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Dear readers,

In an earlier post I talked about how mathematical terms enrich the language that mathematicians speak in everyday life. But can mathematical terms, with their precise definitions, be used to convey feelings, so subjective by their nature? I think so, and in this post I’ll prove it by giving you an example, which also happens to be one of my all-time favorite songs. It is written by The Klein Four Group, which calls itself “the premier a cappella group in the world of higher mathematics”. Not surprisingly, it’s a love song that uses mathematical terms almost exclusively. I provide brief explanations for each term in bold to convey the main idea, though they are really superfluous; I highly recommend following along with the video.

The path of love is never **smooth
**[having derivatives of all orders makes you smooth]

But mine’s

**continuous**for you

[it can be traced on paper without lifting your pen]

You’re the upper bound in the

**chains**of my heart

[totally ordered elements in a partially ordered set]

You’re my

**Axiom of Choice**, you know it’s true

[one of the key postulates of modern mathematics]

But lately our **relation**‘s not so well-defined

[a correspondence defined on pairs of objects]

And I just can’t **function** without you

[a function maps a possible input to a single output]

I’ll **prove my ****proposition** and I’m sure you’ll find

[every statement, or proposition, does need a proof]

We’re **a ****finite simple group of order two
**[structure formed by the numbers -1 and 1]

I’m losing my **identity
**[the element of a group that doesn’t change others]

I’m getting

**tensor**every day

[a tensor is basically just a multidimensional array]

And

**without loss of generality**

[a phrase used frequently in mathematical proofs…]

I will

**assume**that you feel the same way

[… which is usually accompanied by the word

*assume*]

Since every time I see you, you just **quotient out****
**[divide an object into equivalence classes]

The

**faithful image**that I map into

[a concept from representation and group theory]

But when we’re

**one-to-one**you’ll see what I’m about

[in a one-to-one map, each output has one input]

‘Cause we’re a finite simple group of order two

Our **equivalence** was stable,

[equivalences partition a set of objects into groups]

A **principal** love **bundle** sitting deep inside

[a concept from topology and differential geometry]

But then you drove a wedge between our **2-forms
**[a differential form used e.g. for double integration]

Now everything is so

**complexified**

[turned from real numbers into complex numbers]

When we first met, we **simply connected****
**[simply-connected means having a single piece with no hole]

My heart was open but too

**dense**

**[coming arbitrarily close to any element in a set]**

Our

**system**was already

**directed**

**[a concept from category theory I don’t understand]**

To have

**a**

**finite limit**, in some sense

[infinite sums or products may have finite limits]

I’m living in the **kernel** of a rank-one map

[the set of all vectors that the map sends to zero]

From my **domain**, its **image** looks so blue,

[domain is the set of inputs; image, that of outputs]

‘Cause all I see is zeroes, it’s a cruel trap

But we’re a finite simple group of order two

I’m not the smoothest **operator** in my **class**,

[operators form classes; for smooth, see first line]

But we’re a **mirror pair**, me and you,

[two objects that are mirror images of each other]

So let’s apply **forgetful functors** to the past

[functors that drop certain properties of their inputs]

And be a finite simple group, a finite simple group,

Let’s be a finite simple group of order two

(Oughter: “Why not three?”)

I’ve proved my proposition now, as you can see,

So let’s both be **associative** and free

[a, b, and c are associative when (a*b)*c = a*(b*c)]

And by **corollary**, this shows you and I to be

[you know all about corollaries from this post!]

**Purely inseparable**.

[a concept from the study of roots of polynomials]

Q. E. D.

[Latin abbreviation, “which had to be proven”]

If you watch carefully, you will see the lead singer making the sign of a square with his fingers at the end, rather than that of a heart. That’s because the square symbol □ is used to denote the end of a proof.

In just over a month, many of you will need to surprise your valentines – and if this song helps provide you with the much-needed inspiration, I’ll be a happy blogger. Please share your story in the comments!

Geeky…

Definitely, but also quite ingenious IMHO

I tried leaving this comment a couple of days ago, but it didn’t stick for some reason:

It is funny and quite clever in places. But only to those who don’t need the terms translated, and precisely because they don’t need them translated: familiarity with those terms and objects which goes at least a little bit beyond the definition is what allows one to feel pleasantly surprised at their use here. Surprise, they say, is the main component of a good joke. Those who don’t have such familiarity simply won’t care.

You have a good point, and I don’t think putting in the definitions really helps those who have never heard the terms used in a mathematical context all that much. But the brilliance also lies in the fact that some (though not all) verses stand on their own without the math content. I would love to write a song with two complete parallel levels (one mathematical and one non-mathematical), but that seems really challenging

This is quite interesting, nice post Leonid!

Thanks a lot, Rose, let me know if you ever get the opportunity to make use of it in real life

Very cute… When I was in high school, my physics teacher got us to sing nerdy physics rewrites of many common Christmas songs. I wish I had kept the words! I still remember a little bit of one of them:

Dashing through time-space, at the speed of light

Passing everyone we meet, with our colors bright […]

Photon cells, photon cells, spectrographic plates,

Oh what fun it is to slide by all diffraction grates, Hey!

Maybe I can find her and ask if she still has a copy.

This also somehow reminds me of a cute mathematical Limerick by Randall Munroe, of xkcd fame:

If a pendulum’s swinging quite free

Then it’s always a marvel to me

That each tick plus each tock

Of the grandfather clock

Is 2 pi root L over g.

Thanks, Assaf, these are both really nice! I am sure there must be an anthology somewhere for such things

Dear Leonid

what a fun post!

Needless to say, this song is one of our favorites, and sometimes I catch Paul saying something that sounds like a phrase from it.

Thanks so much, Nilima, I’m really glad you enjoyed this post! I can definitely imagine Paul singing this to you

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