It’s the 10th of October, 1582. Except that it can’t be. Not just because time travel isn’t possible, but because the 10th of October 1582 never happened. Neither did the 5th, 6th, 7th, 8th, 9th, 11th, 12th, 13th, or 14th of October in that particular year. And just to be clear, the rest of the year was present and correct, but those dates were skipped. If you had a birthday in that period, well, you were just fresh out of luck.
And the reason why it was skipped speaks to humankind’s desire to assert order on the universe, and how the universe really couldn’t care less about what we desire.