International Day of Mathematics

When I first learned about the tradition of “Name Days”—a celebration similar to a birthday whose timing is attached to a calendar of names—my first thought was naturally wondering when my name day would be. If I were named nearly anything other than Patrick, that would be an interesting question, but of course my name day is obvious: 17 March, St. Patrick’s Day.

You may or may not be surprised to know that the United Nations celebrates an International Day of Mathematics, and may similarly wonder when such a day would be celebrated. Similar to my name day in both story and timing, the International Day of Mathematics is, of course, on π (Pi) day: March 14th.

The theme this year is “Mathematics, Art, and Creativity,” which may sound like an odd connection to make, or perhaps an attempt to reflect a yin and yang of concepts. Traditionally, mathematics has a reputation of strict rule following; to some, this is touted as a benefit, that there is one right answer to a question. Others bemoan the lack of flexibility. Yet, this reputation is misplaced. I recall a talk at the 2019 Joint Mathematics Meetings by Ben Orlin from Math With Bad Drawings that started with a series of questions to poll the crowd of professional and amateur mathematicians:

How many of you think math is about following rules?

Nearly no hands were raised in response to this. This is definitely not part of the spirit of mathematics.

How many of you think math is about breaking the rules?

This got a spattering of hands. Certainly, many advances in math are made by taking rules developed by other people and seeing what happens when you disregard them, but this characterization is still not quite right.

How many of you think math is about making up your own rules?

Here’s where all the hands went up. And it’s true: the mathematics we use, develop, and rely on today did not come from the Tablets of Stone, but rather from people merely pursuing the eternal questions of “what happens if…” and “how can I…”

This approach is evident from the way mathematicians talk about the objects they work with: objects like matrices are not merely numbers in rectangular arrangements, but objects for whom some can be described as “nice” while others are “poorly-behaved.” I liken this to a sculptor, who might use similar terms to describe such rough and mundane objects as rocks.

Mathematics is all about exploring what happens when certain assumptions are made, and investigating what needs to be done to yield properties that we wish to explore. In this way, is mathematics not a natural partner to—or member of—to the creative arts? This International Day of Mathematics, keep an eye out for the rules underlying mathematics around you and ask: What makes those rules the ones we’ve decided to use? What might break if they changed, and what might arise?