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Research mathematicians apply advanced mathematical techniques to solve complex problems, develop new theories and generate innovative models across a range of disciplines

In your work as a research mathematician, you'll typically combine theoretical analysis and practical applications to explain or predict real phenomena.

Your area of focus and work activities will depend on whether you work in applied or pure research, the type of employer you work for - usually an academic institution, industry firm or a government body - and what you are working on.

Types of research mathematician

Research mathematicians generally work in either applied research or pure research:

• Applied research - using mathematical knowledge not just to expand theory, but to tackle real-world challenges, turning equations and models into tools that help solve tangible problems or help develop commercial products or intelligence about business trends.
• Pure research - exploring abstract concepts in areas such as number theory, topology, group theory, algebraic geometry, or logic. Contributing to the foundational understanding of mathematics which often leads to later breakthroughs and future applications.

Collaboration with other scientists and people in commercial functions in industry is common because the application of mathematics is so varied.

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 Python or C/C++, to develop programs that perform mathematical functions
• conduct original mathematical research
• apply mathematical principles to identify trends in data sets
• identify solutions by learning and applying new methods, for example, designing mathematical models that interpret data meaningfully
• 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 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
• stay up to date with new mathematical developments
• write applications for funding
• manage a research team (or group of research students in academic settings)
• develop tailored solutions to business problems using innovative and existing methods, and suggest new ways to analyse data
• provide sophisticated insights into available data
• share the implications of new research by producing regular reports on the development of work and write original papers for publication in peer-reviewed scientific journals.

Salary

• 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. For the academic year 2025/26, the minimum stipend is £20,780. Students in London receive an additional London weighting.
• 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 more than £75,000.

For current details on PhD studentship stipends, see .

Most academic institutions in the UK have a  for all grades of staff. Pay varies according to whether you're a 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

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

• Much of the work is office based and you'll use specialist computer systems. There'll often be strict deadlines and projects can be long in duration with no guarantee of a successful outcome.
• Jobs are available throughout most of 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.
• Organisations such as the Institute of Mathematics & its Applications and UKRI run widening participation initiatives to encourage equality, inclusion, and diversity.
• You'll travel within the UK and abroad to present the results of research at conferences and symposiums, and you may also need to travel to meet with colleagues you're collaborating with on projects.

Qualifications

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. Employers highly value the advanced technical communication skills developed through thesis writing. Career progression without a PhD (particularly in academia) is likely to be limited.

You may be able to access a scholarship or bursary as many research institutions obtain funding for mathematical research that they pass on to students. The is the main body funding mathematics in the UK, but funding is also sourced from other government bodies, research councils, charitable foundations and industry partnerships.

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.

Skills

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 to adapt quickly to changing market needs and to develop original solutions.

Work experience

Pre-entry work experience is desirable, and your undergraduate dissertation topic can be a good starting point for your 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 for more information.

Find out more about the different kinds of work experience and internships that are available.

Employers

Research mathematicians are employed across a variety of industry sectors, including:

• aerospace - enabling innovation, precision and safety
• data science - shaping the development of new tools, models and methodologies
• finance - using quantitative analysis for financial modelling
• public sector organisations - using mathematical techniques and models to help support decision-making, inform policy, optimise systems and solve complex societal problems
• telecommunications - supporting everything from signal clarity and network design to cybersecurity and predictive analytics
• technology - driving innovation and helping to ensure systems are efficient, secure, scalable and intelligent, and developing AI (artificial intelligence).

You'll also find research mathematician positions in:

• research councils and other research institutions
• government departments, including Government Communications Headquarters (GCHQ)
• private research laboratories
• manufacturing companies
• universities.

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:

Individual companies and academic institutions advertise vacancies on their websites. National newspapers also advertise vacancies. See, for example, .

Research potential employers thoroughly and be prepared to make speculative applications.

Professional development

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 , 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:

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've progressed in your career and built up substantial experience, you can gain advanced membership either at member (MIMA) or fellow (FIMA) grades. You can then go on to apply for but you will need to demonstrate that you meet certain criteria first.

Career prospects

Companies in industry provide opportunities for promotion and development. For example, you could work as a specialist in a senior research role, or in a more commercial role such as sales and marketing, or as a manager of a technical team. If the company is international there may be scope to take on projects or secondments overseas.

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.

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.