved November 20, 2022.Franklin, James (2017). "Discrete and continuous: a fundamental dichotomy in mathematics". Journal of Humanistic Mathematics. 7 (2): 355–378. doi: 10.5642/jhummath.201702.18. S2CID 6945363. Archived from the original on November 10, 2022 . Retrieved November 10, 2022. Khan Academy is a nonprofit whose resources are always free to teachers and learners – no ads, no subscriptions Convex geometry, the study of convex sets, which takes its importance from its applications in optimization.