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Unsolved Problems -- from Wolfram MathWorld

http://mathworld.wolfram.com/UnsolvedProblems.html There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include
lógica

álgebra

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http://terrytao.wordpress.com/ A few days ago, Endre Szemerédi was awarded the 2012 Abel prize “for his fundamental contributions to discrete mathematics and theoretical computer science, and in recognition of the profound and lasting impact of these contributions on additive number theory and ergodic theory.”