We will be looking for the “heart” of the Torah, but it won't be the mathematical center of the Torah, it will be the thematic center. To do this we will look at the structure of the text to reveal its meaning.
Scholars have come to appreciate the significance of literary structure for determining the meaning of a work: that the form conveys meaning.
This quote and most of the quotes here come from the L. Michael Morales book Who Shall Ascend the Mountain of the Lord? .
Between The Ears BLOG INDEX, with titles and summaries.
Form Conveys Meaning
The form that I'm talking about is the chiasm, a literary device in which ideas or simply words are presented and then repeated in reverse order. Often, the chiasm will have a center passage which can be the main point, or simply a turning point in a story (Esther is such a story - Luke 810 , Chiasmus Exchange ). See my blog post Rhythm and Rhyme  for an introduction to chiasms in the Bible.
The first thing to notice is that there are five books in the Torah. It's easy to see that Leviticus is the center book. But that's not quite enough for us to jump straight to Leviticus, but yes, we do end up there. Think of Genesis and Deuteronomy like bookends, framing the Torah as a chiasm, these two books end with a patriarch blessing the 12 tribes of Israel (Jacob and Moses). One scholar called them Prologue and Epilogue. Surprising to me is a Jewish custom for children to begin their Torah education in Leviticus, not in the fascinating stories of Genesis or Exodus - Israel Bible .
The chiastic elements are more numerous in Exodus and Numbers, meaning that events in Exodus are mirrored in Numbers in reverse. In broad terms, in Exodus, Israel journeys through the desert TO Sinai. In Numbers. Israel journeys through the desert FROM Sinai.
Smith also points out how the second half of Exodus deals primarily with setting up the tabernacle, while the first half of Numbers is concerned with taking it down, Leviticus itself comprising God’s speeches from the tabernacle. 
Not only does Leviticus take place in Sinai, but it takes place in the Tabernacle. The chiasm identifying Leviticus as the center of the Torah shown in Morales' book is eight levels deep.
Note the pattern of the chiasm: every item A - G in Exodus is mirrored as G' - A' in Numbers.
*Moses appoints judges in Ex 18 at the suggestion of his father-in-law. He appoints elders at God's command in Num 11.
**That is, Leviticus occurs between these dates (1/1/2 is shorthand for the first day of the first month of the second year), that is Leviticus takes place during the first month of the second year after leaving Egypt. In a sense, Leviticus is timeless because it has no chronological markers.
I think it's safe to say Leviticus is the center of the Torah.
One third of the way there. Let's apply chiastic analysis to Leviticus itself.
Chiasm Of Leviticus
Leviticus can be divided into seven sections, though scholars will disagree over the exact boundaries of the sections. These seven sections are not of equal size. However, most scholars do agree that the center of the seven sections happens to be the Day of Atonement.
BTW, the mathematical center of the Torah depends on whether you mean the middle chapter, the middle verse, the middle word, or the middle letter. The middle letter is in Lev 8:28 - Kefirah of the Week .
God wanted to dwell with his people Israel, and through the book of Leviticus He is showing them how to do that, how to approach Him, how to be reconciled, and then how to dwell with Him. Think of it as a spiritual journey from common to holy. One moves from a state of unclean to clean to holy, with Atonement being the pivot point in the process. Scholars will label the seven sections differently, I like this one that Morales includes in his book.
R.M Davidson diagram of Leviticus
In other words: Laws, Laws, Laws ATONEMENT, Laws, Laws, Laws.
One may consider Leviticus in two halves, with chapter 16 serving as the fulcrum. ... The first half deals primarily with the approach to God through blood, while the second half is taken up with life in God’s Presence through increasing holiness, the overall goal being fellowship and union with God. 
Rom 5:10 … we were reconciled to God by the death of his Son , much more, being reconciled, we shall be saved by his life.
We can see that Atonement (chapter 16) is the center of Leviticus. Two thirds done. Can we use this chiasm trick once more?
Chiasm of Atonement
Atonement has the most detailed description of any holy day, compare it to the Feast of Trumpets, which is summed up in less than a verse as a memorial of blowing. Atonement is unusual in that the High Priest does almost all the work – sacrificing animals, sprinkling blood, entering the Holy of Holies etc., while the people are told to rest and fast. Morales shows that Leviticus 16, the Atonement chapter, is itself a chiasm. It is a chiasm within a chiasm within a chiasm – Chapter 16 within Leviticus within Torah. The chiasm of Leviticus 16 goes seven layers deep.
*The most holy place inside the tabernacle is called the Holy of Holies. The Atonement ceremony is performed by the holiest person in the holiest place at the holiest time.
**Verses 16-20, between the sacrifice of the two goats, is the heart of the Torah, the center of the innermost chiasm. Summary of vs 16-20 - The High Priest makes atonement for the Holy Place, for the tent of meeting, for himself and his household, and the altar. He purges the holy places from the impurities of the assembly of Israel.
Lev 16:16 He shall make atonement for the Holy Place, because of the impurities of the sons of Israel and because of their unlawful acts regarding all their sins; and he shall do so for the tent of meeting which remains with them in the midst of their impurities. 17 When he goes in to make atonement in the Holy Place, no one shall be in the tent of meeting until he comes out, so that he may make atonement for himself and for his household, and for all the assembly of Israel. 18 Then he shall go out to the altar that is before the LORD and make atonement for it; he shall take some of the blood from the bull and some of the blood from the goat, and put it on the horns of the altar on all sides. 19 With his finger he shall sprinkle some of the blood on it seven times and cleanse it, and consecrate it from the impurities of the sons of Israel. 20 “When he finishes atoning for the Holy Place and the tent of meeting and the altar, he shall offer the live goat.
Morales thesis is that Israel went from unclean to clean through the sacrifices and rituals of chapters 1 – 15, then is made holy by the Atonement ceremony of chapter 16, and then gets laws in chapters 17 – 27 on the subject of holy living, that is, living in communion with God. BTW, this material is from chapter 1 of Morales' book.
Let me share some thoughts about the “Heart of the Torah”
The Bible is more organized than I was aware of. When I read about the chiasms in the Torah in Morales's book, I got excited. Whenever I learn something new in the Bible, I want to share it. I only learned about chiasms five years ago, now I learn that the entire Torah is structured like this. I don't think that Moses could have designed it that way. He was recording events as they happened, he couldn't possibly have known that Israel would fight a second war with Amalek, that he would strike the rock a second time, etc. To me, it shows that God Himself is the author, that the Bible is His word. I find these “wonders in His word” to be faith boosters. And you can see it for yourself, in any translation – I did not resort to Hebrew to show the chiasms. Many more chiasms exist in the Torah and the rest of the Bible (1900 of them ) – just do an Internet search to dig deeper.
One other thought I get from this is the importance of Atonement. We have just reviewed the structure that shows Atonement is the heart of the Torah. The way the text is structured (form conveys meaning) shows that it is important to God. It should also be important to us. To learn more about the Day of Atonement, see UCG Bible Study Tools . It is the pivotal ceremony where Israel became holy. It represents the pivotal atoning work of Jesus where all mankind will become holy.
Heb 9:12 “by his own blood he entered in once into the holy place, having obtained eternal redemption for us.“