Math

# Benjamin Banneker’s Prime Observation

Benjamin Banneker is an important mathematician in history, not only for being a wide-ranging thinker who studied astronomy, clocks, nature, and mathematics (to name a few), but also for being an early important Black scientist and intellectual. Born in 1731 near Baltimore, Maryland, he became known for helping to survey the original border of Washington, D.C., publishing almanacs, and building extremely accurate clocks.

Banneker became intrigued by one mathematical piece of nature: cicadas—in particular, one species that first arrived when he was a teenager. His instinct at the time? Destroy them! (Teens will be teens.) But in 1766, the cicadas arrived again. Now in his thirties, Banneker chose to respect the buzzing-and-clicking creatures instead. They arrived again in 1783, always showing up in precisely 17-year increments. At this point, Banneker not only respected the cicadas, he was studying them. He correctly predicted that they would appear again in 1800, and ventured guesses as to why the insects waited that particular number of years to reemerge each time. In fact, there are several periodic cicadas in the U.S., and their life cycles are either 13 or 17 years.

So, why have the cicadas settled on 13 and 17? If you’re a math teacher reading this, consider posing that question to your students and see if they spot one key trait those two numbers have in common: they’re both prime. This is nature’s way of ensuring that a 13-year species and a 17-year species are almost never around at the same time—or during the time of any other periodically emerging species, for that matter.

Compare their appearances with two fictional cicadas that appear every 12 and 16 years, two numbers that are decidedly not prime:

Every 48 years (why 48?), the two cicada species would appear at the same time. Scientists agree that this is an evolutionary strategy, and there are two dominant theories for why this is the case. Either it is an evolutionary strategy to avoid parasites that typically have 2- or 3-year periodic life cycles, or it is to avoid possible hybridization of species. Either way, when the cycles are 17 years and 13 years, the two species will only appear simultaneously every 221 years! (Why 221?)

Banneker was not the first person to identify the 17-year cycle, but he was among its first notable observers. His work reveals both his keen observation of the world around him and a greater truth about mathematics: it’s everywhere you look.

***

To explore the endless ways that math is used in the real world, check out HMH's solutions for every math classroom.