2021 Was a Mess, Unless You Count the Palindrome Days
(Bloomberg Opinion) -- Math fans like me love to find joy in numbers everywhere — and 2021 was a mathematically exciting year however you look at it.
The year was full of palindrome days, whose dates read the same forward and backward (at least in the U.S. date convention). There was a string of them in January — 1/20/21 through 1/29/21, as well as 1/2/21. Then we had another run in December, including 12/1/21 through 12/9/21, 12/11/21 and 12/22/21.
Many of these dates also had 180° rotational symmetry, making them examples of what are called “ambigrams.” January 20 and December 2 could even be expressed as palindrome-ambigram dates with the year written out in full: 1/20/2021 and 12/02/2021. Plus 12/22/21 was the last six-digit palindrome day in the U.S. date convention for almost a decade.
May 15, 2021 had an even rarer property: When written as 15/05/2021, the date has reflective symmetry across the center, since 2021 looks like 1505 when you put a mirror next to it. And April 3 (or March 4 in the European date convention) was a “countdown day,” the likes of which we won’t see again until 2121: 4/3/21 (BLASTOFF!).
On August 13 — 8/13/21 — the date lined up with three adjacent elements of the Fibonacci sequence, a famous mathematical progression that crops up everywhere from pineapple spirals to financial trading. The sequence is constructed by starting with 1 and 1, and adding each pair of consecutive elements to get the next one: 1 + 1 = 2; 1 + 2 = 3; 2 + 3 = 5; and so forth, yielding 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ….
Looking at those numbers, it becomes clear that the most recent Fibonacci date before this year was May 8, 2013 (5/8/13), almost a decade ago. And moreover, there won’t be any more dates of that form until 2102 — although under a different reading of the date, we’ll see the Fibonacci numbers again in just over a year, since New Year’s Day 2023 is 1/1/23!
These special dates weren’t the only mathematically interesting things about the year either: 2,021 itself has some pretty elegant numerical properties.
The number 2,021 = 43 × 47 is semi-prime, meaning it’s the product of two prime numbers. And that’s not all: It’s a product of “cousin primes” that differ by only 4. The last such year was 1517, and the next is 4757. (Even the next product of consecutive primes is a long way off — that’s 2491.)
Plus, 2,021 is a prime in base 3 and base factorial. And it’s also the sum of the first 24 pairs of consecutive primes, and it yields a prime whenever you insert a “0” between any two of its digits (which last happened in 1909).
Meanwhile, if you add the 2,021-st prime (17,579) to 2,021, then you get a perfect square: 17,579 + 2,021 = 19,600 = 140^2. That last occurred in 1334, and happens next in 2455 and then in 2600.
So all told, there were lots of reasons to be excited about 2021 from a mathematical perspective.
But you know, even with all of that, the most important mathematical fact about 2021 is perhaps the simplest: 2,021 is unambiguously greater than 2,020. And numerically, at least, 2,022 promises to be greater still.
Mathematician Noam D. Elkies pointed out to me that 1/22/21 was miraculously also a palindrome in Hebrew (9 Shvat). And as electrical engineering professor Aziz Inan noted, 1/20/21 was also particularly special because 1 + 20 = 21.
December 2 was also a palindrome-ambigram in year-month-day format: 2021/12/02.
There’ll be even more Fibonacci excitement on 11/23/58.
That is, 2,021 = (2+3) + (3+5) + (5+7) + … + (89+97).
The sequence runs 13; 6; 19; 25; 44; 69; 113; 182; 295; 477; 772; 1,249; 2,021; 3,270; 5,291; 8,561 ….
This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.
Scott Duke Kominers is the MBA Class of 1960 Associate Professor of Business Administration at Harvard Business School, and a faculty affiliate of the Harvard Department of Economics. Previously, he was a junior fellow at the Harvard Society of Fellows and the inaugural research scholar at the Becker Friedman Institute for Research in Economics at the University of Chicago.
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