A mathematician


A mathematician is a professional who uses an extensive knowledge of mathematics to solve mathematical problems. They are concerned with numbers, data, quantity, structure, space, models, and change.

Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. They use high-level mathematics and technology to develop new mathematical principles, understand relationships between existing principles, and solve real-world problems in various fields such as economics, science, engineering, physics, and business.

Here are some typical duties of mathematicians:

  • Conduct original research to explore new mathematical concepts, theories, and applications, contributing to the advancement of mathematical knowledge.
  • Analyze complex problems in diverse fields, such as physics, engineering, computer science, finance, and more, using mathematical techniques to develop solutions.
  • Develop and prove mathematical theorems, lemmas, and conjectures, advancing the theoretical foundations of mathematics.
  • Apply mathematical principles to real-world situations, collaborating with scientists, engineers, and researchers to solve practical problems and optimize processes.
  • Create mathematical models to represent and simulate phenomena in the natural or social sciences, aiding in the understanding and prediction of complex systems.
  • Develop algorithms for solving computational problems, optimizing processes, or analyzing data, contributing to advancements in computer science and technology.
  • Educate students at various levels, from primary education to postgraduate studies, sharing mathematical concepts, theories, and problem-solving techniques.
  • Collaborate with interdisciplinary teams, including physicists, engineers, computer scientists, and researchers, to address multifaceted challenges.
  • Publish research findings in academic journals, present at conferences, and contribute to the dissemination of mathematical knowledge within the scientific community.
  • Provide expert consultation to industries, government agencies, and organizations seeking mathematical expertise for specific projects or problem-solving.
  • Stay updated on advancements in mathematics, embracing new theories, methodologies, and technologies that enhance the field.

Other titles

The following job titles also refer to mathematician:

mathematics science researcher
logic scientist
mathematics scientist
logic research scientist
mathematics researcher
logic science researcher
mathematics scholar
logic researcher
mathematics research scientist
logic scholar

Working conditions

Mathematicians work in academia, research institutions, government agencies, and industries that require mathematical expertise. The role may involve a combination of independent research, collaboration with peers, teaching, and presenting findings at conferences.

Minimum qualifications

A Ph.D. in mathematics or a related field is typically required for research and academic positions, while master’s degrees may be sufficient for some industry roles. Practical experience gained through research projects, internships, or postdoctoral positions contributes to the development of mathematicians. Strong analytical skills, creativity, and the ability to communicate complex ideas effectively are essential for success in this role. Continuous learning and staying updated on advancements in mathematical research enhance a mathematician’s effectiveness in their field.

ISCO skill level

ISCO skill level is defined as a function of the complexity and range of tasks and duties to be performed in an occupation. It is measured on a scale from 1 to 4, with 1 the lowest level and 4 the highest, by considering:

  • the nature of the work performed in an occupation in relation to the characteristic tasks and duties
  • the level of formal education required for competent performance of the tasks and duties involved and
  • the amount of informal on-the-job training and/or previous experience in a related occupation required for competent performance of these tasks and duties.

Mathematician is a Skill level 4 occupation.

Mathematician career path

Similar occupations

These occupations, although different, require a lot of knowledge and skills similar to mathematician.


Essential knowledge and skills

Essential knowledge

This knowledge should be acquired through learning to fulfill the role of mathematician.

  • Mathematics: Mathematics is the study of topics such as quantity, structure, space, and change. It involves the identification of patterns and the formulation of new conjectures based on them. Mathematicians strive to prove the truth or falsity of these conjectures. There are many fields of mathematics, some of which are widely used for practical applications.
  • Algebra: The subdiscipline of mathematics that uses formulae, symbols, and equations to represent and manipulate numbers and quantities.
  • Statistics: The study of statistical theory, methods and practices such as collection, organisation, analysis, interpretation and presentation of data. It deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments in order to forecast and plan work-related activities.
  • Scientific modelling: Scientific activity consisting in selecting the relevant aspects of a situation and aiming to represent physical processes, empirical objects and phenomena to allow a better understanding, visualisation or quantification, and to enable simulation that shows how this particular subject would behave under given circumstances.
  • Scientific research methodology: The theoretical methodology used in scientific research, involving doing background research, constructing a hypothesis, testing it, analysing data and concluding the results.

Essential skills and competences

These skills are necessary for the role of mathematician.

