# Adele’s ’30’: A mathematician explores number patterns in album titles

December 8, 2021 - 3:24 PM
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Adele, the 33-year-old British top-selling and award-winning recording artist, released her sensational new album, 30, in November. Reviewers are raving, with the New York Times calling it a “musical tour de force,” and Rolling Stone naming it her best album yet.

Besides how great the album is, everyone, it seems, is also talking about Adele’s numbers, as in: how many albums she has sold? But as a mathematician, I’m interested in how she has used numbers to sequence all of her albums. Her previous album was called 25. In fact, Adele’s album titles are always numbers, and they reflect the age that she wrote them. She wrote her debut album 19 at 19, followed by 21, then 25, and now, 30 Adele recently turned 33 but she started writing the album at 30.

Is there a pattern to Adele’s albums? The chronological list of Adele’s album titles 19, 21, 25 and 30 was coined the “Adele sequence” by David Patrick, senior math and science curriculum director at the Art of Problem Solving.

Mathematicians love sequences, and they pop up all over the field. Sequences are simply numbers listed in a given order. The simplest sequence we learn about as children are the counting numbers 1, 2, 3, 4 and so on.

A vast, searchable catalogue of sequences is the On-line Encyclopedia of Integer Sequences, or OEIS, for short. The OEIS is your one-stop shop for everything on sequences, containing more than 340,000 entries.

As Patrick points out in his article on the Adele sequence, searching OEIS for 19, 21, 25, 30 uncovers the curious sequence with the catchy title A072666, whose first few numbers are: 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 18, 19, 21, 25, 30, 31, 36, 41, 43 and 44. The Adele sequence is there in the middle: 19, 21, 25, 30 and suggests her next album will be 31.

A sequence of significant mathematical and real-world importance is the one consisting of prime numbers. Prime numbers and their properties form an expansive topic in mathematics, with applications from blockchains to encryption. A major open mathematical problem is to determine if there are infinitely many pairs of prime numbers whose difference is two (as is the case for 3 and 5 or 17 and 19).

A number is prime if it is larger than 1, and not the product of two smaller numbers. For example, 2 and 3 are prime, but 4 is not prime, as 4 is the product of 2 with itself. The primes form the sequence A000040: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 …. The ancient mathematician, Euclid of Alexandria proved in 300 BC that the sequence of primes never ends.

To define the nth number in the A072666, we take the nth prime number (where “n” stands for a number), add it to the (n+1)th prime, and subtract 1. If the resulting number is prime, then we include n in the sequence. Otherwise, we skip it.

For example, the 19th prime is 67, and the 20th is 71. We then have 67 + 71 – 1 = 137, which is a prime number, and so 19 belongs to the sequence. In contrast, if we perform a similar check with the 20th and 21st prime, we have 71 + 73 – 1 = 143, which is the product of 11 and 13 and so is not prime. That tells us that 20 is skipped in the sequence.

OEIS lists a total of nine sequences containing 19, 21, 25, 30, such as A142958, whose next entry after 30 is 41. If, instead, Adele follows A142958, her next album will be 41. That would be sad news for her millions of devoted fans, as they’d have to wait almost a decade for more of those heartfelt ballads.

### The inspiration of numbers

Adele may be unique in naming her albums only by numbers, but she is far from alone in using them in song and album titles. Musicians appear to often draw inspiration for their titles from numbers.

A tiny sample of popular songs with numbers in their title are “Eight Days a Week” and “When I’m Sixty Four” by the Beatles, “Edge of Seventeen” by Stevie Nicks, “Fifteen” and “22” by Taylor Swift, “99 Luftballons” by Nena, “10,000 Hours” by Dan + Shay and Justin Bieber, “99 Problems” by JAY-Z, “2 Become 1” by the Spice Girls, “Whalien 52” by BTS, “7/11” by Beyoncé, “Five Years” by David Bowie, “Three Times a Lady” by the Commodores and “7” by Prince.

Avant-garde techno artist Aphex Twin, aka Richard David James, went a mathematical step further and named one of his songs after an equation.

Besides using numbers in their titles, some recording artists also completed advanced degrees in mathematics. There is Dan Snaith of the Polaris-winning band Caribou, whose doctoral dissertation at Imperial College London was entitled Overconvergent Siegel Modular Symbols, and Art Garfunkel, who holds a master’s in mathematics education from Columbia University.

No one, not even possibly Adele, knows her next album title. Her love of literature, ignited early in school by an English teacher, may also point to an appreciation of math (or maths as she might say).

For whatever reasons, musical artists like Adele, Taylor Swift and the Beatles drew on inspiration from numbers for their song and album titles. Adele herself may be doodling with numbers and mathematical sequences as you read this, plotting her next sonic masterpiece.