This paper explores the potential impact of a national pilot initiative in England aimed at increasing and widening participation in advanced mathematical study through the creation of a new qualification for 16- to 18-year-olds. This proposed qualification pathway--"Use of Mathematics"--sits in parallel with long-established, traditional advanced level qualifications, what we call "traditional "Mathematics"" herein. Traditional "Mathematics" is typically required for entry to mathematically demanding undergraduate programmes. The structure, pedagogy and assessment of "Use of Mathematics" is designed to better prepare students in the application of mathematics, and its development has surfaced some of the tensions between academic/pure and vocational/applied mathematics. Here, we explore what "Use of Mathematics" offers, but we also consider some of the objections to its introduction in order to explore aspects of the knowledge politics of mathematics education. Our evaluation of this curriculum innovation raises important issues for the mathematics education community as countries seek to increase the numbers of people that are well prepared to apply mathematics in science and technology-based higher education courses and work places.