  • Create solutions to problems: Solve problems that arise in planning, prioritising, organising, directing/facilitating action and evaluating performance. Use systematic processes of collecting, analysing, and synthesising information to evaluate current practice and generate new understandings about practice.
  • Execute analytical mathematical calculations: Apply mathematical methods and use calculation technologies to perform analyses and devise solutions to specific problems.
  • Think analytically: Produce thoughts using logic and reasoning in order to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.
  • Apply scientific methods: Apply scientific methods and techniques to investigate phenomena, by acquiring new knowledge or correcting and integrating previous knowledge.
  • Conduct quantitative research: Execute a systematic empirical investigation of observable phenomena via statistical, mathematical or computational techniques.
  • Use logical reasoning: Use cognitive abilities to make decisions and to move logically from one idea to another.
  • Study the relationships between quantities: Use numbers and symbols to research the link between quantities, magnitudes, and forms.

Optional knowledge and skills

Optional knowledge

This knowledge is sometimes, but not always, required for the role of mathematician. However, mastering this knowledge allows you to have more opportunities for career development.

  • Sas language: The techniques and principles of software development, such as analysis, algorithms, coding, testing and compiling of programming paradigms in SAS language.
  • Philosophy of mathematics: The subdiscipline of mathematics that examines the philosophical foundations and implications of mathematics. It studies the methodology of math and how people use it in their daily lives.
  • Geometry: Branch of mathematics related to questions of shape, size, relative position of figures and the properties of space.
  • Logic: The study and use of accurate reasoning, where the legitimacy of arguments is measured by their logical form and not by content.
  • Algorithms: The self-contained step-by-step sets of operations that carry out calculations, data processing and automated reasoning, usually to solve problems.
  • Computer science: The scientific and practical study that deals with the foundations of information and computation, namely algorithms, data structures, programming, and data architecture. It deals with the practicability, structure and mechanisation of the methodical procedures that manage the acquisition, processing, and access to information.
  • Philosophy: The different philosophical systems, their basic principles, values, ethics, ways of thinking, customs, practices and their impact on human culture.
  • Mechanical engineering: Discipline that applies principles of physics, engineering and materials science to design, analyse, manufacture and maintain mechanical systems.
  • Statistical analysis system software: Specific software system (SAS) used for advanced analytics, business intelligence, data management, and predictive analytics.
  • Instrumentation engineering: The science and engineering discipline that attempts to control process variables of production and manufacturing. It also focuses on the design of systems with desired behaviours. These systems use sensors to measure the output performance of the device that is being controlled.
  • Metalogic: The subdiscipline of logic that studies the languages and systems that humans use to communicate truths. It studies the properties of these logical systems.
  • Set theory: The subdiscipline of mathematical logic that studies the properties of well-determined sets of objects, relevant to mathematics.

Optional skills and competences

These skills and competences are sometimes, but not always, required for the role of mathematician. However, mastering these skills and competences allows you to have more opportunities for career development.

  • Prepare lesson content: Prepare content to be taught in class per curriculum objectives by drafting exercises, researching up-to-date examples, etc.
  • Perform lectures: Present lectures to various groups.
  • Apply statistical analysis techniques: Use models (descriptive or inferential statistics) and techniques (data mining or machine learning) for statistical analysis and ICT tools to analyse data, uncover correlations and forecast trends.
  • Create software design: Transpose a series of requirements into a clear and organised software design.
  • Develop financial statistics reports: Create financial and statistical reports based on collected data which are to be presented to managing bodies of an organisation.
  • Perform scientific research: Gain, correct or improve knowledge about phenomena by using scientific methods and techniques, based on empirical or measurable observations.
  • Use software tools for site modelling: Use software and other modelling tools to create simulations of and develop scenarios for possible outcomes of site operations. Use the information gathered from simulations and models for analysis and decision-making.
  • Develop scientific theories: Formulate scientific theories based on empirical observations, gathered data and theories of other scientists.
  • Develop statistical software: Participate in the various development stages of computer programs for econometric and statistical analysis, such as research, new product development, prototyping, and maintenance.
  • Carry out statistical forecasts: Undertake a systematic statistical examination of data representing past observed behaviour of the system to be forecast, including observations of useful predictors outside the system.
  • Write scientific papers: Present the hypothesis, findings, and conclusions of your scientific research in your field of expertise in a professional publication.
  • Provide lesson materials: Ensure that the necessary materials for teaching a class, such as visual aids, are prepared, up-to-date, and present in the instruction space.
  • Assist scientific research: Assist engineers or scientists with conducting experiments, performing analysis, developing new products or processes, constructing theory, and quality control.

ISCO group and title

2120 – Mathematicians, actuaries and statisticians

  1. Mathematician – ESCO
  2. Mathematicians and Statisticians : Occupational Outlook Handbook – U.S. Bureau of Labor Statistics
  3. Featured image: By Ecole polytechnique Université Paris-Saclay – CMAP – Centre de Mathématiques Appliquées de l’Ecole polytechnique, CC BY-SA 2.0
Last updated on February 2, 2024