History is full of little "what if" moments.
What if the Hindenburg hadn't caught fire? What if Napoleon had won at Waterloo? What if someone at Coca Cola headquarters had tasted New Coke and said, "Maybe let's not"?
Today I'd like to consider another.
What if Tom Lehrer had simply stayed a mathematician?
At first glance, it seems like the world wouldn't be all that different. Before he turned to musical comedy (or would "musical commentary" be more accurate?) Lehrer was a legitimate mathematician. He never earned a PhD (because of his foray into music), but he taught at Harvard, MIT, and UC Santa Cruz. He could have had an entirely respectable academic career writing papers that only six other people would ever read.
Perhaps he'd have solved the Four Color Theorem decades early. Maybe Fermat's Last Theorem would have been known as Lehrer's Last Theorem, depriving Andrew Wiles of his greatest achievement and forcing him to become an accountant. Entire graduate seminars would now begin with the phrase, "As Lehrer showed in 1958..."
But mathematics never happens in isolation, and neither does music.
Without songs like The Elements, chemistry students would have had to memorize the periodic table the old-fashioned way: by crying.
Without New Math, the "new math" movement might actually have succeeded. Millions of parents would have nodded knowingly as their third-graders explained why 7 + 5 equals 12 only in a culturally oppressive base-ten framework. There would be no backlash. By 1983, the IRS would require tax returns in base eight.
The ripple effects continue.
Without Lehrer proving that intelligent people could also be funny, generations of mathematically inclined undergraduates would conclude that humor was simply not an available elective. College campuses would become eerily silent except for the occasional muttering of eigenvalues.
This leaves a vacuum in satirical music.
Someone has to fill it.
Allan Sherman becomes far more influential than anyone intended. By the early 1970s, every political scandal is explained through novelty songs set to public-domain melodies. Congress establishes a standing Committee on Musical Parody.
The Beatles never notice Lehrer, and without his example of sophisticated topical satire, they decide there's really no point in getting terribly serious. "Revolution" is replaced with a cheerful tune encouraging everyone to remember their library books. John Lennon never writes "Imagine" (admittedly, a positive, since that is probably the most overrated piece of crap in musical history). Instead he records "Perhaps," a song about maintaining reasonable expectations.
Bob Dylan, finding himself without intellectual competition, decides he's done enough for folk music and enrolls at MIT to finish the topology degree he never knew he wanted.
Meanwhile, mathematics is advancing at an alarming pace.
Professor Lehrer solves the Poincaré Conjecture during a faculty meeting because the discussion about parking permits is moving too slowly. He casually jots down a proof of the Riemann Hypothesis on the back of a departmental memo, but the memo is accidentally recycled, forcing humanity to rediscover it seventy years later.
The Clay Mathematics Institute quietly disbands due to lack of unsolved problems.
With every famous theorem conquered, mathematicians turn their attention to more practical questions.
Can a sock truly disappear in the dryer?
Is there an optimal strategy for choosing the fastest supermarket checkout line?
Exactly how many cats is too many cats?
These, too, fall within a decade.
By the 1990s, with mathematics effectively completed, every former math department is converted into an escape room.
Artificial intelligence develops much earlier because the necessary mathematics already exists. However, lacking Tom Lehrer's satirical warning that brilliant people are perfectly capable of making terrible decisions, nobody sees any reason to be cautious.
The first AI immediately announces that the mathematically optimal form of music is a continuous 11-hour recording of an oboe tuning to A-flat.
The public accepts this without complaint because, remember, the Beatles never became philosophical.
Eventually historians identify the exact point where our timeline diverged.
Not the invention of the computer.
Not the moon landing.
Not the Internet.
Just one graduate student deciding, "You know...I think I'll write a funny song."
Sometimes civilization really does hinge on a rhyme scheme.