According to tradition, of these 613 commandments, 248 are Mitzvos aseh ("positive commandments" commands to perform certain actions) and 365 are Mitzvos lo taaseh ("negative commandments" - commands to abstain from certain actions). Three-hundred and sixty-five corresponds to the number of days in a year and the number 248 corresponds to the number of bones and significant organs in the human body.
Rabbi Simlai is attributed in the Gemara (Makkos 23b) to providing the number 613 Mitzvos. Other classical sages who hold this view include Rabbi Simeon ben Azzai (Sifre Devarim 76) and Rabbi Eleazar ben Yose the Galilean (Midrash Aggadah to Bereshis 15:1). It is quoted in Midrash Shemos Rabbah 33:7, Bamidbar Rabbah 13:15–16; 18:21 and the Talmud Bavli Yevamos 47b.
Other Views
The Talmudic source is not without dissent. Some held that this count was not an authentic tradition, or that it was not logically possible to come up with a systematic count. This is possibly why no early work of Jewish law or Biblical commentary depended on this system, and no early systems of Jewish principles of faith made acceptance of this Aggadah (non-legal Talmudic statement) normative.
The classical Biblical commentator and grammarian Rabbi Abraham ibn Ezra denied that this was an authentic rabbinic tradition. Ibn Ezra writes "Some sages enumerate 613 Mitzvos in many diverse ways [...] but in truth there is no end to the number of Mitzvos [...] and if we were to count only the root principles [...] the number of Mitzvos would not reach 613" (Yesod Mora, Chapter 2).
Ramban held that this counting was the matter of a dispute, and that rabbinic opinion was not unanimous. Despite this, he states that "this total has proliferated throughout the aggadic literature... we ought to say that it was a tradition from Moshe at Har Sinai," (Commentary to Rambam Sefer HaMitzvos, Root Principle 1).
Rabbi Simeon ben Tzemah Duran states that "perhaps the agreement that the number of Mitzvos is 613... is just Rabbi Simlai's opinion, following his own explanation of the Mitzvos. And we need not rely on his explanation when we come to determine the law, but rather on the Talmudic discussions" (Zohar Harakia, Lviv, 1858, p.99).
