Being smart, being intelligent, being brilliant is something that in no way guarantees success, but can be noticed for what it is, and we have had our share of Presidents who have been among the brightest public figures we have been blessed with.
Chronologically, this select list would include:
John Adams (1797-1801)
Thomas Jefferson (1801-1809)
James Madison (1809-1817)
John Quincy Adams (1825-1829)
James A. Garfield (1881)
Theodore Roosevelt (1901-1909)
Woodrow Wilson (1913-1921)
Herbert Hoover (1929-1933)
Richard Nixon (1969-1974)
Jimmy Carter (1977-1981)
Bill Clinton (1993-2001)
Notice that only three or four of these Presidents are seen as having been successful, including Jefferson, Roosevelt, Wilson and Clinton.
Notice that Hoover, Nixon, and Carter are seen by many as failures or certainly as being in the bottom half of the Presidents.
The two Adamses and Madison are saved by their other massive accomplishments, so are rated in the second ten of our Presidents by most historians.
Garfield, considered the most brilliant between the second Adams and TR is the great unknown, being shot after four months in office and dying after six and a half months in office, but believed to be brilliant and an unknown factor as to his potential for greatness.
Notice that George Washington, Andrew Jackson, Abraham Lincoln, Franklin D. Roosevelt, Harry Truman, and John F. Kennedy, all rated very high in rankings of Presidents, do not qualify on intellect or pure brilliance, and yet some, particularly Lincoln, FDR, and Kennedy have long been highly honored and respected, despite not fitting the definition of being part of the most brilliant intellects we have had in the Presidency!