The quick answer is no, you do not “need” a medium for oil painting. You can paint with oils right out of the tube if you desire. The main reason people use a medium is because oil paint straight from the tube tends to be quite thick and may be difficult to move around with a brush, or perhaps you want a certain desired effect that oil straight from the tube doesn’t provide.
Many artists will start a painting with a wash layer. A “wash” is oil paint thinned with a medium like turpentine. This gives the paint a watery like consistency enabling the artist to apply the paint very thinly or in “washes”. This also makes the initial layer dry quickly. Then with subsequent layers, a dryer medium like linseed oil is used in various amounts being sure to follow the “fat over lean” rule of oil painting.
But again, painting with oils straight from the tube is perfectly fine, especially if you are after an impasto effect, or you could simply add a few drops of a dryer oil like linseed to thin the paint a bit and start that way remembering to follow the fat over lean rule, otherwise layers of your painting may crack over time.
There are other mediums available for oil painting like copal, alkyd and damar, all with their specific purpose, but again not necessary. It really depends on the effect you are after which will become apparent as you become more experienced with the various supplies that are available. I hope this answered your question.
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