The Gemara (Kiddushin 30a) states the following: The vav of “gachon” (Lev. 11:42) is the middle of the letters of the Torah, “darosh darash” (Lev. 10:16) is the middle of the words of the Torah, and the “ayin” of “miya’ar” (Ps. 80:14) is the middle letter of Psalms. Elsewhere (link), I quoted R. Yitzchak Yosef Zilber’s explanation, as quoted in Torah Shelemah (vol. 28 addenda ch. 12), that this refers to unusual letters.
Be that as it may, my friend Mark Zomick brought the following to my attention:
The number of pages of Gemara in the Vilna (Romm) Talmud, excluding pages with only Mishnah and no Gemara, is 2690 (2711 in total, minus 21 with only Mishnah). Therefore, the midpoints are pages 1345-6.
According to Mark’s calculations, those pages fall out on Kiddushin 29-30. As pointed out above, Kiddushin 30 discusses the midpoint of the Torah. In other words, the midpoint of the Talmud is the location of the discussion of the midpoint of the Torah.
I don’t place much theological significance on this. The definition of the midpoint of the Talmud is somewhat vague. However, it is still a cool trivia fact.