What shows that Greeks strongly influenced the English language?
The English language is full of Greek prefixes and suffixes, even in words that are not completely of Greek etymology (itself Greek in origin.) Just to name a very few, "anti," "eu," "poly," and "hyper" are all prefixes of Greek origin. Suffixes include "-ism" and "-ist" as well as other obvious examples like "phobia."
The list of words that have been derived from Greek would encompass thousands of words and word combinations, but suffice it to say that Greek, by way of Latin and the interest of Western scholars in classical studies, has permeated English and other western languages. It is particularly pervasive in the sciences. Interestingly, many Greek words have made their way into English through other languages, like Latin, as mentioned above, and French. These words include such words as "atheism," atmosphere," "ecstasy," "scheme," and "syllable." Some words have their origins traced directly from Greek to English, including "catastrophe," "crypt," and rhythm." Whatever the etymology of particular words, the influence of Greek on English, as well as other languages, has been profound.