I just started a software job right out of school and have only been here a couple months. I found out another new hire with my same title and similar academic background (statistics for me, cognitive science for him with a machine learning emphasis) has a $5k higher base salary than I do.
I don't want to rock the boat since I'm so new but I want to find a way to bring this up to my supervisor because this feels like an arbitrary pay decision. What should I do?
Rather than the pay on hire being arbitrary, it sounds like your new coworker did a better job negotiating with the company while being hired. There isn't much you can do without rocking the boat, and "S/He gets paid more" is never a valid reason for a pay raise.
The best you can do short of finding another company to work for and trying to negotiate a higher rate is to develop your professional skills at the company you're at, then use that development to negotiate larger raises/promotions in the future. Unfortunately, starting at a lower base tends to lend itself to smaller raises (same percentage leads to a smaller amount), but a promotion always opens the door to a renegotiation of the base.
I agree with @GOATNine's core premise, but I would like to add additional experience and perspective.
Aside from leaving or getting a direct promotion, your company may also offer performance-based raises, in which case you can also catch up to or pass your peer's "lead" by doing work that's more highly regarded (because it is directly more valuable, or you are more innovative, etc). This is related to GoatNine's recommendation about professional development, but is more focused on achieving results rather than improving your credentials.
I can say my first-hand experience with this has been very positive. In my current employment, I didn't negotiate starting salary well and later discovered that my salary was well below peers. I went out of my way to demonstrate value, however, and within a couple years I was in a higher pay bracket than peers and not long after that I got significant promotions as well.
To me, it's mostly a difference in perspective. Do you want to spend your time showing that you're more well-trained / well-educated, or do you want to spend your time showing that you have real value to the company?
If you ever choose to leave, I will say that (now that I've been a hiring manager also) most companies will care more about a track record for high-impact project work than they will about additional education or training notes.
What should I do?
Do nothing.
There are many possible reasons for the new hire getting paid more than you such as:
Regardless of any of this, when approaching your supervisor with salary increase requests the only person that matters is you. Do you have more responsibilities than you did before? Are you performing at a higher level than before? Are you more valuable to the company than before? If you can't answer yes to these questions then you should not expect your supervisor to give you a raise.
It may seem unfair that two people with the same title are paid differently, but much more goes into salary decisions than a title and "similar academic background".
Negotiation skills are a soft skill a company might deem as part of communication skills and so the higher paid employee is actually a better candidate - hence the pay discrepancy is justified.
