Gauss has famously described Mathematics as the "Queen of the Sciences" and Number Theory as the "Queen of Mathematics". As a subject Number Theory was established by the ancient Greeks who called it Arithmetic. The subject has flourished since the Renaissance and today is as vigorous as ever.

Until the middle of the 20th century, Number Theory was considered to be the purest area of Mathematics and least likely to be sullied by applications. This has all changed since then with the advent of digital computing, the growth of cryptography, telecommunication and the emergence of links with dynamical systems and physical phenomena. Nowadays, the subject is an exciting mix of ideas pursued for their own interest and a rather exotic variety of applications.

People in the Number Theory Group at York have varied interests (the list of group members is here). The main research interests include:

• Analytic number theory
• Metric Number Theory
• Diophantine approximation
• Irrationality, transcendence and and algebraic independence
• Random Matrix Theory
• Connections with dynamical systems, fractals and ergodic theory

Read more about our reserarch here; see the publication list here.

The group has enjoyed substantial research funding over many years from  a variety of sources. The largest currently held award is an EPSRC Programme Grant.

Seminars in Number Theory at York are held in the Number Theory Study Group. Apart from specialist research seminars in Number Theory, the Number Theory Study Group is used to work on a pre-chosen topic or research paper. The starting level is reasonably elementary so as to clarify the importance of the work under discussion. The aim is to provide an invigorating research climate within the Number Theory group leading to new research and further collaborations.

Prospective PhD students can choose from a variety of topics suggested here as well as come up with their own suggestions. Please contact relevant staff members or simply apply (see here for further details).

Undergraduate as well as graduate students are offered a variety of specialised modules including Introduction to Number Theory (2nd year), Number Theory (3rd year), Algebraic Number Theory (3rd/4th year), Metric Number Theory (MMath) and Analytic Number Theory (MMath), and a course on applications in Cryptography (3rd year). The details can be found here.