The findings you produce as a research mathematician can be used to further knowledge in academia or improve performance and solve problems in a commercial setting
As a research mathematician you can work in a variety of areas, however you would typically be involved in proving deep and abstract theorems, developing mathematical descriptions (models) to explain or predict real phenomena and applying mathematical principles to identify trends in data sets.
If you work in applied research you could be contributing to the development of a commercial product or developing intelligence about business trends.
You can undertake research into a diverse range of pure and applied maths, including:
- differential equations
- dynamic systems
- fluid mechanics
- geometry and topology
- mathematical biology
- numerical analysis.
Collaboration with other scientists and people in commercial functions in industry is common because the application of mathematics is so varied.
Types of research mathematician
You could work for:
- Academic and research organisations - where you'll undertake projects to develop the understanding of particular areas of maths. There are relatively few pure-research posts and you'll likely have additional teaching responsibilities.
- Commercial organisations - where you'll help to develop new products and provide an insight into business performance. You may be allocated specific projects or could be involved in all stages of the product, from concept to customer.
As a research mathematician you'll typically need to:
- use specialist mathematical software such as Mathematica, MATLAB or Mathcad or programming languages such as C/C++ to develop programs to perform mathematical functions
- produce original mathematics research
- identify solutions by learning and applying new methods, for example designing mathematical models that interpret data in a meaningful way
- present findings at group and departmental meetings, as well as to senior management
- attend, and sometimes present at, national and international scientific conferences and meetings in your particular field of interest
- meet with clients throughout projects to discuss ideas and results
- advise clients on how to benefit from mathematical analysis, making recommendations based on these analyses
- keep up to date with new mathematical developments
- write applications for funding
- manage a research team (or group of research students in academic settings)
- produce tailored solutions to business problems using innovative and existing methods, as well as suggesting new ways to analyse data
- provide more sophisticated insights into available data
- share the implications of new research by producing regular reports on the development of work, as well as writing original papers for publication in peer-reviewed scientific journals.
- If you're doing a PhD and have been awarded a studentship, it will usually come with a tax-free stipend to help cover living costs. This is currently at least £15,285, although some may be higher if industry funded or if you’re based in London.
- If you've completed a PhD, you're likely to earn in the region of £25,000 to £40,000, depending on your background, experience and specialist subjects.
- With experience, salaries for mathematicians can range from £30,000 to over £50,000.
- Salaries at top senior levels and for university professors or researchers with high levels of responsibility can range from £50,000 to in excess of £75,000.
For current details on PhD studentship stipends, see UKRI - Funding for research training.
The majority of academic institutions in the UK have now implemented a single pay spine for all grades of staff. Pay varies according to whether you're leader of your own research group, part of a team of researchers or whether you've secured a lectureship while continuing your research.
Pay is generally higher in the private sector. Larger companies may pay more than smaller, specialist employers, although these smaller employers may offer earlier responsibility and a broader range of activities.
Income figures are intended as a guide only.
Working hours may include regular extra hours, although weekend work is rare. If you're an academic researcher with additional responsibility for postgraduate students you may do more evening or weekend work.
What to expect
- Work usually involves office-based activities and the use of specialist computer systems.
- Jobs are fairly widely available throughout the UK, but posts related to specialist research are restricted to a few institutions in certain areas.
- Self-employment and freelance work is possible once you've developed a technical specialism.
- Initiatives are in place in various sectors to encourage equality, inclusion and diversity. This includes the Institute of Mathematics & its Applications, which has several diversity and inclusivity policies, including one on women in mathematics. UKRI also has equality, diversity and inclusion policies and guidance with the aim to create a dynamic system of research and innovation in the UK.
- The work often involves strict deadlines and projects can be long in duration with no guarantee of a successful outcome.
- You may need to travel to meet with colleagues you're collaborating with on particular projects. You'll also travel, both in the UK and abroad, to attend conferences and symposiums to present the results of research.
You'll need a good honours degree, usually a 2:1 or above, to become a research mathematician. Relevant degree subjects include those with significant mathematical content, particularly mathematics or physics.
Most people entering this field of work will have completed, or be working towards, a postgraduate qualification, usually a research-based Masters or a PhD. The high-level, technical communication skills developed through writing a thesis are very attractive to employers. Career progression without a PhD (particularly in academia) is likely to be limited.
Funding is made available to research institutions via the Engineering and Physical Sciences Research Council (EPSRC). This is then passed on to students in the form of scholarships and bursaries. Contact individual institutions to find out more about funding options.
