New Proofs Expand the Limits of What Cannot Be Known
1 min read
Summary
For over a century, mathematicians have been trying to solve Hilbert’s tenth problem, which asks if it’s possible to devise a method for determining whether any given Diophantine equation has a solution, and whether such a method could be automated by a computer.
Now, two independent teams of mathematicians have taken a major step toward settling the problem, which has been unresolved since 1970.
Both groups have proved that there’s no general algorithm that can determine if any given Diophantine equation has solutions outside of the realm of integers.
The work allows mathematicians to get a more precise view of what they can and cannot know and gives them a new level of control over one of the most central objects in math.
“It reminds us there are things that are just not doable,” said Andrew Granville of the University of Montreal. “It doesn’t matter who you are or what you are.
