I think this is a suitable mechanism for grants for well defined mathematical problems, but not for more vaguely defined ones. To be frank, the well defined ones tend to be less interesting.
For example the Cray problems are all well defined, and are certain very interesting, but mostly not actually that fundamental to mathematics.
The Hilbert problems are in some ways far more important, and most of these are more vague questions or directions for research than an actual concrete conjecture.
Nobody would have been trading shares in godels incompleteness theorem before he proposed it—and rendering the theorem in concrete terms would already be halfway towards solving it.
How would you suggest making sure funding gets pointed towards these kinds of problems as well?
How would you suggest making sure funding gets pointed towards these kinds of problems as well?
However we currently do it, I guess; I don’t have any improvements in this particular direction. Though do note that P vs NP, and P vs PSPACE, and BQP vs P or NP are all examples of precisely-defined problems that are also very significant. These are problems that I would much rather have an answer for than the Riemann hypothesis. Though even there, the process isn’t guaranteed to generate an interpretable proof.
I think this is a suitable mechanism for grants for well defined mathematical problems, but not for more vaguely defined ones. To be frank, the well defined ones tend to be less interesting.
For example the Cray problems are all well defined, and are certain very interesting, but mostly not actually that fundamental to mathematics.
The Hilbert problems are in some ways far more important, and most of these are more vague questions or directions for research than an actual concrete conjecture.
Nobody would have been trading shares in godels incompleteness theorem before he proposed it—and rendering the theorem in concrete terms would already be halfway towards solving it.
How would you suggest making sure funding gets pointed towards these kinds of problems as well?
However we currently do it, I guess; I don’t have any improvements in this particular direction. Though do note that P vs NP, and P vs PSPACE, and BQP vs P or NP are all examples of precisely-defined problems that are also very significant. These are problems that I would much rather have an answer for than the Riemann hypothesis. Though even there, the process isn’t guaranteed to generate an interpretable proof.