As a mathematician, Vince wrote on many aspects of his expertise, including logarithms and imaginary numbers. His Observations on the Theory of the Motion and Resistance of Fluids and Experiments upon the Resistance of Bodies Moving in Fluids had later importance to aviation history. He was also author of the influential A Complete System of Astronomy (3 vols. 1797-1808).
Vince also published the pamphlet The Credibility of Christianity Vindicated, In Answer to Mr. Hume's Objections; In Two Discourses Preached Before the University of Cambridge by the Rev. S. Vince. In this work, Vince made an apology of the Christian religion and, like Charles Babbage, sought to present rational arguments in favor of the belief in miracles, against David Hume's criticism. A review of this work with direct quotations can be found in The British Critic, Volume 12, 1798.