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"I know one thing, that I know nothing" (Ancient Greek: ἓν οἶδα ὅτι οὐδὲν οἶδα hèn oîda hóti oudèn oîda; Latin: scio me nihil scire or scio me nescire) is a well-known saying that is derived from Plato's account of the Greek philosopher Socrates. This saying is also connected and/or conflated with a contemporary Pythian oracular answer "Socrates" to the question "who is the wisest man in Greece?".
The saying, though widely attributed to Plato's Socrates in both ancient and modern times, actually occurs nowhere in Plato's works as is. Two prominent Plato scholars have recently argued that the claim should not be attributed to Plato's Socrates.
[…] οὖτος μὲν οἴεταί τι εἰδέναι οὐκ εἰδώς, ἐγὼ δέ, ὥσπερ οὖν οὐκ οἶδα, οὐδὲ οἴμαι
– This man, on one hand, believes that he knows something, while not knowing [anything]. On the other hand, I – equally ignorant – do not believe [that I know anything].
The impreciseness of the paraphrase of this as I know that I know nothing stems from the fact that the author is not saying that he does not know anything but means instead that one cannot know anything with absolute certainty but can feel confident about certain things.
Chaerephon, a friend of Socrates asked Pythia, The Oracle of Delphi : "Is anyone wiser than Socrates?". The answer was: "No human is wiser". Socrates tried to find someone who is wiser than himself, since he denied any knowledge, among politicians, poets, and craftsmen. It appeared that politicians claimed wisdom without knowledge; poets could touch people with their words, but did not know their meaning; and craftsmen could claim knowledge only in specific and narrow fields. The interpretation of Oracle's answer might be Socrates' awareness of his own ignorance.
καὶ νῦν περὶ ἀρετῆς ὃ ἔστιν ἐγὼ μὲν οὐκ οἶδα, σὺ μέντοι ἴσως πρότερον μὲν ᾔδησθα πρὶν ἐμοῦ ἅψασθαι, νῦν μέντοι ὅμοιος εἶ οὐκ εἰδότι.
– So now I do not know what virtue is; perhaps you knew before you contacted me, but now you are certainly like one who does not know. (trans. G.M.A. Grube)
Here, Socrates aims at the change of Meno's opinion, who was a firm believer in his own opinion and whose claim to knowledge Socrates had disproved.
It is essentially the question that begins "post-socratic" Western philosophy. Socrates begins all wisdom with wondering, thus one must begin with admitting one's ignorance. After all Socrates dialectic method of teaching was based on that he as a teacher knew nothing, so he would derive knowledge from his students by dialogue.
There's also a passage by Diogenes Laertius in his work Lives and Opinions of Eminent Philosophers where he lists, among the things that Socrates used to say: "εἰδέναι μὲν μηδὲν πλὴν αὐτὸ τοῦτο εἰδέναι", or that he knew nothing except that he knew that very fact [i.e. that he knew nothing]
Again, closer to the quote, there's a passage in Plato's Apology, where Socrates says that after discussing with someone he started thinking that
τούτου μὲν τοῦ ἀνθρώπου ἐγὼ σοφώτερός εἰμι· κινδυνεύει μὲν γὰρ ἡμῶν οὐδέτερος οὐδὲν καλὸν κἀγαθὸν εἰδέναι, ἀλλ' οὗτος μὲν οἴεται τι εἰδέναι οὐκ εἰδώς, ἐγὼ δέ, ὥσπερ οὖν οὐκ οἶδα, οὐδὲ οὄιμαι· ἔοικα γοῦν τούτου γε σμικρῷ τινι αὐτῷ τούτῳ σοφώτερος εἶναι, ὅτι ἃ μή οἶδα οὐδὲ οἴομαι εἰδέναι
Where the translation is roughly
I am wiser than this man, for neither of us appears to know anything great and good; but he fancies he knows something, although he knows nothing; whereas I, as I do not know anything, so I do not fancy I do. In this trifling particular, then, I appear to be wiser than he, because I do not fancy I know what I do not know.