Celebrating Pi (π) Day (March 14th or, sometimes, July 22nd) is a great chance to spread the word that math is exciting and fun.* In many ways, math is like a game: there are rules, but the interesting part is what you can do while following those rules. However, math goes much beyond that: for one, you get to define your own rules or, even better, explore how different rules and their combinations lead to different results.
That’s not to say that math is totally abstract and unconnected to the real world. As Galileo Galilei (whose birthday was just under a month ago) said: “[the book of nature] is written in the mathematical language”. In fact, one of the earliest discoveries of Galileo was that the period of all pendula of the same length is the same (independent of their mass), and pi prominently figures in the formula for this period (at least, for small swings). The physics revolution in the early modern era can be directly traced to Galileo and Newton prioritizing the mathematical formulation of physical principles, and concretely working out predictions with mathematical reasoning.
In all of math, Pi has a special significance of its own – not just because it appears twice in my last name.1 It’s certainly ubiquitous in geometry, as it’s obviously related to circles and other round objects, but also crops up in most other areas of mathematics. In fact, one of the most interesting applications of pi is in probability theory. There, pi is needed to properly normalize the normal distribution, which is fundamental in studying what happens when combining many random degrees of freedom. This connection, through the roundabout way of complex analysis, is crucial in understanding randomness in real life, from the random walk of pollen particles to the equally seemingly random behavior of stock prices.
The ubiquity of pi is a strong hint to how interpenetrating the different areas of mathematics are and often gives some of the earliest instances of delight in discovering unexpected connections. Pi is also one of the first mathematical constants discovered; exploring how different mathematicians studied it (from the ancient Egyptians to Euclid and other ancient Greeks to Euler to Gauss to Ramanujan and so on) gives a vibrant picture of math as a human activity and thriving culture, as opposed to an impersonal body of knowledge.
At Intech, we employ mathematicians and physicists with a strong passion for math, and for collaborating with others, especially in academia, who share this passion. Our investment process is grounded in math, rather than looking for empirical anomalies or signals, and some of our best investment insights come from deep dives into mathematical models. We’re proud to be able to play an epsilon role in mathematics’ noble history in our efforts to take care of our clients’ assets.
* Pi Approximation Day is observed on July 22nd (22/7 in the day/month format), since the fraction 22⁄7 is a well-regarded approximation of Pi.
1. Alpha appears four times, which is the right amount.
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