As a songwriter, Lehrer wrote satirical songs on many topics but, of course, some of his songs were on mathematics. Here are four of his Mathematical Songs.

**There's A Delta For Every Epsilon (Calypso).**The words and music are by Tom Lehrer. The song appears in the*American Mathematical Monthly***81**(1974), 612.There's a delta for every epsilon,

It's a fact that you can always count upon.

There's a delta for every epsilon

And now and again,

There's also an*N*.But one condition I must give:

The epsilon must be positive

A lonely life all the others live,

In no theorem (A delta for them.)How sad, how cruel, how tragic,

(How pitiful, and other adjec-

Tives that I might mention.)

The matter merits our attention.

If an epsilon is a hero,

Just because it is greater than zero,

It must be mighty discouragin'

To lie to the left of the origin.This rank discrimination is not for us,

We must fight for an enlightened calculus,

Where epsilons all, both minus and plus,

Have deltas

To call their own.**The Derivative Song.**Words by Tom Lehrer to the tune "There'll be Some Changes Made".The song appears in the*American Mathematical Monthly***81**(1974), 490.You take a function of

*x*and you call it*y*,

Take any*x*-nought that you care to try,

You make a little change and call it delta*x*,

The corresponding change in*y*is what you find nex',

And then you take the quotient and now carefully

Send delta*x*to zero, and I think you'll see

That what the limit gives us, if our work all checks,

Is what we call*dy*/*dx*,

It's just*dy*/*dx*.**The Professor's Song.**Words by Tom Lehrer to the tune "If You Give Me Your Attention" from Princess Ida by Gilbert and Sullivan. The song appears in the American Mathematical Monthly 81 (1974), 745.If you give me your attention, I will tell you what I am.

I'm a brilliant math'matician - also something of a ham.

I have tried for numerous degrees, in fact I've one of each;

Of course that makes me eminently qualified to teach.

I understand the subject matter thoroughly, it's true,

And I can't see why it isn't all as obvious to you.

Each lecture is a masterpiece, meticulously planned,

Yet everybody tells me that I'm hard to understand,

And I can't think why.My diagrams are models of true art, you must agree,

And my handwriting is famous for its legibility.

Take a word like "minimum" (to choose a random word),

For anyone to say he cannot read that, is absurd.

The anecdotes I tell get more amusing every year,

Though frankly, what they go to prove is sometimes less than clear,

And all my explanations are quite lucid, I am sure,

Yet everybody tells me that my lectures are obscure,

And I can't think why.Consider, for example, just the force of gravity:

It's inversely proportional to something - let me see -

It's*r*^{3}- no,*r*^{2}- no, it's just*r*, I'll bet -

The sign in front is plus - or is it minus, I forget -

Well, anyway, there is a force, of that there is no doubt.

All these formulas are trivial if you only think them out.

Yet students tell me, "I have memorised the whole year through

(Ev'rything you've told us, but the problems I can't do."

And I can't think why![Note. When Tom Lehrer performs this song he writes on the blackboard

for the word "minimum".]

**Lobachevsky**For many years now, Mr Danny Kaye, who has been my particular idol since childbirth, has been doing a routine about the great Russian director Stanislavsky and the secret of success in the acting profession. And I thought it would be interesting to stea... to adapt this idea to the field of mathematics. I always like to make explicit the fact that before I went off not too long ago to fight in the trenches, I was a mathematician by profession. I don't like people to get the idea that I have to do this for a living. I mean, it isn't as though I had to do this, you know, I could be making, oh, 3000 dollars a year just teaching.Be that as it may, some of you may have had occasion to run into mathematicians and to wonder therefore how they got that way, and here, in partial explanation perhaps, is the story of the great Russian mathematician Nicolai Ivanovich Lobachevsky.

Who made me the genius I am today,

The mathematician that others all quote,

Who's the professor that made me that way?

The greatest that ever got chalk on his coat.One man deserves the credit,

One man deserves the blame,

And Nicolai Ivanovich Lobachevsky is his name.

Hi!

Nicolai Ivanovich Lobach-I am never forget the day I first meet the great Lobachevsky.

In one word he told me secret of success in mathematics:

Plagiarize!Plagiarize,

Let no one else's work evade your eyes,

Remember why the good Lord made your eyes,

So don't shade your eyes,

But plagiarize, plagiarize, plagiarize -

Only be sure always to call it please 'research'.And ever since I meet this man

My life is not the same,

And Nicolai Ivanovich Lobachevsky is his name.

Hi!

Nicolai Ivanovich Lobach-I am never forget the day I am given first original paper

to write. It was on analytic and algebraic topology of

locally Euclidean parameterization of infinitely differentiable

Riemannian manifold.

Bozhe moi!

This I know from nothing.

What-i'm going-to do.

But I think of great Lobachevsky and get idea - ahah!I have a friend in Minsk,

Who has a friend in Pinsk,

Whose friend in Omsk

Has friend in Tomsk

With friend in Akmolinsk.

His friend in Alexandrovsk

Has friend in Petropavlovsk,

Whose friend somehow

Is solving now

The problem in Dnepropetrovsk.And when his work is done -

Ha ha! - begins the fun.

From Dnepropetrovsk

To Petropavlovsk,

By way of Iliysk,

And Novorossiysk,

To Alexandrovsk to Akmolinsk

To Tomsk to Omsk

To Pinsk to Minsk

To me the news will run,

Yes, to me the news will run!And then I write

By morning, night,

And afternoon,

And pretty soon

My name in Dnepropetrovsk is cursed,

When he finds out I publish first!And who made me a big success

And brought me wealth and fame?

Nicolai Ivanovich Lobachevsky is his name.

Hi!

Nicolai Ivanovich Lobach -I am never forget the day my first book is published.

Every chapter I stole from somewhere else.

Index I copy from old Vladivostok telephone directory.

This book was sensational!

Pravda - well, Pravda - Pravda said: "Zhil-bil korol kogda-to, pree nyom blokha zhila"* It stinks.

But Izvestia! Izvestia said: "Ya idoo kuda sam czar idyot peshkom!"**

It stinks.

Metro-Goldwyn-Moskva buys movie rights for six million rubles,

Changing title to 'The Eternal Triangle',

With Ingrid Bergman playing part of hypotenuse.And who deserves the credit?

And who deserves the blame?

Nicolai Ivanovich Lobachevsky is his name.

Hi!* "a king lived once upon a time, a flea lived with him", a line from Goethe's "Faust" (as translated by A. Strugovschik)

** "I am going where even the king has to go on foot" (as opposed to riding, etc.), meaning "to the bathroom"