What is a synonym for "jack of all trades, master of none"?

A polymath is a person of encyclopedic learning.

A Renaissance Man is a person whose expertise spans a significant number of different subject areas.

A person who is a jack of all trades, but a master of none might be called a dabbler.

A dilettante is a person who dabbles in a variety of pursuits but is not dedicated to any particular one.

A sage, a savant, a genius, an expert, a diviner, an Olympian, a guru, a god (small G)--all describe a multi-talented person who is exceedingly capable in seemingly everything and is "master of all." A dilettante, on the other hand, is a "master of none."

The phrase you refer to, by the way, is a rhetorical figure called antithesis, an expression of contrasting elements. In "Jack of all trades, master of none," we have the following contrasts: Jack (a common name and common nickname for John) and master; all and none; trades (plural--many) and trade (implied singular--or one).

I have seen the use of "factotum" to replace "jack of all trades". I had to look it up the first time I read it.