According to Greek history, Diogenes of Sinope, was most notably known for searching for what?

Diogenes made a virtue of poverty. He begged for a living and often slept in a large ceramic jar, or pithos, in the marketplace. He became notorious for his philosophical stunts, such as carrying a lamp during the day, claiming to be looking for a man (often rendered in English as "looking for an honest man"). He criticized Plato, disputed his interpretation of Socrates, and sabotaged his lectures, sometimes distracting listeners by bringing food and eating during the discussions. Diogenes was also noted for having mocked Alexander the Great, both in public and to his face when he visited Corinth in 336 BC.

Diogenes was captured by pirates and sold into slavery, eventually settling in Corinth. There he passed his philosophy of Cynicism to Crates, who taught it to Zeno of Citium, who fashioned it into the school of Stoicism, one of the most enduring schools of Greek philosophy. No writings of Diogenes survive but there are some details of his life from anecdotes (chreia), especially from Diogenes Laërtius' book "Lives and Opinions of Eminent Philosophers" and some other sources.