Unsolved Problems
Showing 1-8 of 8 problems
Category
Problem Set
Status
SMA-004
Open
Smale's 4th Problem: Integer Zeros of Polynomials
Find efficient algorithms for deciding whether a polynomial with integer coefficients has an integer root....
L4
287
16
SMA-005
Open
Smale's 5th Problem: Height Bounds for Diophantine Curves
Find effective uniform bounds for the heights of rational points on algebraic curves....
L4
234
13
SMA-006
Open
Smale's 6th Problem: Finiteness of Central Configurations
For the Newtonian $n$-body problem with positive masses, are there only finitely many central configurations (relative equilibria) for each $n$?...
L4
198
11
SMA-009
Open
Smale's 9th Problem: Linear Programming in Polynomial Time
Find a strongly polynomial algorithm for linear programming....
L4
312
18
SMA-010
Open
Smale's 10th Problem: The Pugh Closing Lemma
Is the $C^r$ closing lemma true for dynamical systems?...
L4
176
9
SMA-016
Open
The Jacobian Conjecture
If $F: \mathbb{C}^n \to \mathbb{C}^n$ is a polynomial map with constant non-zero Jacobian determinant, then $F$ is invertible....
L4
298
17
SMA-011
Open
Smale's 11th Problem: One-Dimensional Dynamics
Is one-dimensional dynamics generally hyperbolic?...
L4
198
11
SMA-012
Open
Smale's 12th Problem: Centralizers of Diffeomorphisms
Determine the structure of centralizers of generic diffeomorphisms....
L4
176
9