My favorite genre of tumblr post is “humans are adorable.” We like to decorate ourselves with shiny things! We burn things for fun even though fire is inherently very scary! We bond with nonhumans and even feel empathy for spaceships and robot vacuum cleaners! We are ridiculous creatures, but at least we're cute. I think the way we do math is no different. Here are five of the most adorable things about our relationship with numbers and other aspects of math.
1. Between 2003 and 2013, U.S. universities awarded almost 15,000 doctorates in mathematics, statistics, and biostatistics, so there are tens of thousands of mathematicians running around the country. But not a single one of them knows whether π+e is rational or irrational! I mean, odds are in favor of it being irrational because almost all number are, but they don’t know for sure. And it’s not just π+e. Combine some irrational (or even transcendental) numbers in pretty much any way you want, and chances are no one can figure out whether it’s rational or irrational! They don’t know whether π×e is rational either, but they do know π+e and π×e cannot both be rational. What a silly amount of knowledge to have!
2. Even though most numbers—in a sense, 100% of them—are irrational, humans are strangely obsessed with rational numbers. The fewer and further between the numbers are, the more they care about them. They love integers more than non-integer rational numbers, and they seem to love prime numbers the most of all, even though a smaller and smaller proportion of integers are prime the further out on the number line you look! They are especially fascinated with twin primes, which are rarer still and may even peter out entirely at some point.
3. Humans define π to be the ratio of a circle’s circumference to its diameter and then say with a straight face that it is irrational! Even though the word irrational is based on the word ratio!
4. Despite the fact that numbers are largely constructed in their own minds, humans have favorite numbers and numbers they are afraid of or believe to be unlucky. Seven is the most favorite number, according to a poll conducted by Alex Bellos, even though that is the wrong answer because six is clearly the best number. Many people are afraid of four or 13. Some hotels and other tall buildings avoid labeling a floor as the 13th floor and then pretend there’s nothing wrong with the 14th floor! Humans will use their favorite numbers when they play games of chance even though they confer no extra benefit and in some sense could even lower their payout on a win.
5. When they’re working on a problem, humans sometimes stop when they learn that a solution exists and not bother to find the actual solution! Sometimes they don’t even know how to find the solution—they just know that it exists—and they still give themselves credit for solving the problem. Only a few mathematicians, known as constructivists, insist on being able to provide examples of quantities or objects asserted to exist, and they are considered a bit odd.