1. Four-color Theorem: This is a famous graph theory problem and an important application of algebraic geometry. Its content is that any plane map can be painted with four colors, so that adjacent areas have different colors. This problem was proved by computer in 1976.
2. Fermat's Last Theorem: This is one of the most famous problems in algebraic geometry. Its content is that for any natural number n greater than 2, the equation x n+y n = z n has no positive integer solution. This problem was proved by the British mathematician andrew wiles in 1994.
3. Riemann conjecture: This is an unsolved problem in algebraic geometry, and it is also one of the Millennium prizes of Clay Institute of Mathematics. Its content is that the real part of zero of all nontrivial zeta functions is equal to 1/2. This problem has not been proved so far.
4. Mo Deer's conjecture: This is a famous problem in algebraic geometry, and it is also one of the Millennium prizes of Clay Institute of Mathematics. Its content is that any smooth complex algebraic curve is rational. This problem was proved by Russian mathematician grigory perelman in 2002.
5. David's conjecture: This is a famous problem in algebraic geometry, and it is also one of the Millennium prizes of Clay Institute of Mathematics. Its content is that any nonsingular projective algebra family is algebraically closed. This problem was proved by American mathematician David Mountford in 1984.
These topics are classical problems in algebraic geometry, which not only promote the development of this field, but also have a far-reaching impact on other mathematical fields.