This Was a Great Year to Be a Math Geek

(Bloomberg Opinion) -- For math geeks like me, 2018 was a banner year: not only was it a year in which the field’s top prize was awarded, it was the only year in this century featuring days lining up with both the Golden ratio, an elegant proportion found throughout art and nature, and the mathematical constant e, which is at the core of calculus.

But the mathematician in me also can’t help but note that the number 2,018 has some ominous properties: It’s deficient, meaning that the sum of all its positive divisors is less than itself. And it’s also odious, meaning that it has an odd number of ones in its binary expansion, 11111100010.

This year is pretty cryptic, as well -- it features prominently in the first of the three Beale ciphers, an 1880s cryptographic puzzle that supposedly describes the location of a multimillion-dollar treasure. (Hint: check the cipher’s second line.)

And 2,018 is a crystallogen number, giving it a property derived from chemistry that means it’s slightly unbalanced: atoms with full shells containing 2,022 electrons are electronically stable. But 2,018? It’s, well, just a few short. (Maybe three years from now will be less volatile?)

But that shouldn’t stop us from having fun! Although 2,018 might seem a bit concerning on the whole, its constituent parts are much more salutary.

As I pointed out a year ago, 2,018 is two times 1,009. And 1,009 is prime however you look at it: its only divisors are one and itself, and when you read it backward -- 9,001 -- you get another number with the same property. This makes 1,009 a special kind of number that mathematicians call an emirp. (Can you guess why?) Not only that, if you write 1,009 in binary -- 1111110001 -- you get a number that is the decimal representation of a prime.

And 1,009 is happy, meaning that if you take the sum of the squares of its digits, and then take the sum of the squares of the digits of the result, and so forth, you eventually get to 1. It’s also lucky, which means that it survives the following curious elimination process: Start with the odd numbers, note the second-largest is three; and delete every third number. The third-largest number remaining is then seven, so now delete every seventh. The fourth-largest is then nine, so delete every ninth, and so on.

Putting the preceding two observations together, we see that 1,009 is happy-go-lucky! Numbers like that are pretty rare -- although there’s another one coming up soon.

Indeed, 2,019 is another happy-go-lucky number. So that gives us something to look forward to as the New Year’s clock counts down. That said, 2,019 is also an apocalyptic power  -- so what the year will bring is anyone’s guess.

This is all just mathematical musing, of course -- any resemblance to actual events is purely coincidental.

This means that two raised to the 2,019th power contains 666, the number of the beast.

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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