I take it the professor's comment relates to the objective of "finally understanding the Mystery of the Trinity." As to that, truly, "proof" of that which ultimately lies beyond our human comprehension is lacking. But that's not to say there isn't ample proof from Scripture and Tradition to affirm the Athanasian Trinitarian view as correct as against the competing viewpoints.
I take it the professor’s comment relates to the objective of “finally understanding the Mystery of the Trinity.”
That’s the way I took it. We cannot prove the concept of the Trinity in human terms, but we can confidently assert based on revealed truth that the Son of God, the Word made flesh in the person of Jesus Christ, is equally God with the Father, along with the Spirit who gave life to His human flesh.