Area of investment and support

Mathematical physics

This research area is concerned with developing new mathematics inspired by, or relevant to, physics.

• Partners involved: Engineering and Physical Sciences Research Council (EPSRC)

The scope and what we're doing

This area encompasses developing new mathematics inspired by, or relevant to, physics. This research area has close connections to the Science and Technology Facilities Council’s (STFC) particle physics theory remit and our own physical sciences capability, as well as strong intradisciplinary connections within our mathematical sciences portfolio.

We aim to:

• support and develop a portfolio of high-quality core research across the full breadth of sub-fields in mathematical physics
• advance the strong intradisciplinary links to both pure and applied mathematics, to further developments in areas such as network science, number theory, statistics and applied probability, and quantum information
• ensure that the research base has the appropriate people and skills to keep the UK at the forefront of advances in mathematical physics, including providing skills and training for the next generation of leaders in the field
• encourage novel interactions between mathematical physics and new research challenges of national importance relating to EPSRC’s outcomes, including through links to pure and applied mathematics and theoretical physics (for example, quantum computing and superconductivity)
• maintain regular dialogue with STFC to ensure that research proposals at the interface between us are managed appropriately.

Why we're doing it

Traditionally, mathematical physics is one of the strongest fields of mathematics in the UK and continues to be recognised for its excellence through prizes, awarded fellowships of the Royal Society (FRS), and European Research Council (ERC) awards. Its links to both pure and applied mathematics, as well as the obvious links to physics, mean it is highly intradisciplinary and interdisciplinary

Mathematical physics has a long history of stimulating important developments in other fields of the mathematical sciences, for example algebraic geometry and geometric analysis, making it key to the health of other disciplines. It draws on ideas from both pure and applied mathematics, while feeding back to them new techniques, examples and conjectures.

The UK continues to have world-class research programmes in several of the more mathematical areas of theoretical physics, for example general relativity, cosmology, string theory and quantum chaos.

The Research Excellence Framework (REF) 2014 expert panel noted that, “the large submission in mathematical and theoretical physics showed breadth and depth in areas where the UK has been strong for decades. For example, there were many world-leading outputs in quantum field theory (including string theory, integrable systems, high energy particle physics and cosmology), and aspects of general relativity and statistical mechanics”.

Today, world-leading groups in mathematical physics are located both in many small institutions and in the larger, well-established centres. A distinctive feature in the UK is that mathematical physics groups are placed in mathematics departments rather than physics departments. This has emerged as a great strength, leading to more cross-fertilisation with pure mathematics than arises elsewhere.

In terms of the national importance of mathematical physics, in addition to the high quality research this area has produced, it has contributed to progress towards understanding a variety of important phenomena such as quantum entanglement and superconductivity.

It is important to note the underpinning nature of this research area and its indirect contributions to advances in many areas of engineering and physical sciences.

View evidence sources used to inform our research strategies.

Past projects, outcomes and impact

Visualising our portfolio (VoP) is a tool for users to visually interact with the EPSRC portfolio and data relationships. Find out more about research area connections and funding for mathematical physics.

Find previously funded projects on Grants on the Web.

Last updated: 22 December 2022