Hilbert's 10th problem is (in modern terminology) to find an algorithm that will, given a poly
p(x1,...,xn) in Z[x1,...,xn], determine if it has a solution in the integers.
This was shown undecidable by the combined efforts of Davis-Putnam-Robinson and Matiyasevich.
I posted here about the question of: For which (d,n) is H10 undecidable when restricted to degree d and number of vars n?
I was invited to make an article out of the blog post and what I learned from the comments for the Algorithms column of BEATCS. That first draft is
Did I miss an important reference? (Note- I had meant to get out Matiyasevich's book on H10 but have been unable to because of the Pandemic, so if you have it my have stuff I need to know.)
Did I misspell Matiyasevich?
Did I say something stupid?
Please leave comments or email me directly if you have suggestions.
Incidentally I am usually the one who is asking someone else to do an open problems column, a book review, a guest blog. Nice to be the askee instead of the asker for a change of pace.