Research mathematicians produce original research which can be used to further develop our understanding of complex numbers, and applied to businesses to improve performance and solve problems
The work of a research mathematician is varied, but often involves 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.
Applied research can also contribute to the development of a commercial product or develop 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 can work in a range of areas. Common employers include private or government research laboratories, commercial manufacturing companies and universities.
Your role will vary depending on your area of employment. For example, mathematicians in commercial organisations 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.
In academic and research organisations, on the other hand, you'll undertake projects to develop the understanding of particular areas of maths. There are very few pure research posts, however, and you're likely to have additional teaching responsibilities.
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.
- PhD studentships, which allow you to study for a PhD while also carrying out research work, usually pay a stipend. The UK Research and Innovation national minimum doctoral stipend for 2019/20 is £15,009, but some employers may pay more.
- 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. Academic researchers with additional responsibility for postgraduate students 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.
- 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.
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 being 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. These range from student membership, for those starting out, to advanced membership at member (MIMA) and fellow (FIMA) level, for those with relevant qualifications and substantial experience.
Fellows and members of IMA who meet the Institute's education, postgraduate training and experience, professional standing and continuing professional development (CPD) requirements can apply for Chartered Mathematician (CMath) status.
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.