American Mathematical Society

Tom Lehrer (1928–2025): A (Mostly) Mathematical Appreciation

Ted Courant

Amanda Palmer

Joseph Silverman

1. Introduction

The recent passing of Tom Lehrer (1928–2025), mathematician and songwriter extraordinaire, has prompted a plethora of remembrances and appreciations. The NY Times obituary 13 praises Lehrer’s “wickedly iconoclastic songs” with “lyrics [that] were nimble, sometimes salacious and almost always sardonic,” representing a marked improvement over an earlier 1958 Times review 14 which opined that “Mr. Lehrer’s muse [is] not fettered by such inhibiting factors as taste,” an observation that Lehrer was fond of quoting. The interested reader may read about Lehrer’s life and career from many sources, so in this short note we aim to celebrate Lehrer from a (mostly) mathematical perspective.

However, we would be remiss not to highlight Lehrer’s extraordinary act of generosity in releasing his entire oeuvre to the public. “All copyrights to lyrics or music written or composed by me [Lehrer] have been permanently and irrevocably relinquished, and therefore such songs are now in the public domain.” He further provided links to lyrics, sheet music, and recordings of his work 6, although his website warns that “it will be shut down at some date in the not-too-distant future, so if you want to download anything, don’t wait too long.”

2. A Brief Stroll Through Lehrer’s Mathematically Inspired Songbook

Tom Lehrer’s songbook is voluminous, with many mathematically themed songs. Rather than attempting a comprehensive review, we provide commentary on two Lehrer math songs, one quite famous, one less well-known. We hope that this small sample will lead the previously uninitiated to experience the joys of Lehrer’s complete works, while reminding Lehrer aficionados of the genius of his lyrics.

3. Lehrer as Singer/Songwriter

Pigeons the world over are celebrating the passing of mathematician, teacher and songwriting legend Tom Lehrer.⁠Footnote¹

As a 50-year-old veteran touring satirical pianist myself, I would like to share how deeply influenced I was by this inimitable master of silly song and stage; I listened to Tom’s handful of live recordings from the 1960s over and over (and over) again on my little yellow Sony Walkman, taking songwriting seminars through time and space, via dubbed cassette tape.

Tom Lehrer taught me masterclass perspectives on song structure, war, New Math, censorship, racism and hypocrisy in America, global figures in history, and so much more. Throughout his active stage and recording years, he entertained people by the boatload, but above all (as we survey the impact of this work), he taught.

I write from the perspective of a musician, not a mathematician, and I find myself often thinking about Tom—who enjoyed his brief era as a satirical piano-playing rock star and then hung it up to take a “real” job in academia—as I navigate the choppy waters of show business myself. At some point in his young career, this highly celebrated performer decided to run away from the (amplified) piano, the road, the dressing rooms, the applause, the recording contracts. I wonder how often he played at home, for friends.

Legend has it in the music business—among my many cabaret-compatriots who also grew up influenced by his songs—that he just decided to up and quit one day in order to…teach math. We speak his name in a hallowed and reverent tone: he left the music industry to teach math. The mark of a true citizen artist.

There’s an equation to cobble together here, I think, about teaching, scale, time, and impact.

They quip that “those who can’t do, teach,” but my guess is that Tom probably had the last laugh. The long-lasting impact of his songwriting is going to speak through me and through this whole next generation of songwriters; and perhaps he anticipated—in the 1960s, when he “quit”—that his work in the song department was simply finished (finished like a mural, finished like a building), and it was time to move on to loftier and more impactful pursuits in Math-World.

Who is to say where one human being can have the most profound impact? Making soup for the poor? Building bombs? Designing bridges? Dancing wildly? Exploring theorems? Playing piano for money? Teaching math creatively? Crooning about poisoning pigeons in a park, just for funsies?

There’s no clear formula, but perhaps the equation to deduce the measurable impact of a creative career lies somewhere in calculating the degree of happiness and contentment in the heart of the creator and the audience, whether it be an audience of 20,000 in Madison Square Garden or an audience of twenty at a seminar.

So, anyway, if you’re out there in the field of mathematics wondering if there are musicians fretting about whether we should have followed Tom’s lead and quit show business while we were ahead, I can report from the field that a fair number of us are looking at you academics with considerable envy as we assess our life choices.

Long live Tom Lehrer and the wisdom, music, humor, and general inspiration he left in his wide wake. To honor his memory (and not just because the funding has all dried up and the venues are shuttering, I swear!) I’m quitting show business and I’m off to apply for a job as a math teacher.

Maybe Harvard will take me; they seem to be defending the weirdos this year.

Who’s hiring?

4. Lehrer as Professor

By Ted Courant

In the spring of 1990, while serving as a visiting assistant professor at the University of California, Santa Cruz, I had the privilege of auditing Tom Lehrer’s ten-week liberal arts mathematics course, The Nature of Mathematics.

Tom’s lectures combined clarity, precision, and his own brand of wit. I especially enjoyed his treatment of logic. He liked having students use truth tables and Venn diagrams to parse convoluted headlines or confusing court decisions, and even Fats Waller’s lyric, “Everybody Loves My Baby, But My Baby Don’t Love Nobody But Me.”

Each day revealed his genius as a communicator and mathematical evangelist. The course was a wide-ranging survey, blending rigorous treatments of familiar topics with excursions into areas I had not encountered as an undergraduate or graduate student.

