Logic

Tarski's exponential function problem ★★

Author(s): Tarski

Conjecture   Is the theory of the real numbers with the exponential function decidable?

Keywords: Decidability

Posted by Charles
updated July 8th, 2008
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Number Theory » Analytic N.T.

Schanuel's Conjecture ★★★★

Author(s): Schanuel

Conjecture   Given any $ n $ complex numbers $ z_1,...,z_n $ which are linearly independent over the rational numbers $ \mathbb{Q} $, then the extension field $ \mathbb{Q}(z_1,...,z_n,\exp(z_1),...,\exp(z_n)) $ has transcendence degree of at least $ n $ over $ \mathbb{Q} $.

Keywords: algebraic independence

Posted by Charles
updated January 19th, 2010
3 comments
Number Theory

Algebraic independence of pi and e ★★★

Author(s):

Conjecture   $ \pi $ and $ e $ are algebraically independent

Keywords: algebraic independence

Posted by porton
updated April 29th, 2012
6 comments
Topology

Rank vs. Genus ★★★

Author(s): Johnson

Question   Is there a hyperbolic 3-manifold whose fundamental group rank is strictly less than its Heegaard genus? How much can the two differ by?

Keywords:

Posted by Jesse Johnson
updated July 13th, 2008
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