Ludwig van Beethoven

Ludwig van Beethoven was a German composer. He was arguably the most famous of all classical composers on Earth. He continued to compose music even after becoming completely deaf.

The Sixth Doctor was present at the birth of Beethoven and gave his mother enough money to raise the child that her husband did not want. (PROSE: Gone Too Soon)

The Tenth Doctor claimed to have learned how to play the organ (or possibly keyboard instruments in general) from Beethoven, suggesting the two had met. (TV: The Lazarus Experiment) After the Doctor and Beethoven were abducted by Momus for a dinner party, the Doctor told Beethoven that he loved his Fifth. (WC: The Lonely Computer)

In an unconfirmed incident at the Royal Albert Hall, the Tenth Doctor claimed to have once asked Beethoven if he could "rattle off a tune," to which Beethoven reportedly replied, "Pardon?" (TV: Music of the Spheres)

On Nocturne, Korbin Thessinger played Beethoven to lure a noise creature into a trap. (AUDIO: Nocturne)

When the TARDIS landed in the Hanging Gardens of Babylon, the First Doctor said that the music they were hearing was not Beethoven. (AUDIO: Farewell, Great Macedon)

Beethoven wrote "Ode to Joy", which was part of Beethoven's Ninth. (PROSE: Ode to Joy) The Twelfth Doctor used the hypothetical non-existence of Beethoven in a story (which didn't happen) as an example of the "Bootstrap paradox", where a time traveller travelled back to 18th century Germany and copied out the concertos and symphonies he had brought with him and gets them published after finding out no-one knew who Beethoven was; the time traveller essentially becoming Beethoven. He described Beethoven as a "[n]ice chap, very intense," and that he "[l]oved an arm wrestle." (TV: Before the Flood)

Behind the scenes
Beethoven was played by Paul Rhys in the BBC miniseries Beethoven.