Highly relevant tasks include:

• Formulating mathematical models to simulate processes.
• Applying models to experimental observations, and adjusting and recasting the models.
• Using numerical analysis methods to develop algorithms and perform computations.

Additional tasks may include:

• Developing mathematical theory underlying processes in the physical, biological, and social sciences.
• Developing theoretical mathematical constructs and hypotheses.
• Applying mathematical principles and techniques to solve problems in research, development, production, distribution, and other functional areas.
• Liaising with management and clients to determine the subject area to be examined.

An applicant should be undertaking the majority of these tasks as their core duties in an employment role. Although it is not mandatory to perform all the tasks listed, an applicant must demonstrate that their daily tasks and skill set match the nominated occupation.

Employment Context

In Australia, there are currently no legal requirements for licensing or registration for the occupation of Mathematician.

Mathematicians typically do the following:

• Expand knowledge in mathematical areas, such as algebra or geometry, by developing new rules, theories, and concepts
• Use mathematical formulas and models to prove or disprove hypotheses and conjectures
• Apply mathematical theories and techniques to solve practical problems in business, engineering, the sciences, or other fields

Applied Mathematicians

Mathematicians use theories and techniques, such as mathematical modeling, to solve practical problems. They typically collaborate with individuals in other fields to address these issues. For example, they may work with chemists, materials scientists, and chemical engineers to analyze the effectiveness of new drugs. Other applied mathematicians might work with industrial designers to study the aerodynamic characteristics of new automobiles.

Theoretical Mathematicians

Mathematicians conduct research to identify and resolve unexplained issues in mathematics. They focus on exploring new areas and relationships within mathematical theories to enhance knowledge and understanding of the field. While some may not consider the practical applications of their findings, the knowledge they develop can significantly contribute to many scientific and engineering advancements. Despite the differences between applied and theoretical mathematics, these areas often overlap, and many mathematicians use both applied and theoretical knowledge in their job duties.

Operations Research Analyst (ANZSCO specialization) 

An Operations Research Analyst utilizes scientific methods to address issues related to managing systems involving people, machines, materials, and finances in various sectors such as industry, business, government, and defense.

Highly relevant tasks include, but may not be limited to:

• Identifying and solving real-world problems in areas such as business, logistics, healthcare, or other fields.
• Collecting and organizing information from a variety of sources, such as computer databases, sales histories, and customer feedback.
• Examining information to determine its relevance to a problem and identify suitable analysis methods.
• Using optimization, data mining, statistical analysis, simulations, predictive modeling, or other methods to analyze information and develop practical solutions to business problems.
• Advising managers and decision-makers on the potential impacts of various courses of action to address a problem.

Computational Scientist (specialization)

A Computational Scientist aims to understand scientific and engineering issues primarily by implementing, utilizing, and analyzing mathematical models on high-performance computers.

Highly relevant tasks include, but are not limited to:

• Conducting numerical simulations of complex systems and natural phenomena that would be impractical or hazardous to study through direct experimentation.
• Collaborating with specialist scientists and engineers to develop computer-based mathematical models in fields such as climate modeling, oceanography, mining, nuclear engineering, and medical imaging.

Mathematical Modeller / Quantitative Analyst (specialization)

Mathematical Modelers are Applied Mathematicians who create mathematical representations of real-world situations or hypothetical scenarios. These models are used to predict outcomes, consequences, or to create visualizations. Applications can vary widely, from manufacturing and environmental modeling to computer/video games and computer-generated imagery (CGI).

Highly relevant tasks include, but are not limited to:

• Quantifying real-world problems and scenarios using appropriate mathematical tools in collaboration with domain specialists.
• Collaborating with software engineers and computational scientists to translate mathematical models into computer algorithms, incorporating suitable user interfaces and visualization tools.
• Providing advice to researchers, managers, and decision-makers in scientific and commercial environments regarding the likely outcomes and impacts of various hypothetical scenarios.

Cryptographer (specialization)

Cryptographers/cryptanalysts employ mathematical theories of cryptology and computer coding to develop and decipher digital codes. They are hired by various entities such as companies, institutions, government agencies, police, and armed forces to ensure the security and privacy of sensitive commercial and government transactions and communications.

Highly relevant tasks include, but may not be limited to: 

• Creating, setting up, and evaluating algorithms to solve number theory problems.
• Protecting sensitive communication and data systems in government and military sectors from foreign governments and hackers.
• Providing decryption expertise for intelligence and counterintelligence services.
• Ensuring the security of financial transactions, including credit card, inter-bank, and online transactions.
• Developing technology to protect mobile phone and internet networks in the communications sector.

Employment not considered

Employment that emphasizes data analysis, prediction/interpretation, survey design, and statistical modeling aligns more closely with the occupation of Statistician. Conversely, roles in the financial and commercial sector that focus on business and data analysis, as well as budgetary forecasting, may be better suited to the occupation of Information and Organization Professionals NEC (ANZSCO 224999).

To qualify as a Mathematician, an individual must demonstrate that their primary responsibility involves developing and applying mathematical principles and techniques.