Advice on advice

Recently I was at a conference for graduate students that featured a panel on collaboration.  This was super cool - I really like the idea of having some professional development panels at a conference, especially ones that I haven't seen at conferences in the past.  There was a lot to take in, but I think there was some really good advice on collaboration.  I had some tangential thoughts from the panel experience I wanted to share.  Warning: I don't think what's written below may be that helpful or even cohesive, but I'm still going to post it in case it's useful for sparking some conversation.    

I asked a graduate student after the collaboration panel what they thought about it.  This student explained to me that they just started research recently - collaboration was not on their mind at all.  Why am I pointing it out?  Often, we feel we need to be put on high alert for all things: make sure to seek out any possible opportunity to collaborate, don't miss out on the potential nugget of wisdom from a senior person, you can't skip this talk opportunity because you need the line item in your CV, etc.  In fact, there's often an excess of information, opportunities, and advice from people - it can be overwhelming, we may not need it currently for our short-term goals, and it can cause even cause us to get hyperfixated on checking certain boxes.  While I think it's important to try to take advantage of many opportunities, I do also feel it's worth warning of a system overload that might actually impede you from putting focus on the right things.  I don't personally have good hard and fast rules for how to hit this balance - in my view a successful math career really involves focusing on both short-term and long-term and it requires different emphases at different time points (even over the course of a year).  For example, if you are going on the job market, it might not make sense to start a collaboration a month before job applications are due.  If you're a tenure-track faculty member, everyone will give you different advice about what is important for getting tenure, which is more than anyone can handle - they might tell you to say yes to every speaking opportunity but is it important to overextend yourself to speak at an AMS Sectional Meeting which might have no impact on your career at this stage?  

Honestly, it's tough because in general most reasonable advice can be useful - try to build collaborations, go to seminar regularly, devote time to learning new math, look at past grant proposals for examples, etc - and this is a good longer term investment.  Further, we may think we know what's best but sometimes we're just wrong; this is especially true on things we might have only been on one side of e.g. what makes for a good graduate school application.  What I will say is that it can be particularly helpful to have some trusted people (ideally a few years further along) who know you well.  Those people can often help to balance advice with what lines up with your goals, particular situation, well-being, knowing your collaboration has been going nowhere, etc.  I think even just stepping back sometimes and asking yourself if this is the right thing to be worry about is an important task that I don't practice enough.  

I'll end with something that Alex Wright said on the panel, which I really liked.  Students were concerned with the less common scenarios, like how do you start collaboration with someone in a totally different field or someone you've never met?  His view, which I agree with, is that collaborations, like a lot of things in math, tend to happen more organically.  If you follow the "general principles": be curious, ask questions, read papers, talk to people in your department and mathematical community, etc, then collaborations, and theorems more generally, should happen.  Not everything will work out and it doesn't make sense to try to force it.  This all applies more generally to advice.  You don't need to do every single thing, but be present in and listen to the community, figure out what works well for you, learn from lots of different people, be introspective, and don't be afraid to ask others for advice.