**For Mathematicians: The Main Idea**

In the history of set theory, it became apparent to many researchers in the late
1960s that, a characteristic feature of bigger large cardinals is that they
arise as critical points of elementary embeddings of the universe. These
are typically of the form

*j : V -> M*, where *M* is a transitive
model of ZFC that is a proper subclass of *V*. Moreover, the stronger the
large cardinal notion, the more closely *M* is seen to resemble *V* itself.
The natural question in those early days was: Could *M = V*?

Soon after such questions arose, Kunen showed that there could be no
elementary embedding from *V* to itself other than the identity. Since
the statement could not be formulated in the language of ZFC, Kunen pointed out that
his proof must be formalized in an appropriate class theory, such as Kelley-Morse
or Godel-Bernays class theory.

The author of *The Infinite According to Master Wu*, as a young set theorist,
became convinced that there "ought" to be a nontrivial elementary embedding from *V*
to itself. His conviction arose from the natural parallels he found between the
structure of *V* and the structure of "wholeness" or "Absolute Infinte" according
to certain ancient visions of infinity. Looking more closely at Kunen's work, the author
noticed that Kunen's proof actually depends on the context in which it is formulated -- in
the standard class theories, any elementary embedding from *V* to itself
ends up being *(weakly) definable*, which forces it to have additional properties
beyond elementarity. Indeed, it is these additional properites in combination with
elementarity that lead to inconsistency, not the elementarity of the embedding on its own.

The author formulated a context for studying elementary embeddings from *V* to itself
in which one could axiomatically decide exactly which properties, in addition to elementarity,
an embedding from *V* to itself would have. In this context, the author showed that many different
large cardinal strengths arise when the axiomatic assumptions imposed on the embedding
vary, with inconsistency arising as an extreme special case. See a description of the
main research papers here.

The author proposed, in several articles, a new axiom schema, which he called the
*Wholeness Axiom*, intended to be added to the usual axioms of ZFC (in the expanded
language described above) as a way of providing an axiomatic account for virtually all
large cardinals. He found that inclusion of the Wholeness Axiom among the foundational
axioms revealed much deeper connections to the view of the Infinite in ancient texts.
The ancient texts suggested certain dynamics within the Infinite; natural analogues to
these dynamics became apparent once the Wholeness Axiom was assumed.

The author also found through experience that many of the ideas related to the Wholeness Axiom were accessible to non-mathematical audiences, especially when the analogies found in the ancient texts were included in the presentation of the subject. This observation inspired the author to provide an accessible treatment of these ideas, and some of their practical application, in the form of a book.