This new colleague sounds like he comes from the cutthroat dog-eat-dog world of the academy, and might be unused to a more collaborative workplace. Keep in mind that there are dozens of qualified applicants for every professor job. (The academy is churning out far too many new PhDs for the available teaching jobs.)
He's probably scrambling for recognition because he's afraid of losing out. And you and your supervisor are probably blindsided by that kind of behavior and don't know what to make of it. At the same time, it probably hurts to have his dream of an academic job go down the tubes, as indeed it will for almost every PhD.
Now, sure, he's smart and a hard worker. And he likes to brag. OK. Pain in the neck. Unpleasant. But OK.
You and he are assigned to work on a project together for a reason. You didn't say what the reason was. But you surely bring something to the project. Could it be knowledge of the customer? Of the way other parts of your company expect work to be delivered? It must be something.
As unpleasant as it may be, you and the supervisor need to teach this fellow to work as part of a team. If your supervisor won't do it, you can try.
Have a private conversation. Tell him something like this:
"When you hustle all night and make an end run around me, you undermine my trust in you. You surely can do a lot of work fast, but in this group it's important to work collaboratively. Each of us contributes useful knowledge. What's more, it's important for more than one of us to know about each project's details.
"Please, in future, remember that. Remember we're all in this together. What matters in this company is delighting our customers for the long term, not individual heroics. Please talk to me as you are working. I can help you and you can help me."
Don't expect him to change instantly. That kind of feedback takes time to sink in.
That kind of conversation tries to address his lone superhero behavior by explaining why another way is better. It doesn't sound like jealously because that's not the problem here.