Hilbert's tenth problem

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Hilbert’s tenth problem (2019, methodology): “Hilbert’s Tenth Problem Abhibhav Garg 150010 November 11, 2018 Introduction This report is a summary of the negative solution of Hilbert’s Tenth Problem, by Julia Robinson, Yuri Matiyasevich, Martin Davis and Hilary Putnam.”
Affine linear sieve, expanders, and sum-product (2010, background): “[44] on Hilbert’s 10-th problem shows that given any recursively enumerable subset S of the positive integers N there is an f ∈ Z[x0, x1, .”
Communication lower bounds and optimal algorithms for programs that reference arrays - Part 1 (2013, background): “However, by the celebrated theorem of Matiyasevich-Davis-Putnam-Robinson [17], no such algorithm exists.”
Families of L -Functions and Their Symmetry (2014, methodology): “According to the solution of Hilbert’s 10th problem [75] one cannot say much about such sets W(Z), for example deciding if they are finite or not, and in general these sets may be unwieldy (see the example below).”