Is it normal for things to be so cutthroat, and what to do about it? I am a postdoc in mathematics. I like doing math, but I do not feel like I belong to a community, in the true sense of the word.

My vision of mathematical research is that it should be a massive collaborative effort to solve puzzles and publish the solutions, and no one should be excluded without a good reason. Also people should be allowed to openly talk about each others' results objectively without any feelings hurt.

However, in my field, people seem to see research as a competition. They form factions and play the game of inclusion-exclusion and loyalty matters more than truth, so does pride and it is almost impossible to be sure if an error is an error in a paper without making enemies.

People also treat knowledge as private property (within their factions or to oneself) and tend to keep secrets.

There are two types of secret-keeping generally practiced in my field:


When working on a project one would avoid talking about what they are working on and what are the partial results etc. in fear of being scooped.
When the work is done one should avoid proper exposition in the paper or explanation to the public so that:


they can stay ahead in the competition
they can make their results look as non-trivial as possible.



As much as I do not want to force people to disclose their secrets, I value clear explanations and talking to people about my work in progress. But as I do not belong to any faction I seem to be taking a huge risk on my career in doing so.

The fact that everyone is expecting secret-keeping also makes me reluctant to work with them because I do not want to sign an invisible NDA and unwittingly make enemies when I discuss with others on joint projects (and it is hard to set a boundary on discussion). This is not particularly helpful to my current state of isolation.

Perhaps it is just my field that has an environment incompatible with my belief, or perhaps all this is considered normal in any field. Nevertheless do you think this is a good reason for me to seek a different career path than academia?

Is it feasible to make a career doing open research?
Reality is very complicated. It is not one way or the other, often a mixture, and lots of judicious decision-making is required. Some environments are nicer than other, some people more trustworthy than other. If atmosphere disturbs you, choose your environment and the people to suit your taste, there are more pleasant subfields than others. 

Careers do depend on individual success, so you cannot just plainly discount people trying to keep their ideas for themselves until they are ready to capitalise on that - success, as measured by hiring committees, is individual, not collective. 

Yes, a fully open community is a bit like communism - great if it works, but usually works only to a commune of a limited size, or if the work to be done cannot hope to progress more than differentially faster than the community as a whole  and also if there are no "bad apples" who do not play ball and prey on the goodwill of the group.

That being said, you can encounter very friendly communities, but if that is a priority for you, you need to include that into your criteria for choosing a research topic.