Después de que se anunciara la resolución de la Conjetura de Poincaré recientemente, a lo mejor te ha quedado la sensación de que ya está todo resuelto, y de que te hubiera gustado pasar un rato pensando la solución. Si es así, no te preocupes, ya que según The Clay Mathematics Institute of Cambridge, aún quedan unos 7 millones de problemas matemáticos por resolver, entre los que destacan:
1. The Goldbach conjecture.
2. The Riemann hypothesis.
3. The conjecture that there exists a Hadamard
matrix for every positive multiple of 4.
4. The twin prime conjecture (i.e., the conjecture that there are an infinite number of twin primes).
5. Determination of whether NP-problems
are actually P-problems.
6. The Collatz problem.
7. Proof that the 196-algorithm
does not terminate when applied to the number 196.
8. Proof that 10 is a solitary number.
9. Finding a formula for the probability that two elements chosen at random generate the symmetric group .
10. Solving the happy end problem for arbitrary.
11. Finding an Euler brick whose
space diagonal is also an integer.
12. Proving which numbers can be represented as a sum of three or four (positive
or negative) cubic numbers.
13. Lehmer’s Mahler measure problem and Lehmer’s
totient problem on the existence of composite
numbers such that, where is the totient function.
14. Determining if the Euler-Mascheroni constant is irrational.
15. Deriving an analytic form for the square site percolation threshold.
16. Determining if any odd perfect
numbers exist.
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