Written the way most of the world writes dates (DD/MM/YYYY), the next palindrome date is 3 February 2030 — 03/02/2030, which reads the same backwards as 03022030. In the American order (MM/DD/YYYY) it is 2 March 2030, and in the ISO order (YYYY-MM-DD) it is 2 March 2030.
A palindrome date reads the same forwards and backwards once the separators are removed. Because countries write dates in different orders, the answer genuinely differs depending on where you live, which is why all three common orders are shown above.
These dates are found by stepping forward through the calendar one day at a time from today, so the answer always reflects the current date.