Van Buren was born just before the United States won its independence in 1783, but he doesn't have the distinction of being the last president born before independence to hold the office. One-monther William Henry Harrison, who succeeded Van Buren, was considerably older, having been born not only before American independence was won, but even before it was declared (he was born in 1773).
Woodrow Wilson was the last president born before the Civil War to hold the office. His successor, Warren Harding, was the first one born after that war -- just barely, in November 1865.
George Washington was the first president born, the first to hold the office, and the first to die. Moreover, he was the only president whose entire live span fell within the 18th century.
Only two men who have been Vice President of the United States were born in December: Martin Van Buren and Andrew Johnson. No vice president who hasn't also been president has ever been born in December.