So, Johns Hopkins University Press asked me to write a blog post for Pi Day. Well . . . other than as a marketing tool for mathematics, Pi Day is a bit of a silly idea. So, I thought I'd tell you why, at least from the perspective of this pure mathematician, it’s somehow missing the point.
Pi Day is celebrated on March 14th, because that date can be written (in America) as “3/14”. This looks like “3.14”, the first three significant digits of the mathematical constant pi. Let’s put aside the fact that in many countries the 14th of March is written as “14/3”—there’s a bigger problem here, which is that there aren’t a hundred days in each month. The numerals in “3/14” correspond to months and days. The numerals in “3.14” correspond to units, tenths and hundredths, and these don’t have much to do with months or days. Pi is only a little bigger than 3, but the 14th day of the month is almost halfway through counting up to the number that would make the "3" roll over to become "4". If anything, "3/14" could be expressing the fraction "3 and 14/31", or about 3.45161.
Well, ok, you may say, at least “3/14” looks like “3.14”—it’s got the same numerals in the same order. But, then, what is so special about those numerals “3.14”? The decimal system, which is what we use to write "3.14" is artificial—it comes from the fact that we (mostly) have ten fingers, which doesn't really matter in the bigger scheme of things. The date "3/14" only matches with the approximation "3.14" by an accident of evolution. It's a bit like a pun—the symbols match, even though the two meanings have little to do with each other.
Mathematics is really about structure. How things relate to each other. The labels we use for those things don't really matter. Pi is really about the relation between the circumference and the diameter of a circle. Alien mathematicians would also know about pi, but they would write it differently if they had a different number of fingers/tentacles, and they would certainly count their days and years (and would they even have months?) in a different way. They might not even write numbers using a positional system like we do now—the ancient Romans didn't.
However, alien mathematicians would (most likely) still live on an approximately round planet, that orbits their sun in an approximately circular orbit. Circles are timeless and universal, the symbols aren't: All the rest of it is arbitrary, the trappings of mathematics without the actual mathematics.
Having said all of that, it is good that we celebrate mathematical ideas. It's not as if there is some other more meaningful date for an annual mathematical event, so I guess it will do. But the date itself is only tangentially related to pi. (Pun intended.)
Henry Segerman is one of the leading figures in the new world of math and 3D printing. He is an assistant professor of mathematics at Oklahoma State University. His latest book is entitled Visualizing Mathematics with 3D Printing.