Introduction

Some of you who have small children may have perhaps been put in the embarrassing position of being unable to do your child's arithmetic homework because of the current revolution in mathematics
teaching known as the New Math. So as a public service here tonight, I thought I would offer a brief lesson in the New Math. Tonight, we're gonna cover subtraction. This is the first room I've worked
for a while that didn't have a blackboard, so we will have to make do with more primitive visual aids, as they say in the ed biz. Consider the following subtraction problem, which I will put up here: 342
minus 173. Now, remember how we used to do that: But in the new approach, as you know, the important thing is to understand what you're doing, rather than to get the right answer. Here's how they
do it now:

You can't take three from two,
Two is less than three,
So you look at the four in the tens place.
Now that's really four tens
So you make it three tens,
Regroup, and you change a ten to ten ones,
And you add 'em to the two and get twelve,
And you take away three, that's nine.
Is that clear?

Now instead of four in the tens place
You've got three,
'Cause you added one,
That is to say, ten, to the two,
But you can't take seven from three,
So you look in the hundreds place.

From the three you then use one
To make ten ones...
(And you know why four plus minus one
Plus ten is fourteen minus one?
'Cause addition is commutative, right!)...
And so you've got thirteen tens
And you take away seven,
And that leaves five...

Well, six actually...
But the idea is the important thing!

Now go back to the hundreds place,
You're left with two,
And you take away one from two,
And that leaves...?

Everybody get one?
Not bad for the first day!

Hooray for New Math,
New-hoo-hoo Math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!

Now, that actually is not the answer that I had in mind, because the
book that I got this problem out of wants you to do it in base
eight.  But don't panic!  Base eight is just like base ten really -
if you're missing two fingers!  Shall we have a go at it?
Hang on...

You can't take three from two,
Two is less than three,
So you look at the four in the eights place.
Now that's really four eights,
So you make it three eights,
Regroup, and you change an eight to eight ones
And you add 'em to the two,
And you get one-two base eight,
Which is ten base ten,
And you take away three, that's seven.
Ok?

Now instead of four in the eights place
You've got three,
'Cause you added one,
That is to say, eight, to the two,
But you can't take seven from three,
So you look at the sixty-fours...

Sixty-four?  "How did sixty-four get into it?"  I hear you cry!
Well, sixty-four is eight squared, don't you see?  (Well, ya ask a
silly question, ya get a silly answer!)

From the three, you then use one
To make eight ones,
You add those ones to the three,
And you get one-three base eight,
Or, in other words,
In base ten you have eleven,
And you take away seven,
And seven from eleven is four!
Now go back to the sixty-fours,
You're left with two,
And you take away one from two,
And that leaves...?

Now, let's not always see the same hands!
One, that's right.
Whoever got one can stay after the show and clean the erasers.

Hooray for New Math,
New-hoo-hoo Math!
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!

Come back tomorrow night...we're gonna do fractions! 

Y'know, I've often thought I'd like to write a mathematics textbook someday because I have a title that I know will sell a million copies; I'm gonna call it Tropic of Calculus
 

Introduction

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 st... 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.  Oy!
Nicolai Ivanovich Lobache...

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.  Oy!
Nicolai Ivanovich Lobache...

I am never forget the day I am given first original paper to write.  It
was on analytic and algebraic topology of locally Euclidean metrization
of infinitely differentiable Riemannian manifold.
Bozhe moi!
This I know from nothing.
But I think of great Lobachevsky and I get idea - haha!

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 -
Haha! - 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 published first!

And who made me a big success
And brought me wealth and fame?
Nicolai Ivanovich Lobachevsky is his name.  Oy!
Nicolai Ivanovich Lobache...

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, this book was sensational!
Pravda - ah, Pravda - Pravda said: (Russian double-talk)
It stinks.
But Izvestia!  Izvestia said: (Russian double-talk)
It stinks.
Metro-Goldwyn-Moskva bought the movie rights for six million rubles,
Changing title to 'The Eternal Triangle',
With Brigitte Bardot playing part of hypotenuse.

And who deserves the credit?
And who deserves the blame?
Nicolai Ivanovich Lobachevsky is his name.
Oy!