離線未解決之數學難題
較有名的有由 Clay Mathematics Institute 所定的千禧年大獎難題
http://en.wikipedia.org/wiki/Millennium_Prize_Problems
# 1 P versus NP
理論電腦科學最重要難題
The question is whether, for all problems for which a computer can verify a given solution quickly (that is, in polynomial time), it can also find that solution quickly.
# 2 The Hodge conjecture
屬代數幾何的難題。
# 3 The Poincaré conjecture
已解決....
兩年前佩雷爾曼因解決此題獲 Fields Medal，但他拒受。
留要一點其實數學家已証明這道題於多維空間的情況，就只欠三維空間。佩雷爾曼就証明了三維空間的情況。
# 4 The Riemann hypothesis
屬 Number Theory 的難題。
The real part of any non-trivial zero of the Riemann zeta function is 1/2.
# 5 Yang–Mills existence and mass gap
屬 Mathematical Physics 的難題。Yang 是楊振寧。
# 6 Navier–Stokes existence and smoothness
屬流體力學的難題。
In three space dimensions and time, given an initial velocity field,there exists a vector velocity and a scalar pressure field, which areboth smooth and globally defined, that solve the Navier–Stokesequations.
# 7 The Birch and Swinnerton-Dyer conjecture
其他未解決難題有
哥德巴赫猜想
http://en.wikipedia.org/wiki/Goldbach%27s_conjecture
這條中學生也看懂，可是未有証明。
Fermat's last theorem 也是中學生看懂的，可是証明卻要用上現代 Number Theory。
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理論電腦科學最重要難題//
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