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The Investigative person will usually find a particular area of science to be of interest. They are inclined toward intellectual and analytical activities and enjoy observation and theory. They may prefer thought to action, and enjoy the challenge of solving problems with clever technology. They will often follow the latest developments in their chosen field, and prefer mentally stimulating environments.

Occupation Details

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Job Zone

Most of these occupations require post-graduate qualifications. For example, they may require a masters degree, and some require a Ph.D., or M.D.

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Employees may need some on-the-job training, but most of these occupations assume that the person will already have the required skills, knowledge, work-related experience, and/or training.

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These occupations often involve coordinating, training, supervising, or managing the activities of others to accomplish goals. They may also require very specialist skills. Very advanced communication and organisational skills are required. Examples include lawyers, aerospace engineers, wildlife biologists, school psychologists, surgeons, treasurers, and most scientists.

€35k > 65
Salary Range
(thousands per year)*
€35 - 65
Related Information:
Entrants: 35
Senior: 65
Data Source(s):

Last Updated: March, 2011

* The lower figures typically reflect starting salaries. Higher salaries are awarded to those with greater experience and responsibility. Positions in Dublin sometimes command higher salaries.
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At a Glance... header image

Uses mathematics to solve problems in industry, commerce and technology.

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The Work header image

Mathematics is one of the oldest and most fundamental subjects studied at university. Mathematicians use mathematical theory, computational techniques, algorithms, and the latest computer technology to solve problems in business, government, and engineering and in the physical, life, and social sciences.  
Some mathematicians work on developing new theories, and developing new principles and recognizing previously unknown relationships between existing principles of mathematics. Although this work is focused more on increasing human's basic knowledge, and less on its practical use, such pure and abstract knowledge has resulted in many scientific and engineering achievements. Many theoretical mathematicians are employed in academic institutions, dividing their time between teaching and conducting research.  
For example, they may analyse the most efficient way to schedule airline routes between countries, the effects and safety of new drugs, the aerodynamic characteristics of an experimental automobile, or the cost-effectiveness of alternative manufacturing processes.  
Some mathematicians, called cryptanalysts, analyse and decipher encryption systems designed to transmit military, political, financial information in code.  
Mathematics is the foundation on which so many other disciplines are built, for example, statistics, actuaries, and research analysts.  
Frequently, mathematicians are required to collaborate with other workers in their organisations to achieve common solutions to problems.  
Mathematicians often use computers to analyse relationships among the variables and solve complex problems by developing models with alternative solutions.

Tasks & Activitiesheader image

The following is a list of the most commonly reported tasks and activities for this occupation


Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.


Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.


Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.


Assemble sets of assumptions and explore the consequences of each set.


Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.


Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.


Disseminate research by writing reports, publishing papers, or presenting at professional conferences.


Perform computations and apply methods of numerical analysis to data.


Develop new principles and new relationships between existing mathematical principles to advance mathematical science.


Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.

Work Activities header image

The following is a list of the most commonly reported work activities in this occupation.


Thinking Creatively: Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.


Processing Information: Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.


Analyzing Data or Information: Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.


Updating and Using Relevant Knowledge: Keeping up-to-date technically and applying new knowledge to your job.


Interacting With Computers: Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.


Getting Information: Observing, receiving, and otherwise obtaining information from all relevant sources.


Making Decisions and Solving Problems: Analyzing information and evaluating results to choose the best solution and solve problems.


Identifying Objects, Actions, and Events: Identifying information by categorizing, estimating, recognizing differences or similarities, and detecting changes in circumstances or events.


Estimating the Quantifiable Characteristics of Products, Events, or Information: Estimating sizes, distances, and quantities; or determining time, costs, resources, or materials needed to perform a work activity.


Communicating with Supervisors, Peers, or Subordinates: Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.

Knowledge header image

The following is a list of the five most commonly reported knowledge areas for this occupation.


Mathematics: Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.


Computers and Electronics: Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.


English Language: Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar.


Engineering and Technology: Knowledge of the practical application of engineering science and technology. This includes applying principles, techniques, procedures, and equipment to the design and production of various goods and services.


Physics: Knowledge and prediction of physical principles, laws, their interrelationships, and applications to understanding fluid, material, and atmospheric dynamics, and mechanical, electrical, atomic and sub- atomic structures and processes.

Skillsheader image

The following is a list of the most commonly reported skills used in this occupation.


Mathematics: Using mathematics to solve problems.


Active Learning: Understanding the implications of new information for both current and future problem-solving and decision-making.


Reading Comprehension: Understanding written sentences and paragraphs in work related documents.


Critical Thinking: Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.


Complex Problem Solving: Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.


Science: Using scientific rules and methods to solve problems.


Writing: Communicating effectively in writing as appropriate for the needs of the audience.


Active Listening: Giving full attention to what other people are saying, taking time to understand the points being made, asking questions as appropriate, and not interrupting at inappropriate times.


Judgment and Decision Making: Considering the relative costs and benefits of potential actions to choose the most appropriate one.


Speaking: Talking to others to convey information effectively.

Personal Qualitiesheader image

Mathematicians need good reasoning power, persistence and the ability to apply basic principles to new types of problems.  
They need a very high level of numeracy and a love of working with numbers and calculations.  
They need to be prepared for spending a lot of time thinking and working solutions out, often on their own. It is likely that they will spend a lot of their time sitting down, and also using a computer.

Entry Routesheader image

Entry to Mathematics as a career will require a degree level qualification (BA or BSc. in Mathematics), together with a postgraduate qualification at masters or Doctorate Level.

Background experience in the related STEM areas (Science, Technology and Engineering)  is also valuable.

Last Updated: October, 2014

Related Occupationsheader image

Contactsheader image


Organisation: School of Mathematics
Address: Trinity College Dublin, Dublin 2
Email: Click here
Url Click here

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This occupation is popular with people who have the following Career Interests...

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Physics, Mathematics & Space Science

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