Romans 11:13-15 — For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office:
If by any means I may provoke to emulation them which are my flesh, and might save some of them.
For if the casting away of them be the reconciling of the world, what shall the receiving of them be, but life from the dead?
Paul was specifically given a ministry to Gentiles and pursued it passionately, but he also hoped that ministry would result in the salvation of individual Jews.
In verse 1, "cast away" means to abandon forever. In verse 15, a different Greek word is used, one that means "exclusion from favor."
reconciling of the world — not the whole world, but all who will. It is available to the whole world.
life from the dead — enjoyment of God's blessings, reconciliation instead of the current alienation.
In verse 13, Paul answers a hypothetical question by Gentiles: If he's the apostle to the Gentiles, why is he worrying about Jews? Paul knew that salvation of Israel would bring salvation to even more Gentiles.