Scott Harper attended Kirkcaldy High School, a comprehensive state school in Fife, and he was awarded the school's Dux Medal. He then studied Mathematics at the University of St Andrews, graduating with an MMath and receiving the Sanderson Prize as the top mathematics undergraduate.
Following a PhD in Mathematics with Prof Tim Burness at the University of Bristol, he held research fellow positions at the University of Padua, the Heilbronn Institute for Mathematical Research in Bristol and at the University of St Andrews, the last of these being supported by an Leverhulme Early Career Fellowship and then an EPSRC Postdoctoral Fellowship. In April 2025, Scott was appointed as an Assistant Professor at the University of Birmingham, and he is one the 125th Anniversary Fellows.
Scott's general area of research is group theory: the mathematical study of symmetry. He is interested in properties of abstract groups, such as generating sets and subgroup structure, and he is also interested in properties of group actions, such as derangements and bases of permutation groups. While group theoretic questions are usually the motivation for his work, some of his projects would be better described as representation theory, geometric group theory, Lie theory or combinatorics. Lately, he has become involved in formalising proofs in Lean. He is also interested in mathematics education and the philosophy of mathematical practice.
In 2024, Scott was awarded the Reinhold Baer Prize, and his presentation in the Houses of Parliament at STEM for Britain 2021 won the Gold Medal.