Check out zojirushi's vacuum flask. The drink lid is fantastic and easy to clean.
If he's at all into iced coffee, a cold brew kit would be a great gift. It makes a coffee concentrate that you can dilute with water, milk, or creamer and serve over ice. Or add boiling water for hot coffee. My household goes through a carafe of cold brew per week, and we get less acidic, great tasting coffee from pretty low quality coffee beans.
If fancy hot coffee is more his style, a french press is great option. You could make up a cute coffee basket with a nice mug, insulated thermos, coffee grinder, or whole bean coffee.
Edit: for the record, I posted this before the lasybugs thing took off
You're not going to make any great progress on a PC build for that price. Besides, PC tech is changing so quickly, you shouldn't buy any one piece of it until you can buy all of it.
If you're looking for X1 games, I'm a huge fan of Destiny, but it's not for everyone. If you're looking for more of a sure hit, check out Shadows of Mordor or Dragon Age: Inquisition.
If you want to change things up a little, here are some of my favorite purchases (I'm a minor Amazon addict):
A super high quality door-hung b-ball hoop (you'll want to buy a nerf ball with it, the one it comes with is dangerous to valuables in the room)
A classy and useful EDC knife (there are lots of options on this front, /r/knifeclub has great recommendations)
Check out my sub /r/everymanshouldhave for more recommendations like this. It's not super active of late, but it has some great suggestions if you look at the history
If he's a coffee or tea drinker, this thermos. It'll keep your coffee hot 8 hours.
Non-sequitur: How did you find a mathematician who doesn't use chalk? I haven't ever met a mathematician who prefers dry erase ...