The syllabus moved from number systems, proofs, and binary numbers to logic and hands-on explorations of error-correcting codes. The interplay of logic, algebra, geometry, and computation created a rich and varied collection of ideas that kept everyone fully engaged. Tom’s course was intellectually demanding and thoroughly entertaining. He was a master teacher, as his name, Lehrer (“teacher” in German), suggests.

And in the spirit of Tom Lehrer’s wit, I propose that Fats Waller’s song could, with perfect logical precision, be titled “I Am My Baby.”

5. Lehrer at the NSA: A Prank That Went Undiscovered for 60 Years

Lehrer wrote two research papers 1012 on random samples and random walks that appear in the MathSciNet database. But his most famous paper, despite being “co-authored,” uncredited, and entirely fictitious, is surely “Analytic and Algebraic Topology of Locally Euclidean Metrizations of Infinitely Differentiable Riemannian Manifolds,” which first appears in the lyrics of “Lobachevsky” 6(a), Lehrer’s ode to the joys of plagiarism. In 1957, Lehrer snuck Lobachevsky’s tongue-twistingly titled paper into the bibliography of an internally circulated article “The Gambler’s Ruin with Soft Hearted Adversary” that he wrote for the NSA 11 (declassified 2018). The NSA manuscript was published in somewhat modified form in 1958 10, but without the fake reference.

Here is a first-person account of how Lehrer’s prank was discovered, posted on BlueSky in August 2025:⁠Footnote²

With Tom Lehrer’s passing, I suppose this is a moment to share the story of the prank he played on the National Security Agency, and how it went undiscovered for nearly 60 years. …So I sent an email to the NSA historians. And I asked them: “Hey, when was this first noticed, and how much of a gas did people think it was? Did he get in trouble for it?” …The answer came back: “We’ve never heard of this before. It’s news to us.” …[Thus] in November of 2016, nearly 60 years after the paper was published internally, I had discovered the joke. A few years later, I filed to have the paper declassified, and the NSA eventually agreed, and even put it up on their webpage: 11. Once that had happened, I wrote to Mr. Lehrer with a copy of the paper and a letter asking if he had ever gotten in trouble for it. He kindly wrote back, including a copy of the paper that had been published in Journal of SIAM in 1958, under a slightly different title. Nobody, he said, caught him.

6. Lehrer’s Performances

Lehrer recorded many of his songs, originally on vinyl and now available from many sources in a variety of formats. In addition, a handful of Lehrer’s public and private performances were video recorded, including one-man shows in Norway 2 and Denmark 1 in 1967. After retiring from the stage, Lehrer continued to make an occasional appearance at select gatherings to celebrate special occasions, such as his advisor Irving Kaplansky’s 80th birthday celebration 4 and a new recording of “That’s Mathematics” that closed a public symposium celebrating Andrew Wiles’ proof of Fermat’s Last Theorem 5.

References

[1]

Tom Lehrer: Live In Oslo, September 1967, with a selection of Lehrer’s darkest and most twisted songs, including “National Brotherhood Week,” “When You Are Old and Gray,” “Poisoning Pigeons in the Park,” “So Long Mom I’m Off to Drop the Bomb,” “Pollution,” “Masochism Tango,” “Send the Marines,” “Who’s Next,” “Wernher von Braun,” “The Vatican Rag,” and “We All Go Together,” youtube.com/watch?v=a1IiVF6Ehw8.

[2]

Tom Lehrer Full Copenhagen Performance, September 1967, another live performance, including “The Irish Ballad,” “Smut,” “Deer Hunting,” “The Elements,” and more, youtube.com/watch?v=QHPmRJIoc2k.

[3]

[4]

Irving “Kaps” Kaplansky’s 80th Birthday Celebration (with Tom Lehrer, T. Y. Lam, and Saunders MacLane), with Lehrer performance of “The Derivative Song,” “There’s a Delta for Every Epsilon,” “The Professor’s Song,” “Sociology,” and “That’s Mathematics,” youtube.com/watch?v=T2Pdxoyt5yU, starting at 1:24:51.

[5]

“That’s Mathematics” (with additional lyrics) at FermatFest 1993, vimeo.com/251379987 starting at 1:34:46.

Lehrer’s Songs and Lyrics

[6]

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[8]

[9]

Additional References

[10]

T. Austin, R. Fagen, T. Lehrer, and W. Penney, The distribution of the number of locally maximal elements in a random sample, Ann. Math. Statist. 28 (1957), 786–790, DOI 10.1214/aoms/1177706893. MR91251,

AMSref

\bib{MR0091251}{article}{ author={Austin, T.}, author={Fagen, R.}, author={Lehrer, T.}, author={Penney, W.}, title={The distribution of the number of locally maximal elements in a random sample}, journal={Ann. Math. Statist.}, volume={28}, date={1957}, pages={786--790}, issn={0003-4851}, review={\MR {91251}}, doi={10.1214/aoms/1177706893}, }

[11]

[12]

R. E. Fagen and T. A. Lehrer, Random walks with restraining barrier as applied to the biased binary counter, J. Soc. Indust. Appl. Math. 6 (1958), 1–14. MR94856,

AMSref

\bib{MR0094856}{article}{ author={Fagen, R. E.}, author={Lehrer, T. A.}, title={Random walks with restraining barrier as applied to the biased binary counter}, journal={J. Soc. Indust. Appl. Math.}, volume={6}, date={1958}, pages={1--14}, issn={0368-4245}, review={\MR {94856}}, }

[13]

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