It is, however, simply not in the new England captain's nature to crow about what has been achieved - more than anything out of respect for a sport which rarely tolerates the proud. Cook's tourists still have a job to do, by at least drawing the final Test in Nagpur, if they are to become the first from England to win a series here in almost 28 years.
The 27-year-old was invited to speculate, as others have, on how many Test centuries he may eventually add to the 23 which have already put him above all other Englishmen. He sensibly declined, and added: "Cricket's got a silly way of biting your arse. You can't look at it like that."
Cook added: "As players you can't look that far ahead. You just have to keep trucking; if you get carried away and start looking ahead, silly things could happen. Unfortunately, as a player, you've got to have that mentality."
Similarly, in the shorter term, Cook is not about to pontificate about a series victory which has yet to happen - or England's apparent success in conquering their demons against subcontinental spin.
"If we have another bad performance, it all flags up again," he said. "But we are going in the right direction. I said at the beginning of this tour, and I'll keep saying it, that we're going to have to keep improving and keep trying to work hard.
"Unfortunately, the job's not done. It would be nice if we were all going home tomorrow, and could be smiling. But it's not done, and we can't get too carried away."
What then of the approach in Nagpur, where anything but defeat will do just fine?
"Clearly, I'll take a draw now if someone offered it to me," he said. "But you can't go into the game with that mentality. You have to go in the same as we have these last two games, and produce the goods again. We can do something very special, but it will take a lot of hard work to do that again.
"It's been a really good tour. But we can't keep patting ourselves on the back - it's not the time to do it. We've got another challenge very quickly round the corner and will have to go into that Test match believing we can win the game."
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