Oh, The Doctor chuckled at that bit. "Ah, but you see, the thing you don't know about me is," he started before turning to grin at the girl once more, "I'm brilliant. Honestly, I doubt anyone around here can compare to me." Was that conceited? Okay, maybe a bit. But, he knew his intelligence level and how it couldn't compare to that of a human. A human brain, after all, couldn't withhold the information his held, it'd shut down. He'd almost seen that first hand.
And The Doctor knew there were no other Time Lords or Gallifreyans, there couldn't be. He was the last.
"It's not just a screwdriver. It's a sonic screwdriver. You'd do best not to forget that bit," he added, the grin still on his face. "You haven't seen a blue police box around here, have you?"