It's easy to dismiss Professor Oak as a doofy academic who can't even remember his grandson's name. But originally, Pokémon Red & Blue designed Professor Oak as a powerful trainer the player could face off sometime near the end of the game.
This battle, as some hardcore Pokémon fans know, was cut. But according to website The Cutting Room Floor, which chronicles cut content from video games, players can use a Game Shark or glitches to trigger the battle. The game contains most of the data for the battle, Game Freak just decided not to include it for whatever reason.
It seems as if Oak's team would have been determined by what Pokémon you chose at the start of the game. He always has a level 66 Tauros, a level 67 Exeggutor, a level 68 Arcanine, and a level 70 Gyarados. The last Pokémon in the roster is the final evolution of either Charmander, Squirtle or Bulbasaur. Your rival's final team—which did end up in the actual game—is somewhat similar. Still, Oak's Pokémon are, on the whole, a slightly higher level than your rival's final team—meaning, he would have been one of the toughest battles you had to face in the game (and why it's assumed that Oak would have been one of the final 'bosses' in the game).
Here's what the battle would have looked like, as filmed by DarkJumpslash:
Remember, this is a battle triggered by Game Shark or glitches. That's why the player talks to a random trainer, only to have the actual battle end up being Oak. The battle is using the data from the Oak fight that's hidden in the game, it just needs to actually use a trainer that's present in the game to do it.
Obviously, Oak is no match for a team full of level 100 Pokémon, but still. I wish this battle would have stayed in the game, since I can't think of a better way to end Red and Blue. Fighting against your rival is definitely cathartic, but defeating Oak—the man who sent you on the adventure to begin with—is a whole other level of cool.
The Pokémon franchise did go on to let players battle against the Professor—Pokémon X & Y lets you face off against Professor Sycamore—but it's just not the same. Oak is the original professor, and it would have been amazing to battle him. Maybe then I wouldn't think Professor Oak is so goofy.