John Piper, Think: The Life of the Mind and the Love of God (Wheaton: Crossway, 2010), 79:

What does it mean to love God “with all your mind” [Matt 22:37]? I take it to mean that we direct our thinking in a certain way; namely, our thinking should be wholly engaged to do all it can to awaken and express the heartfelt fullness of treasuring God above all things.

Chapter 6 (pp. 79–88) unpacks that definition.

Piper has thought about that definition for a long time. As recently as the mid-1990s, he told Don Carson that he wasn’t sure what it means to love God with your mind.

Cf. D. A. Carson, The Gagging of God: Christianity Confronts Pluralism (Grand Rapids: Zondervan, 1996), 484:

Noll and others often cite Jesus’ injunction to love the Lord your God your God “with all your heart and with all your soul and with all your mind and with all your strength” (Mark 12:30) as if that justifies all intellectual effort expended by a Christian. John Piper, in a private conversation, thoughtfully commented that he was unsure what the passage means: What precisely does it mean to love God with one’s mind? It is not obvious. This is not the place to embark on a full-scale exegesis. Remembering, however, that the “heart” in biblical thought is not so much the seat of the emotions as the seat of thought and of the whole person, both “loving God with your heart” and “loving God with your mind” are bound up with thinking the right things about God. They cannot simply be equated with all intellectual endeavor undertaken by a Christian, even though such endeavor must be undertaken coram Deo. But whatever the full sweep of this injunction, it cannot mean less than a God-inspired delight in all of God’s thoughts insofar as he has disclosed them, and a God-given determination to dethrone all competing systems of thought and bring them into captivity to the gospel (cf. 2 Cor. 10:5). And that requires constant, thoughtful Bible reading, theological reflection, interaction with Christian thinkers from the past, humble assessment of the currents of our age and courageous determination not to become their slave.

It is precisely here, I fear, that many evangelical intellectuals have failed.