Research mathematicians work in a range of areas. Common employers include private or government research laboratories, commercial manufacturing companies and universities.
The work is varied but often involves proving deep and abstract theorems, developing mathematical descriptions (mathematical 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.
Research is undertaken into a diverse range of pure and applied maths including:
- differential equations;
- dynamic systems;
- geometry and topology;
- fluid mechanics;
- mathematical biology;
- numerical analysis.
Collaboration with other scientists and people in commercial functions in industry is very common because the application of mathematics is so varied.
The work of a research mathematician varies depending on the area of employment.
Mathematicians in commercial organisations help to develop new products and provide an insight into business performance. They may be allocated specific projects or could be involved in all stages of the product, from concept to customer.
In academic and research organisations, projects are undertaken to develop the understanding of particular areas of maths. There are very few pure research posts in universities though and most research mathematicians have teaching responsibilities.
Although daily tasks vary they can typically include:
- identifying solutions by learning and applying new methods, e.g. designing mathematical models that interpret data in a meaningful way;
- keeping up to date with new mathematical developments and producing original mathematics research;
- using specialist mathematical software such as Mathematica, Matlab or Mathcad or using software languages such as C/C++ to develop programs to perform mathematical functions;
- presenting findings at group and departmental meetings, as well as to senior management;
- attending, and sometimes presenting at, national and international scientific conferences and meetings in a particular field of interest;
- meeting with clients throughout projects to discuss ideas and results;
- advising clients on how to benefit from mathematical analysis, making recommendations based on these analyses;
- writing applications for funding;
- managing a research team (or group of research students in academic settings);
- producing tailored solutions to business problems using innovative and existing methods as well as suggesting new ways to analyse data;
- providing more sophisticated insights into available data;
- sharing 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. Research Councils UK suggest a minimum rate of £13,863 for the stipend but some employers may pay more.
- Research mathematicians who have completed a PhD are likely to start on salaries in the region of £25,000 to £35,000, depending on background and specialist subjects.
- With experience, salaries for mathematicians can range from £30,000 to £45,000.
- At top senior levels, mathematicians can earn £50,000 to £70,000 depending on the sector.
- University professors or researchers with high levels of responsibility, such as at principal investigator level, can achieve salaries of £50,000 to £70,000.
In academic settings pay varies according to whether the researcher is working as a leader of their own research group, as part of another research team, or with a secured lectureship while continuing their research.
Many academic institutions have now implemented a single pay spine for all grades of staff, however some variation does occur.
Pay is typically higher in the private sector. On average, larger companies pay better than smaller, specialist employers, although these smaller employers may offer earlier responsibility and opportunities to remain in preferred technical areas.
Income figures are intended as a guide only.
Working hours may include regular extra hours, but weekend or shift work is rarely, if ever, needed. The exceptions to this are academics who may face weekend working and irregular hours with additional responsibilities for postgraduate students.
What to expect
- Work usually involves some office-based activities and the use of specialist computer systems.
- Self-employment and freelance work is possible once a technical specialism has been developed.
- Jobs are fairly widely available, but posts related to specialist research are restricted to a few institutions in certain areas. Universities, government and other research centres that employ mathematicians are located across the country.
- The work often involves strict deadlines and projects can be long in duration with no guarantee of a successful outcome.
- Travel within a working day is occasionally needed. Researchers often collaborate with other departments within their institution, or with other institutions or companies, and this may involve occasional local travel.
- In academic roles, some national and international travel is required for attendance at conferences and symposiums to present the results of research, often with a stay of a few days.
A good honours degree is required to enter the career of a research mathematician. Employers typically look for a 2:1 or higher. Vacancies are likely to ask for specific techniques or areas of knowledge.
Relevant degree subjects include those with significant mathematical content. In particular, a degree in mathematics or physics will be particularly useful.
Entry is not possible without a degree or with a HND only.
Most people entering this field of work will have completed, or be working towards, a postgraduate qualification, usually a PhD. The high-level, technical communication skills developed through writing a thesis are very attractive to employers. Search for postgraduate courses in mathematics.
While it is possible to work as a research mathematician with only a relevant undergraduate degree, career progression with most employers (particularly in academia) is likely to be extremely limited without a PhD.
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.
If you are planning postgraduate study or postdoctoral contracts, identify researchers in your field of interest using directories and scientific journals, and discuss your interests with your academic tutor or supervisor. Make early speculative applications for research degrees so academic departments have time to apply for funding on your behalf.
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. You should contact the individual institution to find out more about the funding options.
Competition is moderate for research posts in industry if you have a good PhD and some postdoctoral work experience, despite there being comparatively few vacancies (as they are in such specialised areas).
You should research potential employers thoroughly and be prepared to make speculative applications. In academic settings, permanent research posts are very rare and highly sought after.
You will 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;
- commercial awareness;
- the ability to make quick decisions;
- flexibility in order to adapt quickly to changing market needs or develop original solutions.
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.
Employers include research councils and institutions, government departments including Government Communications Headquarters (GCHQ) and universities.
Research and development is not restricted to major companies. Small to medium-sized companies can offer excellent opportunities to mathematicians in the early stages of their career.
Look for job vacancies at:
- Academic Jobs EU
- Institute of Mathematics and its Applications
- London Mathematical Society
- Nature Jobs
- New Scientist Jobs
- Times Higher Education Jobs
Most employers will offer training and support to ensure you are kept aware of developments in your field and that you have the required skills. A relevant PhD is regarded as training for research work.
Most PhD research is funded by universities, research councils or trusts. Throughout the PhD, support is given in the form of advice and guidance from a PhD supervisor.
Transferable-skills training is now recognised as part of a PhD, and as a research student, you can receive formal training provided either by the institution or by Vitae.
Relevant workshops and other events are offered by professional bodies and research organisations, such as:
- The International Centre for Mathematical Sciences (ICMS)
- Isaac Newton Institute for Mathematical Sciences
In addition, professional networks focused on specific areas of research provide peer support and the opportunity to share knowledge.
A number of professional societies offer different grades of membership, which can reflect your status as a skilled researcher. For example, it is possible to become a chartered mathematician with the Institute of Mathematics and its Applications.
It is likely you will be supported and encouraged by your employer to publish research papers to help with your professional development.
Formal training is now more common in academic settings. In industry and the public sector, new techniques are learned through technical courses and larger companies also run internal courses.
Although not essential for career development, MBAs may be supported by employers, usually on a part-time basis, later in a career.
You can take on greater responsibility for projects after gaining several years of practical experience. Once you have managed the work of other mathematicians you can progress to roles such as project manager or technical director.
It is common to be in a managerial role ten to 15 years after graduation.
You may choose to undertake senior research roles as a specialist, or move into other scientific and commercial functions including sales and marketing.
Companies in industry provide opportunities for promotion and development, although these may involve taking on more commercial roles, or the management of technical teams.
Career development in international companies may depend on you being prepared to take on projects or secondments overseas.
In academic settings, a PhD is usually followed by 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, but it is aided by postdoctoral fellowships and other schemes offered by the Engineering and Physical Sciences Research Council (EPSRC). All awards are extremely competitive.
Academic promotion depends on research achievements. These are measured by the quality and quantity of original papers published and success in attracting funding. The presentation of material at national and international conferences remains another key career development opportunity.
Further career development is into lectureships and ultimately to professorial level with managerial responsibility.
Permanent research posts without teaching or administrative responsibilities are rare and highly sought after.