# Definition:Hilbert 23/10

## Hilbert $23$: Problem $10$

### Algorithm to determine whether Polynomial Diophantine Equation has Integer Solution

There is no algorithm to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution.

## Historical Notes

### Historical Note on Hilbert $23$

The Hilbert 23 were delivered by David Hilbert in a famous address at Paris in $1900$.

He considered them to be the oustanding challenges to mathematicians in the future.

There was originally going to be a $24$th problem, on a criterion for simplicity and general methods in proof theory, but Hilbert decided not to include it, as it was (like numbers $4$, $6$, $16$ and $23$) too vague to ever be described as "solved".