In 2005, Gordon was awarded the Berwick Prize of the London Mathematical Society for his article Baby Verma modules for rational Cherednik algebras.
[1] In 2008 he was awarded a 5-year EPSRC Leadership Fellowship to support his research on Rigid Structure in Noncommutative, Geometric and Combinatorial Problems.
In 2010 he was elected as a Fellow of the Royal Society of Edinburgh and was an invited speaker at the International Congress of Mathematicians in Hyderabad on Rational Cherednik Algebras.
[2] In 2014 he won the Edinburgh University Student Association's Van Heyningen Award for Teaching in Science and Engineering.
[3] Since 2018, he has been the Principal Investigator on a 6-year EPSRC Programme Grant with Arend Bayer, Tom Bridgeland, Agata Smoktunowicz and Michael Wemyss on Enhancing Representation Theory, Noncommutative Algebra and Geometry.