Richard Arnold Shore (born August 18, 1946) is a professor of mathematics at Cornell University who works in recursion theory. He is particularly known for his work on ${\displaystyle {\mathcal {D}}}$, the partial order of the Turing degrees.

• Shore settled the Rogers homogeneity conjecture by showing that there are Turing degrees ${\displaystyle a}$ and ${\displaystyle b}$ such that ${\displaystyle {\mathcal {D}}_{a}}$ and ${\displaystyle {\mathcal {D}}_{b}}$, the structures of the degrees above ${\displaystyle a}$ and ${\displaystyle b}$ respectively, are not isomorphic.^[1]
• In joint work with Theodore Slaman, Shore showed that the Turing jump is definable in ${\displaystyle {\mathcal {D}}}$.^[2]

He was, in 1983, an invited speaker at the International Congress of Mathematicians in Warsaw and gave a talk The Degrees of Unsolvability: the Ordering of Functions by Relative Computability. In 2009, he was the Gödel Lecturer (Reverse mathematics: the playground of logic).^[3] He was an editor from 1984 to 1993 of the Journal of Symbolic Logic and from 1993 to 2000 of the Bulletin of Symbolic Logic. In 2012, he became a fellow of the American Mathematical Society.^[4]