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Mathematics at the Turn of the Millennium
by Phillip A. GriffithsThis article originally appeared in:
American Mathematical Monthly
Subject classification(s): Mathematics History | General
Applicable Course(s): 4.8 History of Math | 2.6 Math Liberal Arts
This article is part of the Mathematics of Planet Earth 2013 Collection. This article surveys some achievements of the 20th century and poses some challenges and opportunities awaiting in the 21st century. Among the 20th century achievements mentioned are Fermat's Last Theorem, Kepler's Sphere Packing Conjecture, The four-color problem, solitons, and string theory. Among the challenges for the 21st century discussed by Griffiths are the Riemann Hypothesis, the Poincaré conjecture [solved by Perelman in 2002-03], P=NP, and the fields of theoretical computer science and quantum computing. Griffiths also lists problems that must be overcome to maintain the strength of mathematics in this century. These include supporting education at a time when support for science and mathematics is decreasing and developing interactions among many disciplines.
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