From the Super Mario Wiki
Michelangelo di Lodovico Buonarroti Simoni, referred to simply as Michelangelo Buonarroti or Michelangelo, was a famous artist and sculptor responsible for numerous works of art, including the Sistine Chapel's ceiling, David, Pietà, and Moses. As depicted in the SNES and PC releases of Mario's Time Machine, he is pompously aware of his ability, and he considers himself to be the greatest artist of the Renaissance.
Mario is Missing
In Mario is Missing!, Michelangelo is briefly mentioned in a pamphlet, which was handed out after the Sistine Chapel's ceiling was stolen by Bowser. According to the pamphlet, Michelangelo was commissioned by Pope Julius II in 1508 to add art to the ceiling. He was not used to painting with plaster, and the entire project took over four years to complete. He completed most of the art while either uncomfortably lying down on scaffolds or craning his neck straight up, though the end result is often stated to be his best work.
Mario's Time Machine
According to Mario's Time Machine, Michelangelo was in Florence sometime during 1503, where he was working on the statue of David. At some point, the Chisel that he is using to carve the marble is stolen by Bowser, leaving him unable to continue his work. Mario then travels back in time in an attempt to return the Chisel to Michelangelo, though without knowing that it actually belongs to him. If Mario approaches Michelangelo in his workshop regardless, he only shouts at him to leave, as he wants to free the piece of art hiding in the block of marble in front of him, but he has no tools to do so. After talking to some of Florence's other inhabitants, including famed painter Raphael Sanzio and an apprentice sculptor who idolizes Michelangelo, he eventually learns a lot of Michelangelo, including how he studies human corpses to maintain proper human anatomy for his statues and how he was hired by Pope Julius II to paint the ceiling of the Sistine Chapel, even though he was reluctant to do so. Eventually, after learning everything he possibly can, Mario can return to Michelangelo and give him his Chisel. With his chisel in hand, Michelangelo continues working on the statue of David, and decides that since his fear of losing his chisel was unfounded, his fear of painting the Sistine Chapel is similarly unfounded. He also briefly considers painting Mario on the ceiling, but decides against it.
Later, in 1505, he lived in Florence, where he worked on the Sistine Chapel in his workshop. He is first encountered by Mario after the latter goes back in time again to return Leonardo da Vinci's Notebook, since Bowser had stolen it. Here, Michelangelo mostly boasts about how nobody can compare to him, with the possible exception of Leonardo. However, he quickly dismisses him since he focuses on domains outside of art such as engineering and science. He then mentions a new project of his, but refuses to elaborate further until he receives some plaster. Once Mario brings him a Bucket of Plaster from one of Verrocchio's apprentices (which can only be delivered once Michelangelo specifically mentions that he needs plaster), he goes on to explain that Pope Julius II commissioned him to paint the Sistine Chapel's ceiling in frescos; although he only wants to create sculptures, he cannot refuse a request from the Pope. Mario then changes the topic and asks about Lady Giocondo, which reminds Michelangelo that she left her mirror in his workshop when she came to visit. He then gives Mario Mona's Mirror and asks him to return it to her.