Can Someone Good in Mathematical Economics Be Called a Mathematician?
Posing the question, "Can someone who is good in mathematical economics be called a mathematician?" invites a nuanced exploration into the boundaries and definitions of mathematical competence. The answer to this query is not a simple yes or no; it lies in understanding the scope and complexity of mathematical economics and the broader field of mathematics.
Defining Mathematical Economics
Mathematical economics is a discipline that applies mathematical methods to represent economic theories and investigate economic phenomena. It encompasses a range of topics including, but not limited to, mathematical modeling of economic behavior, econometrics, game theory, and financial mathematics. These areas require a solid foundation in various branches of mathematics, including calculus, linear algebra, stochastic processes, and more advanced topics such as category theory.
Teaching Perspectives and Syllabi
Academic institutions offer various courses that cover different aspects of mathematical economics. For instance, undergraduate and graduate business students often take introductory and advanced mathematics courses such as multivariable calculus, linear algebra, and stochastic calculus. Such courses not only provide a solid mathematical base but also prepare students to tackle complex economic models and theories. While these syllabi cover a significant portion of the mathematical toolkit necessary for economic analysis, they do not exhaust the entire field of mathematics.
The Broader Context of Mathematics
Mathematics, as a field, is vast and diverse, encompassing numerous sub-disciplines such as algebra, geometry, number theory, and analysis, among others. A mathematician, in a strict sense, refers to a person who has expertise or specialization in one or more of these sub-disciplines. Therefore, someone skilled in mathematical economics, although deeply knowledgeable in specific mathematical tools and techniques, may not have the breadth of knowledge required to be universally recognized as a mathematician.
Comparing Competencies
The question of whether an individual skilled in mathematical economics can be called a mathematician hinges on the level of specialization and the depth of knowledge in more specialized branches of mathematics. A mathematician, especially one with a degree in mathematics, typically has a broad understanding of these branches and may have chosen to specialize in a specific area, such as algebraic geometry or number theory.
Specialization vs. Breadth of Knowledge
While a student of mathematical economics will be proficient in necessary mathematical techniques, they may not have the same breadth of knowledge as a mathematician who has studied a wide range of mathematical disciplines. However, if someone's expertise in mathematical economics is substantial and they are capable of contributing to research in advanced mathematical economics, they can certainly be called a mathematician within the context of mathematical economics.
Professional Opportunities
Professionally, the term "mathematician" can be used more flexibly, depending on the specific job or field. In academia, a researcher in mathematical economics might be referred to as a mathematician, particularly if they are tackling problems using advanced mathematical techniques. In industry, especially in financial sectors, such expertise is highly valuable and often equates to the term "mathematician."
It is important to note that, in many contexts, the term is used more broadly to describe someone with significant mathematical skills, regardless of the specific area of specialization.
Conclusion
Summaringly, a person skilled in mathematical economics can be considered a mathematician in the relative sense that they possess a deep understanding and proficiency in the mathematical tools and techniques necessary for economic analysis. However, being a mathematician in the absolute sense requires a broader and more generalized knowledge of the mathematical discipline. Therefore, while it is accurate to say that a skilled mathematical economist can be called a mathematician, their title might more accurately be specified to the field in which they excel.
Keywords
Mathematical Economics, Mathematician, Economics