### Valentine’s Day for Mathematicians

#### by hun

Nice music, and brilliant lyrics 🙂

“Finite Simple Group (of order 2)”

The path of love is never smooth

But mine’s continuous for you

You’re the upper bound in the chains of my heart

You’re my Axiom of Choice, you know it’s true

But lately our relation’s not so well-defined

And I just can’t function without you

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

We’re a finite simple group of order 2

I’m losing my identity

I’m getting tensor every day

And without loss of generality

I will assume that you feel the same way

Since every time I see you, you just quotient out

The faithful image that I map into

But when we’re one-to-one you’ll see what I’m about

‘Cause we’re a finite simple group of order 2

Our equivalence was stable,

A principal love bundle sitting deep inside

But then you drove a wedge between our two-forms

Now everything is so complexified

When we first met, we simply connected

My heart was open but too dense

Our system was already directed

To have a finite limit, in some sense

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

From my domain, its image looks so blue,

‘Cause all I see are 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,

But we’re a mirror pair, me and you,

So let’s apply forgetful functors to the past

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

Let’s be a finite simple group of order 2

(“Why not 3?”)

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

So let’s both be associative and free

And by corollary, this shows you and I to be

Purely inseparable. Q. E. D.