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Got about a free 50-60 days before joining my PhD. Any advice or suggestions on what to do in this free time ?

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There's no point in starting early. Most people burn the first year of their PhD doing coursework, satisfying teaching requirements, and learning about a topic to even just come up with good questions. You can't really study to get ahead. It's a marathon of continuous work to understand the current state of a problem and then to come up with a novel solution. You need to go in rested (take a vacation) and ready to go (get your housing settled, move in, set up new insurance, licenses, etc...) So that you can hit the ground running and keep running.

If I were you, if you have the money to survive the first few months until the stipend kicks in, I would take a nice, super memorable vacation. If not, I would find a way to take a cheap trip with friends.
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Go do something completely not math related, you’ll probably be doing math for the rest of your life so take this time to do something fun and unrelated.  Go backpack through the wilderness or get in really good physical shape or start learning an instrument or something.  You’ll have tons of time to do math so take now to have some unrelated fun.
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Should be enough time to prove the collatz conjecture
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Party, go to the gym and have a few adventures.
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I lean towards suggesting you find something you'll enjoy. Consider playing Dark Souls, that way you'll be used to the frustration of not making progress for PhD.

I jest slightly, but lean towards advising you to focus on learning tactics to research more effectively. The PhD is tons harder than any undergrad projects, having a handle on other stuff will probably help more than learning maths. Do make sure you're rested before starting the thing though, that's probably more important.
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Travel.
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I find the comments in this thread confusing.  They are acting like joining a math grad program is the end of your life.  You don't work all day every day.  You will make a ton of new friends with similar interests as you.  Sure there will be times where you have alot of work to do and are stressed out, but grad school is just a more intensive version of college.  There will be plenty of friends, fun, and partying when you get there.  This will not be the end of fun.  If you can't have fun while in grad school there is no way you will make it to the end.
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While I do agree fully with the comments that say you should take some time off, there is one thing I would advise:

If you haven't already, get organised. Think about how you are going to take, store, and revisit notes (eg a personal wiki), and how you are going to keep track of what you are reading and what you've read (eg zotero).

Again if you haven't already, get some good exercise and diet habits down - learn to cook.

And to be honest, the burnout during a phd comes not from reading and learning about mathematics (which presumably is something you love), but from all the stuff you have to do around it, and especially bashing your head against the wall of a particular piece of mathematics over and over again. There is nothing wrong with spending this time to read some classic paper in your field or part of a graduate textbook or something.
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Enjoy these few days of not feeling guilt for not working on your Ph.D., they'll be the last for a while.
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Establish good self care habits. Tidying up, basic cooking skills, getting enough sleep, and exercise are the big ones that come to mind. It's important that you make these habits because earning a PhD is a grind.

I would also advise taking up a non-math hobby- mine was volleyball.

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