How to deal with animosity between different "factions" in a certain field? In academia, there are sometimes sort of &quot;feuds&quot; between different researchers. For example, one such situation is described here: https://www.quora.com/Mathematicians-What-is-the-story-behind-the-feud-between-Shing-Tung-Yau-and-Gang-Tian?share=1
Lately, something like this has affected me. People I work with will bad-mouth other researchers in our field, or other researchers will bad-mouth people I work with. Sometimes, they will say that so-and-so's results are trivial or that they stole the results from someone else, or that they got a lot of help from a different mathematician and aren't actually very talented. The bad-mouthing seems to happen on both sides and seems to be born out of a kind of vicious competitiveness. Here are some of the ways this has disrupted my PhD:

I am really paranoid about people's intentions and even though it seems like, from the outside, that my PhD is going very well (going into my third year I have one publication already and am making good progress on other projects), I am certain some people in my own university even, have the impression I am not a very good mathematician because they think my advisor is a fraud.
I have recently had the opportunity to work with someone from the &quot;other side&quot; of this conflict and have not yet told my advisor about that. I am afraid she will be very angry with me if/when I do. To complicate things, my advisor has told me some of her research ideas in the past and is extremely secretive about them. I just don't have the same sense of secrecy about my own research ideas. Luckily I don't work on what my advisor works on but she still might be quite upset that I've been &quot;talking to the enemy&quot; so to speak.
Although no one has directly been &quot;mean&quot; to me the ways in which I have seen people try to tear each other down has contributed to my total disillusionment with academia and made my field seem like a place where people compete for reputation rather than trying to do real work motivated by curiosity rather than ambition. It's just very depressing and stressful to imagine having to deal with this kind of thing.

As a young PhD student, I am shocked by the way the &quot;adults&quot; in my academic life behave. My instinct is to pretend this doesn't exist and focus on my math. I do not make any judgments about who is right and generally shut my ears whenever these topics come up. To some extent, it seems very inappropriate to me that my professors and collaborators discuss these kinds of things with me at all. Furthermore, I think one reason I have been successful as a PhD student is because I am very friendly and open to people. This has allowed me to learn a lot and collaborate with a lot of people despite having little to no contact with my advisor most of the time (we are on good terms, she just doesn't really make time for me).
These conflicts seem to have been started long before I was even in college so from my perspective, it has nothing to do with me, it's not really my business, and I don't even pretend to know all the details of who did what and why. And yet people I respect a lot gossip to me like school girls as if they are trying to convince me of a particular position.
Question: Has any of you had to deal with this kind of mean-spirited competitive research environment? How did you handle it? Should I avoid working with people &quot;across the aisle&quot; in order to stay out of conflict with them? Am I being naive to try to be friends with everyone and not hide what I'm working on like it's a secret recipe?
The same happened to me. I stayed friendly towards everybody and participated in both groups. I think it worked for me. It leaves all doors open. I think a key point is never agreeing with any bad-mouthing, ever. Sometimes this is socially difficult. I would play dumb and say &quot;Oh&quot; or &quot;I understand&quot;, but never &quot;You're right&quot; or &quot;Yes, totally&quot;.