You have piqued my interest with your question. I just have to find out for myself, and for you too, what the answer is. Human beings have been creating art for themselves probably as long as there have been human beings. Archaeologists have found what they call pictographs, drawings that represent words or concepts, all over the world.
As far as art for art's sake goes, probably the oldest paintings are the cave paintings that have been discovered in France. The best-known of these are Lescaux cave paintings in the Bordeaux region of France. They are not the oldest paintings, however. The oldest are the paintings in the Chauvet caves; radiocarbon tests date them at 35,000 years old (dating back to 33,000 BCE!)
In 2006, archaeologists discovered what is believed to be the oldest known portrait of a human in a cave near Angouleme, France. The painting is very primitive, but it shows an eye, a nose, and a mouth, clearly meant to represent a person.
I hope this helps you. It was fun to research!
The oldest known cave paintings were found in the Chauvet Cave, located in southeast France. Discovered in 1994, the cave was filled with images of diverse animal species, including rhinoceroses, cats, and bears. Radiocarbon dating showed the images to be more than 30,000 years old.
Eliette Brunel Deschamps, Jean-Marie Chauvet, and Christian Hillaire discovered the Chauvet Cave. This group previously discovered other decorated caves in the region, including Les Deux-Ouvertures, Le Cade, the Grotte du Louoï, and the Caverne de Poitiers. The Chauvet Cave stretches more than 1,700 feet, larger than any previous cave painting discovery. Some of the images they found were of bears, panthers, cacti, handprints, horses, and lions. In addition to the painted images, engravings were found, including horses and mammoths. The images were, for the most part, natural and realistic looking and easily recognizable. Perspective was used as well. Some of the walls were prepared by scraping so the images would stand out better, and scraping was also used to add contours and highlighting. In Chauvet, like most other caves with prehistoric art, it is clear that not only was there more than one artist; different paintings were done at different times, often many years apart.