Disclaimer: Numb3rs belongs to CBS and the Scott brothers and other people who aren't me.
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Casual dress is fairly common among the staff at CalSci. Amita had an astrophysics professor who would often show up to lecture in his pajamas because he got so absorbed in his work that he forgot to change.
Charlie has, thankfully, never been quite that bad. Actually, he can be almost fashionable sometimes (and Amita thinks Mrs. Eppes is to thank for that) with vests and sports coats. But ever since the night they played back the Janus List and heard Colby's name on the tape, Charlie's been falling apart. Sure, he seems okay in lectures--if you ignore the fact that he's talking to undergrads about games of chicken as applied to nuclear annihilation--but he hasn't shaved in days and his t-shirt is the periodic table of elements shirt that she thought had been regulated to yard work after a hole was ripped in the back.
(She had been there for the ripping, which occurred when she pressed him against one of the chalkboards in his garage workshop, popping the button on his jeans and sliding her hand inside his boxers to take hold of his cock. A big step in their relationship, but he'd needed something to distract him from Colby's betrayal—they all had—but while the FBI coped, Charlie threatened to disappear entirely into math. Alan had told her about how Charlie had spent months in the garage working on P vs. NP rather than face the truth that his mother was dying from cancer. She hadn't wanted him to get lost inside his head again.)
And he hasn't, so far. But he's been confining himself to teaching and to Cognitive Immergence Theory and to her, and while she loves the attention, she knows that he's not dealing with it. His sloppy appearance betrays that.