What do we learn from "Lev Chacham li'Ymino v'Lev Kesil li'Smolo"?
Brachos 61a: A person has two kidneys -- one counsels to do good, the other for evil. Our verse implies that the good counselor is on the right, and the bad is on the left. (Refer to 10:1:1:1*.)
Rav Sadya Gaon: A Chacham's understanding and knowledge is prepared on his right [side], and a Kesil's understanding is late 1 , on his left. Ibn Ezra, Metzudas David - i.e. a Chacham's intellect 2 is with him. When needed, he finds it immediately and quickly; the opposite applies to a Kesil. The right is stronger and quicker, because the spring (source) of blood, the liver, is on the right. Do not ask from a lefty; the Mashal is based on most people.
Rashi: His Chachmah is prepared for him, to tilt him to the skilled path, for his benefit. A Kesil's [heart] tilts him away from the skilled path, which would be glory and good for him.
Rashbam: The Da'as of a Chacham's heart is to go in the right path, and that of a Kesil is to go in the left path. Just like the right hand is more important than the left, so the good path is called right, and the bad path left. This is why it says li'Ymino and li'Smolo, and not mi'Ymino and mi'Smolo.
Ri Kara: A Chacham's heart is prepared to show to him the path to go on. It shows to him what will be in the end of the matter. The Kesil's heart is not prepared to show to him the good path, just like the left hand is not skilled for man's work.
R. Avigdor: The Chacham's heart is for Mitzvos and Torah, which was given with the right hand - "Orech Yamim bi'Yminah" (Mishlei 3:16). A Kesil does Mitzvos only to receive reward, for wealth and honor - "bi'Smolah Osher v'Chavod" (ibid.), i.e. for those who go to the left (Shabbos 63a).
Seforno: A Chacham puts intellect on his right, and desire on his left, so intellect overpowers desire. Therefore, when a Chacham does the opposite of this, like a Kesil, this folly spoils him in the eyes of people, and he is shamed.
Teshuvos v'Hanhagos (1:539, citing the Vilna Gaon): A Chacham is constantly going to the right 3 to review his learning. There is no limit to how much one should review his learning!
Magihah (in Toras Chayim): A Chacham immediately senses and knows what to do in every situation. A Kesil begins to sense only after the matter is finished.
Ibn Ezra: This does not refer to the physical heart. For all people, it is in the middle, even though its head leans to the left.
I.e. he goes back to pages on the right side of where he is holding, or rolls the Sefer to the right, in order to read what he already learned. I heard that v'Lev Kesil li'Smolo - he turns pages (or rolls) to the left, to see how much more he needs to learn; he is anxious to finish. (PF)