My professor assigned a final paper due the 12th, and while our exam period extends to the 23rd of December, all my exams were scheduled on the 11th and 12th and a couple before. As this was one of my more interesting classes, I asked the professor if I could have a couple days' extension, because I'd rather not rush the paper but actually engage with the sources. While some might prefer to get on break early, having back-to-back final exams is extremely exhausting, and having them spread out would be much preferred in my eyes. So I explained the circumstances and requested an extension (well in advance) but never got a response. After a couple days passed, I tried again to no avail. I have emailed the professor before and they responded but now seem to be ignoring me. I was one of the only 3 students to have perfect attendance out of a class of about 50, so I thought they would understand my genuine interest. Also, I know 3 other students who got like two week extensions on earlier papers, so I thought it should be fine. Any idea on how to proceed?
Assume your professor is busy and that your request is denied since it hasn't been accepted.
Turn your paper in on time.
If you didn't turn it in and your deadline has already passed, you've made a really bad mistake. Finish it absolutely as soon as possible and beg for forgiveness. It doesn't matter if someone else was granted an extension at some time, you were not granted one this time.
In situations like this I'd advise talking to the professor in person at their office hours. No response to your E-mail could indicate refusal of your request or just that your message was lost in the inbox of a busy professor.
Additionally, the professor might recognize you from class and remember previous interactions, questions and your attendance record.
I explained the circumstances and requested an extension (well in advance) but never got a response. After a couple days passed, I tried again to no avail.
Most professors will work with you if you have multiple finals on the same day. In your case you had ~4 finals and a new paper within a five day period, so your request does not seem unreasonable.
My guess is that the professor just skimmed your e-mail, saw you wanted an extension, frowned, and deleted it. He probably didn't take the time to realize that you were a good student with an overloaded exam schedule. Indeed, I had to read your post several times before I got it, so his confusion is understandable.
So, I think it would be reasonable to talk to him in person and explain how packed your exam schedule is. You're not just another student who wants more time; you're reacting to the university's poorly-designed exam schedule. Of course, he may decide that 5 items in 5 days is not unreasonable, but I still think it's reasonable to ask.
My professor assigned a final paper due the 12th
I can't help but notice that you posted this just after midnight on the 14th. Is your paper late? If so, that changes the situation completely; I think it is highly unlikely he will give a retroactive extension. You should turn your paper in ASAP. It's maybe worth explaining the circumstances and referencing your e-mail, but you should expect some deduction (hopefully he accepts it at all).