Paul’s missionary strategy amazes us at this juncture: his mission to the Gentiles is designed to provoke jealousy among Israel so that it, too, will turn to faith in the Messiah. And his theology shapes it all: his Gentile readers cannot become proud of their status but must see themselves as part of a redemptive process (Rom. 11:13-16).
Israel according to the flesh has rejected the Messiah; that rejection spilled over to Gentile faith; Gentile faith provokes Israel to respond to the Messiah.

And here Paul anticipates that if Gentile inclusion is the reconciliation of the world, then Israel’s future faith is nothing short of a miraculous resurrection (11:15).
Which leads him to an analogy with lump/dough and branches/root. If “part of the dough” as first fruits is holy, then the whole lump is holy; if the root is holy, then the branches become holy.
Who, then, is the “lump” and who is the “root”? Wright scans a few views and concludes that it may be best to see these images christocentrically: they are the Messiah.