Mathematicians in society

SUMMARY: Mathematicians work in a variety of fields and contribute widely to society.

Broadly construed, a mathematician is anyone who actively researches or studies mathematics. Many mathematicians work in academia as professors or as researchers, though a combination of both is most common. However, mathematicians are also employed in large numbers by industry, and there are innumerable amateur mathematicians who are drawn to mathematics, pursuing its study and research as an avocation. Some mathematicians, called “applied mathematicians,” use mathematical ideas to solve problems arising in other disciplines; others, “pure” or “theoretical mathematicians” focus on furthering mathematics for its own sake. Of course, many mathematicians belong to both categories. The image of the mathematician is somewhat stereotyped in popular culture, but, in fact, mathematicians comprise an extremely diverse group. Mathematicians are women and men, girls and boys, old and young, and come from every country and culture.

If mathematicians are introduced to other mathematicians, they are unlikely to describe themselves as just “mathematicians.” Instead, they would use a more precise term indicating their primary research interests, such as “number theorist,” “analyst,” “algebraist,” “combinatorialist,” “probabilists,” or “logicians.” The degree of specialization varies widely from one mathematician to the next. A mathematician may have only one area of research interest or may work across several. It is now seen as impossible for any single person to be expert in all areas of mathematics, but there are still so-called “generalists” who work in as many branches of mathematics as possible.

As technology has changed over time, particularly over the course of the twentieth and twenty-first centuries, more mathematicians are finding careers in fields like engineering, computer science, software development, and computer programming. Furthermore, as companies, schools, and organizations utilize more mathematical tools, they are able to collect data on virtually all aspects pertaining to their development. While this can be helpful, these groups also often need developers who can create meaningful ways to collect data and analysts who can help them decipher the data. Both of these roles are suitable for mathematicians.

Mathematicians, Scientists, and Poets

While there are some overlap and blurred boundaries between the terms “mathematics” and “science” as these terms are used in ordinary discourse, the terms “mathematician” and “scientist” are usually used with more clearly distinct meanings. Scientists apply the scientific method, a continual process of investigating phenomena, collecting empirical data, formulating explanation hypotheses, and testing them by experiment; for scientists, experiments and empirical data provide the ultimate test of a theory. While mathematicians may also use experiments as part of their work, this is chiefly as a source of inspiration, as an aid in formulating conjectures and understanding complex concepts. Some might make the distinction that the scientist is generally an inductive reasoner, while the mathematician is generally a deductive reasoner. However, many applied mathematicians and statisticians may be more like scientists in this regard.

To many people, it might seem that mathematicians and poets are polar opposites, or at the very least unrelated. It is remarkable, as such, how often great mathematicians and great poets speak of the vocations as intertwined. For example, Russian mathematician Sonia Kovalevsky (1850–1891) wrote, “It is impossible to be a mathematician without being a poet in soul.” Likewise German mathematician Karl Weierstrass (1815–1897) wrote, “A mathematician who is not also something of a poet will never be a complete mathematician.” From the other direction, the great English poet John Dryden (1631–1700) wrote, “A man should be learned in several sciences, and should have… , in some measure, a mathematical mind, to be a complete poet.” Of course, there are many major differences between the job of the mathematician and that of the poet. For one, poetry is in some sense purely subjective, while the mathematician is judged on grounds both objective (for example, “is this proof correct?”) and subjective (for example, “are these ideas beautiful? Important?”). Let mathematician G. H. Hardy (1877–1947) have the last word here: “A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

Bibliography

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