I rarely do this, but I’m going to direct you to a different blog this week. I’m in the middle of two big projects, and I didn’t feel like blogging today. The abc Conjecture is one of the most important unsolved problems in math. It is also relatively simple to state. Go read about it at that link if you haven’t heard of it.
A few years (?!) ago someone claimed to have solved it. Unfortunately, the proof was one of the longest and most complicated things the math world had ever seen. Ever since, the status of the conjecture has been up in the air. Some people have attempted to understand it to try to verify if the proof holds up.
A few days ago, we got a massive status update. You can read about it here.