Socratic math is a branch of mathematics from ancient Greece. It is uncertain if it was actually invented by Socrates or if it was invented by Plato and attributed to Socrates to give it more credibility.
Another theory is that it was actually invented by Epicurus to defame the Socrates/Plato/Aristotle school. Another theory is that it is a modern forgery by someone who only understood Classical Greek mathematical terms. Another theory is that it evolved after millions of years of random base pair changes.
The basis of Socratic math is the axiom that for any two types of leaders, the ratio of the pleasurableness of their lives can be calculated by squaring the distance between them and then doing some handwaving. That's pretty much all it is. There's not much else to say.
Reception in the mathematical community
When this mathematics was first published, Socrates (or Plato, assuming the second theory) was met with derision from some of his contemporaries, including all of his students. (Analysis of the extant criticisms cannot solve the authorship problem because documents weren't dated back then. We also know that Plato made up his students.) Over time, however, the ideas began to gain more acceptance. Today, everyone recognizes the 100% correctness of Socratic math.