Wayne MI United States
There are two must read books for anyone with an interest in Buddhist thought and/or Greek Philosophy: "The Shape of Ancient Thought, Comparative Studies in Greek and Indian Philosophies" by Thomas McEvilley and "Greek Buddha, Pyrrho's Encounter With Early Buddhism in Central Asia" by Christopher Beckwith. The former book forever changed my understanding of how interconnected the ancient world was and also about the level of mutual philosophical influence between Greek/ Hellenic and Indian thought both through direct contact and via the medium of Iranian (Mede and Persian) civilization.
This contact was well established as early as the time of the Presocratic philosphers of Greece. Given this fact it's no wonder why the philosophy of the Presocratics had so many parallels with Upanishadic teachings. The later book focuses specifically on the Indian Buddhist influence on the founder of the Greek Pyrronhian school of Skepticism. It also includes a controversial chapter claiming that Lao Tzu and his teachings were an early Chinese adaptation of Buddhism and that Lao Tzu/ Lao Dan, who was also called Kao Dan/ Gao Dan, was in fact Gaotam[a] or Gautama Buddha himself.
This is an interesting theory because the Taoists had a Scripture (Scripture of the Conversion of the Barbarians or Huahujing) that posited that Lao Tzu left China to become the Gautama Buddha of the Indians! Now, according to Beckwith, the theory of the Huahujing may be backwards, he claims instead that the Chinese adopted the Indian teachings, but it does at least imply that the Chinese recognized a strong parallel between said traditions even to the point of recognizing (or claiming) a common origin. Livia Kohns book "Daoist Mystical Philosophy: The Scripture of Western Ascension", besides being an excellent introduction to Taoist mystical thought in general (and the only translation of an important Taoist Scripture as well), also has a chapter that looks at the Huahujing for those who might want some further information on that.
The above picture shows early Greco-Buddhist sculptures of Buddha in a Greek style reminiscent of Apollo Belvedere