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Solved Problems

There are many unsolved problems in mathematics. Several famous problems which have recently been solved include:

1. The Pólya conjecture (disproven by Haselgrove 1958, smallest counterexample found by Tanaka 1980).

2. The four-color theorem (Appel and Haken 1977ab and Appel et al. 1977 using a computer-assisted proof).

3. The Bieberbach conjecture (L. de Branges 1985).

4. Tait's flyping conjecture (Menasco and Thistlethwaite in 1991) and the other two of Tait's knot conjectures (by various authors 1987).

5. Fermat's last theorem (Wiles 1995, Taylor and Wiles 1995).

6. The Kepler conjecture (Hales 2002).

7. The Taniyama-Shimura conjecture (Breuil et al. in 1999).

8. The honeycomb conjecture (Hales 1999).

9. The Poincaré conjecture.

10. Catalan's conjecture.

11. The strong perfect graph theorem.

See also

Unsolved Problems

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References

Appel, K. and Haken, W. "Every Planar Map is Four-Colorable, II: Reducibility." Illinois J. Math. 21, 491-567, 1977a.Appel, K. and Haken, W. "The Solution of the Four-Color Map Problem." Sci. Amer. 237, 108-121, 1977b.Appel, K.; Haken, W.; and Koch, J. "Every Planar Map is Four Colorable. I: Discharging." Illinois J. Math. 21, 429-490, 1977.de Branges, L. "A Proof of the Bieberbach Conjecture." Acta Math. 154, 137-152, 1985.Hales, T. C. "The Honeycomb Conjecture." 8 Jun 1999. http://arxiv.org/abs/math.MG/9906042.Hales, T. C. "A Computer Verification of the Kepler Conjecture." Proceedings of the International Congress of Mathematicians, Vol. II. Invited lectures. Held in Beijing, August 20-28, 20027040086905 (Ed. T. Li). Beijing, China: Higher Education Press, pp. 795-804, 2002.Haselgrove, C. B. "A Disproof of a Conjecture of Pólya." Mathematika 5, 141-145, 1958.Menasco, W. and Thistlethwaite, M. "The Tait Flyping Conjecture." Bull. Amer. Math. Soc. 25, 403-412, 1991.Tanaka, M. "A Numerical Investigation on Cumulative Sum of the Liouville Function" [sic]. Tokyo J. Math. 3, 187-189, 1980.Taylor, R. and Wiles, A. "Ring-Theoretic Properties of Certain Hecke Algebras." Ann. Math. 141, 553-572, 1995.Wiles, A. "Modular Elliptic-Curves and Fermat's Last Theorem." Ann. Math. 141, 443-551, 1995.

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Solved Problems

Cite this as:

Weisstein, Eric W. "Solved Problems." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SolvedProblems.html

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