Q:

Was Jesus quoting from a proverb of His time at Luke 9:62?

At Luke 9:62 (RSVCE) we read:

Jesus said to him, “No one who puts his hand to the plow and looks back is fit for the kingdom of God.”

This saying of Jesus has become a proverb in all prominent languages. I'm curious to know if Jesus was quoting an already existent proverb.
Some further explanation of the saying would also be welcome, regarding what the farmer would have been looking back at. For instance, would he be seeking someone else's assistance to hold on to the plough, or would he be looking at the 'smooth land' he was leaving behind?

A:

Background for the "proverbial" language used by Jesus here can be found in the Septuagint and in ancient Greek literature. The Septuagint does not provide a verbal parallel to 9:62, but it does offer a strong basis for understanding Jesus's invocation of agricultural imagery. This draws on the previous verses in Luke 9 when two men respond to Jesus's command, ἀκολούθει μοι ("Follow me."):

[κύριε,] ἐπίτρεψόν μοι ἀπελθόντι πρῶτον θάψαι τὸν πατέρα μου .... ἀκολουθήσω σοι, κύριε· πρῶτον δὲ ἐπίτρεψόν μοι ἀποτάξασθαι τοῖς εἰς τὸν οἶκόν μου.    
"Lord, let me first go and bury my father" ... "I will follow you, Lord, but let me say farewell to those at my home."  

Their responses echo 1 Kings 19:20 (= 3 Reigns 19:20) when Elijah finds Elisha, καὶ αὐτὸς ἠροτρία ἐν βουσίν ("and he was plowing with oxen"). Elijah casts his mantle upon him, eliciting the following response:

κατέλιπεν Ελισαιε τὰς βόας καὶ κατέδραμεν ὀπίσω Ηλιου καὶ εἶπεν Καταφιλήσω τὸν πατέρα μου καὶ ἀκολουθήσω ὀπίσω σου·   
Elisha left the oxen and ran after Elijah and said, "I will kiss my father and will follow after you."  

Thus, one of the most memorable "following" paradigms in the Hebrew Bible is introduced as a choice between plow and leader. This is probably the reason that Jesus's response to the men in Luke 9:59-61 turns to plow imagery. 
As for the "proverb" itself, commentators consistently identify the closest parallel in the ancient Greek poet Hesiod, a contemporary of Homer. In his "Works and Days", a musing on the necessity of labor, Hesiod emphasizes the benefits of a worker,  

ὃς ἔργου μελετῶν ἰθεῖάν κ᾽ αὔλακ᾽ ἐλαύνοι, μηκέτι παπταίνων μεθ᾽ ὁμήλικας, ἀλλ᾽ ἐπὶ ἔργῳ θυμὸν ἔχων    
who will attend to his work and drive a straight furrow and is past the age for gaping after his fellows, but will keep his mind on his work. (Greek, English)  

In these "well-known lines" (Bruce), the concrete dichotomy presented is between immaturity hankering after leisure on one side, and resolute dedication to profitable work on the other.* This serves to drive home the point: 

the demands of Jesus are more stringent than those of Elijah....A person who harks back to the past way of life is not fit for the kingdom or its work. (Marshall)

*This is better seen with a bit more context:  

 Get two oxen, bulls of nine years; for their strength is unspent and they are in the prime of their age: they are best for work. They will not fight in the furrow and break the plough and then leave the work undone. Let a brisk fellow of forty years follow them, with a loaf of four quarters and eight slices for his dinner, one who will attend to his work and drive a straight furrow and is past the age for gaping after his fellows, but will keep his mind on his work. No younger man will be better than he at scattering the seed and avoiding double-sowing; for a man less staid gets disturbed, hankering after his fellows. 

1. Alexander Balmain Bruce, The Gospel of St. Luke (EGT, Hodder and Stoughton 1897), 537.

2. Joseph A. Fitzmyer. The Gospel According to Luke (AYB, YUP 1974), 837.

3. Alfred Plummer, A critical and exegetical commentary on the Gospel according to St. Luke (ICC, Schribner's 1902), 268.

4. I. Howard Marshall, The Gospel of Luke: a Commentary on the Greek Text (NIGTC). Grand Rapids: Eerdmans, 1978), 412. 

5.  Translation of Hesiod is by Hugh G. Evelyn-White, 1914. Greek NT is NA28; translation is ESV. LXX is Rahlfs, translation mine.  