If you're planning to do postgraduate study or undertake postdoctoral research contracts, identify researchers in your field of interest using directories, scientific journals and your own network of contacts. You should also discuss your interests with your academic tutor or supervisor. Make applications for research degrees early on, so academic departments have time to apply for funding on your behalf.
You'll need to have:
- a creative approach to, and a deep interest in, mathematics
- the intellectual ability to understand and analyse complex problems
- tenacity and patience for developing research projects
- excellent oral and written communication skills
- great attention to detail
- the ability to collaborate and work well in a team
- independent thinking
- commercial awareness
- the ability to make quick decisions
- flexibility in order to adapt quickly to changing market needs or develop original solutions.
Pre-entry work experience is desirable, and sometimes researchers use their undergraduate dissertation topic as a starting point for their PhD research.
Postdoctoral research experience is useful, and usually essential for academic posts. Speculative applications to potential academic supervisors is a good route into work experience or shadowing.
Gaining experience in both academia and industry is useful as it helps to show how the two environments differ and will aid your decision as to which area you’d like to work in.
You should also try to keep up to date with developments in the area. The Engineering and Physical Sciences Research Council can help with this. See EPSRC News, Events and Publications for more information.
Find out more about the different kinds of work experience and internships that are available.
Mathematicians conduct research in any environment where data is analysed and used to identify patterns. These environments include industrial areas and academic disciplines, where mathematics is applied in order to understand such issues as commercial trends or social network development.
You'll find research mathematician positions in:
- research councils and other research institutions
- government departments, including Government Communications Headquarters (GCHQ)
- private research laboratories
- manufacturing companies
Job adverts are likely to ask for specific techniques or areas of knowledge.
Research and development is not restricted to major companies. Small to medium-sized companies also offer opportunities to mathematicians in the early stages of their career.
Look for job vacancies at:
- Institute of Mathematics & its Applications (IMA)
- London Mathematical Society
- Nature Careers
- New Scientist Jobs
Individual companies and academic institutions advertise vacancies on their websites. National newspapers also advertise vacancies. See, for example, Times Higher Education unijobs.
Research potential employers thoroughly and be prepared to make speculative applications.
If you're studying for a PhD while employed in a research post, you'll be supported by a supervisor. You're likely to get additional training, which may be offered by the institution or by Vitae, which supports the professional development of researchers.
If you work at a university you'll typically have access to postdoctoral training during the early stages of your career. In industry, most employers will provide access to training and support to ensure that you have the required skills.
You'll need to keep up to date with developments in your field through attending conferences and events, and by networking with peers. Relevant opportunities are offered by professional bodies and research organisations, such as:
- Institute of Mathematics & its Applications (IMA)
- International Centre for Mathematical Sciences (ICMS)
- Isaac Newton Institute for Mathematical Sciences
Professional networks focused on specific areas of research also provide peer support and the opportunity to share knowledge.
IMA membership is offered at five grades, which reflect your status as a skilled researcher. This includes student membership, for those studying a mathematics degree or a degree with a significant mathematical component, such as some physics and engineering courses. When you have graduated from your degree, you can apply for associate membership.
Once you have progressed in your career and built up substantial experience, depending on your level of responsibility, you can gain advanced membership either at member (MIMA) or fellow (FIMA) grades. You can then go on to apply for Chartered Mathematician (CMath) status but you will need to demonstrate that you meet certain criteria first.
Companies in industry provide opportunities for promotion and development, although these may involve taking on more commercial roles, or the management of technical teams.
You can take on greater responsibility for projects after gaining several years of practical experience. Once you've managed the work of other mathematicians you can progress to roles such as project manager or technical director.
You may choose to undertake senior research roles as a specialist, or move into other scientific and commercial functions including sales and marketing. There may also be opportunities with international companies to take on projects or secondments overseas.
In academic settings, following your PhD you'll typically move on to fixed-term postdoctoral research contracts of up to three years in length. Most newly qualified postdoctoral fellows take up advertised positions or apply speculatively to an established scientist.
Career development at this stage can be challenging. Although postdoctoral fellowships and other schemes are offered by the EPSRC, all awards are extremely competitive.
Academic promotion depends on your research achievements. These are measured by the quality and quantity of original papers you've had published, and your success in attracting funding. Presenting material at national and international conferences will help boost your career prospects.
Further career development is into lectureships, and ultimately to professorial level with managerial responsibility. Permanent research posts without teaching or administrative responsibilities are highly sought after.