From the Super Mario Wiki
Raffaello Sanzio da Urbino, better known as simply Raphael, was a painter who created amazing works at the height of the Renaissance alongside Leonardo da Vinci and Michelangelo Buonarroti. He had many muses and patrons of note, notably making art for the Sistine Chapel, and produced a large body of work across his lifetime, including the Sistine Madonna, the Triumph of Galatea, and The School of Athens (which features Aristotle and Plato). According to Mario's Time Machine, he meets Mario sometime in 1503, as Mario had traveled back in time to return Michelangelo's stolen Chisel.
Mario's Time Machine
In Mario's Time Machine, Raphael is working out of a studio in Florence when he meets Mario. Mario first asks him who he is, and he introduces himself as someone who knows all of the big artists, including Leonardo, Michelangelo, and Fra Bartolomeo. He then says that every good artist needs a Beret, and, despite Mario not claiming to be an artist, he gives him one. Mario then asks him about the Chisel in Mario's possession (as Mario does not know that it belongs to Michelangelo), leading Raphael to point out that Michelangelo has begun working on a new marble statue. Mario attempts to asks Raphael about the statue, but Raphael dismisses him, as he needs to get some more paint for his next portrait. He also tells Mario to go to Venice, as they are apparently in need of plumbers. Instead, Mario brings him some Paint, given to him by a nearby painter, and asks him again about Michelangelo's next project. Raphael, appreciative of his help, tells Mario that Michelangelo has begun working on a thirteen-foot statue of David. Mario attempts to ask about Michelangelo's other projects, but Raphael again attempts to dismiss him, saying that he needs to see someone about obtaining a new paintbrush. The same painter from before also gives Mario a Paintbrush, which he can then give to Raphael. Raphael admits that he simply wanted Mario to leave, but takes the brush anyways and decides to continue talking about Michelangelo's other projects, including the Sistine Chapel's ceiling. However, as Michelangelo is not interested in painting, he wants to let Raphael paint it. Raphael then promptly goes back to painting and does not talk to Mario any further.