A bit to breakdown here.
They interned over the summer for the past few summers and didn't seem
to enjoy working here, but nevertheless accepted a full-time job after
they graduated with their Masters in Science. They were valedictorian
their undergrad year and have an amazing GPA as a grad student. And
yet, they refuse to listen during any of the training and then
complain that they don't know how to do something we just went over
the day before.
There is a bit of a difference between academically learning, and learning a job.
I know some students that never attended a lecture, because they couldn't focus for long periods of time, and hated not being able to control the pace of their learning. They learnt everything via written material, and by trying things out.
It's very possible your employee is very much the same. You should consider documenting what is practical to document.
What's more, they are so negative. Their coworkers praise them for
being critical and a realist, but they are not constructive in their
complaints and incapable of offering solutions to problems.
Sounds like the coworkers agree on some level, so what solutions have they offered? If there is any truth to the statements made, you should consider getting everybody together to try to find better ways of doing things.
I don't like the mentality of "don't complain if you don't have solutions". Sometimes the person with the best solution isn't someone that actually has identified a need for the solution.
They have no intuitive to ask for help. If I do offer them a solution
they don't bother implementing it. It really is draining and they have
been here for less than a month.
Not good enough. You need to explain that if they are stuck, they need to ask for help. You wouldn't even expect an intern to twiddle their thumbs, so you need to set clearer expectations around behaviour when they can't proceed with their work.
I am also really baffled here, because I am stumped why you would even
bother getting your Masters if you have absolutely no drive to learn
anything and again, they have the grades to prove that they can at
least retain information short term.
Maybe they just don't want to become experts in the substandard processes or solutions that your company seems to utilize. They likely learnt some idealised version of reality during their studies, and are a bit despondent that your company is nothing like that.
All their work they have done as an intern had to be redone, because
it was all trash and they ended up creating more issues then they
The irony here is the company didn't like their work but decided to offer them a full time job. Just like they didn't appear to like working there, but decided to commit to a full time job.
I am sure part of it is that they don't see me as their superior so I
am not worthy of listening to... I have tried repeatedly explaining the big
picture so that they understand, but their eyes just glaze over and
they tune out.
It really doesn't matter how much authority you wield. If people cannot operate with a particular learning style, that's just something that needs to be worked around.
They have openly complained in front of
me about my boss and try to extract gossip out of me even after I
attempt to shut it down.
Doesn't mean you seem to lack authority, just means they view you not as an extension of your boss, but someone who can act and speak autonomously.
I am at the point where I am wondering if I should just let them fail
and focus on people who want to work. Any advice on how to get through
to a wayward employee?
If you are their superior, letting them fail is not good enough. You need to do something to address the issues you are seeing, otherwise you are not doing your job. If your approaches don't work, then it's your role to bring it to your manager's attention.
If you have a systematic problem with graduates not being able to find their feet well, you need to look at your company to determine if your processes need to be updated to more modern standards.