Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I was reading a note from called What lurks beneath a scientist's lab coat?, a little gallery of geeky-tattoos.

However, number 11 in the series has the following image and caption text:

Nine axioms?

'From these nine axioms,' writes Turing Eret, a software designer in Colarado, 'one can derive all of mathematics – a field you can likely tell that I love dearly'

Is that really so? Are those the nine axioms? (I guess it means the ZF axioms) If so, how are they expressed like that? (Last question meaning: how does that expression imply the nine axioms?)

I tried to search it around but searching formulas is really hard. Also, Google and TinEye image search wouldn't produce anything relevant.

I really suck at math but I love it, so forgive me if I'm asking something stupid.

share|cite|improve this question
No. Those are not the axioms ZF set theory. (To be precise there are infinitely many ZF set theory "axioms". The "nine" axioms actually include a few axiom schema). The picture is that of some statement of lambda-calculus. – Bill Cook Jan 11 '12 at 1:02
@BillCook Thanks! Took me a while to understand the statement about ZF schematic but re-reading some references, it made sense to me. – Alpha Jan 11 '12 at 1:12
those were some interesting tatoos. I wonder if any of the other tatoos are as inaccurately labeled as the one you posted above. If so, I'd skip buying the book. :) – Bill Cook Jan 11 '12 at 1:15
It looks like they just misplaced the caption. Here is an arm (same person?) with ZF (or is it ZFC?) written on it: Google for "carl zimmer" "nine axioms", it is the first link. – Dan Brumleve Jan 11 '12 at 5:54
Main page of the other gallery of the same work: Unfortunately it doesn't feature the Y combinator image so who knows what he has to say about it (buy the book?). – Dan Brumleve Jan 11 '12 at 6:01
up vote 6 down vote accepted

It is called a Y combinator. This particular one was invented by Haskell Curry according to the Wikipedia page. It has little to do with set theory and I am not sure what are the "nine axioms" referred to. I know it as being a useful tool in constructing a LISP-like language from combinator calculus. It has the effect of applying its argument to itself, i.e. Yx -> x(Yx) -> x(x(Yx)), which can be used to implement recursion. This is not the only expression with such an effect; scroll down the Wikipedia page to see some other examples of Y combinators.

share|cite|improve this answer

That's my arm! Yeah, it was incorrectly labelled in the Guardian article. That is the Y Combinator as others have mentioned. My OTHER tattoo are the ZFC axioms. In the book, both tattoos are pictured but only the ZFC one is described. A bit unfortunate, but oh well. What can you do?

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.