Max Gottlieb is your typical mad scientist. Well, he's not totally nuts; he's just a little eccentric. He's the most uncompromising scientist you'll ever meet, and he spends pretty much every waking hour of his life working in his laboratory. When Martin first sees the guy hovering around the step of the Main Medical Building, he thinks the guy is a God of science. But after meeting him in person, Martin realizes that Gottlieb is actually a bit of a crankypants: "If in the misty April night Gottlieb had been romantic as a cloaked horseman, he was now testy and middle-aged" (2.3.4).
In some ways, Max Gottlieb is a good influence on Martin and in other ways he's a bad one. Gottlieb, for example, doesn't care at all about what other people think of him. The same can't be said of Martin, who can't help feeling that he wants people to admire him. For his part, Gottlieb tries to tell him that there's no point trying to make people think a certain way, as he says,
"Some of you will think that it does not matter; some of you will think, like Bernard Shaw, that I am an executioner and the more monstrous because I am cool about it; and some of you will not think at all. This difference in philosophy is what makes life interesting." (4.1.15)
Ultimately, Martin Arrowsmith considers Max Gottlieb to be the best thing since sliced bread, since all Gottlieb truly cares about is his work. Martin reveres Gottlieb's single-minded devotion, and mourns when Gottlieb eventually gets dementia and loses his memory. Up until the bitter end, Martin really just wants to be Gottlieb when he grows up.
In an interesting life-imitates-art kind of way, we see that Sinclair Lewis was a similar kind of dude. Lewis was so devoted to his ideals that he actually refused the Pulitzer Prize (for Arrowsmith!) because he thought that awards and fame got in the way of creating true literature.
It's hard not to think that Sinclair Lewis thinks as highly of Gottlieb as Martin Arrowsmith does when he writes that "[Gottlieb] had never dined with a duchess, never received a prize, never been interviewed, never produced anything since his schoolboy amours which nice people could regard as romantic. He was, in fact, an authentic scientist" (12.1.10).