If the early philosophical links with the West were Greek, the first mathematical links were Italian. The development of the Concept of Zero, its Western intellectual foundations, begin with Guiseppe Peano [1858-1932] and Fibonacci [1170-1240; ‘The Greatest Western Mathematician of the Middle Period’; see: ‘Venice’].
The latest subscribed research into Number Theory goes back less than 150 years with the formal conceptualization of the Symbol ‘0’ by Guiseppe Peano in his five famous postulates. [The first postulate reads: ‘Zero is a natural number’].
The Mathematician’s notion of Unity or Wholeness is the idea of the Mathematical Set. [In the wonder-world of the Self-Loop, the word with the most number of posted definitions the last time I checked seems to be the word ‘Set’, as in Mathematical Set, which is another word for ‘Definition’. See the Post.]
The problem becomes intractable once the investigators take the notion of ‘Unity’ to its necessary limit. And that required immersion into Set Theory [again, Peano pioneered its early application]. And in Set Theory they hit head-on into the Self-Loop.
The Self-Eating Expression comes alive from the shadows anytime something is used on itself, anytime we are wading, knowingly or otherwise, into the swamp of the Self-Loop.
The single tripper-upper? The notion of Self-Reference [recursion, repetition, reflection and numerous variants].
Bertrand Russell and Alfred Whitehead wanted to produce a founding Bible that built up the rules of Mathematics from the ground-up. So they began with Peano’s work and titled their opus Principia Mathematica. [1910; Latin titles are always dangerous, vide Wittgenstein and his Tractatus Logico Philosophicus.]
The celebrated 3-volume opus was among other much grander ambitions, an attempt to resolve the conflicts between the observing Subject and his inclusion or exclusion in a Set.
The issue never found a resolution [Russell and Whitehead had to use a variety of sequenced exceptions to hold the logic together]. Until Kurt Godel came along.
[No point in repeating here what is well in the public domain. The story of the Godel iceberg is common knowledge among the mathematically-inclined and there is a large readable literature out there on Godel, Russell’s Paradox, Principia Mathematica and the rest. I’ll limit myself to the outlines.]