The study of the properties of integers, using the tools of modern mathematics to address many basic unanswered questions.
Number theory is the study of the properties of integers, using the tools of modern mathematics to address many basic unanswered questions – for example, concerning the distribution of prime numbers among integers, or solubility in integers of polynomial equations.
Techniques used include many from analysis, algebra and geometry.
Supporting novel research
We will continue to support novel research emerging from the significant intradisciplinary overlap between Number Theory and research areas within mathematical sciences – for example, by building on links to topics such as:
- representation theory
- algebraic geometry
- additive combinatorics
- probability theory.
Strengthening interdisciplinary links
We will continue to strengthen interdisciplinary links through topics such as string theory, cryptology and theoretical computer science, as these are key mechanisms to accelerate the impact of number theory research. This will make a significant contribution, for instance, to nationally important fields such as cyber security.
Supporting our researchers
We will monitor the balance of researchers across career stages and ensure appropriate support. We will achieve this by funding new investigator awards, standard grants and programme grants of the highest quality and where fellowship proposals align with the mathematical sciences fellowship priority areas.