TITLE: Mathematical habits of thought and action which would be of use to non-mathematicians
QUESTION [106 upvotes]: Once again I come to MO for help with something I'm writing for the public.
Which habits of mathematicians -- aspects of the way we approach problems, the way we argue, the way we function as a community, the way we decide on our goals, whatever -- would you recommend that  non-mathematicians adopt, at least in certain contexts?  
In other words:  if you can imagine a situation in which someone came to you for advice, and you said, "Look, I think you should be a little more like a mathematician about this and...."  what would be the end of the sentence?

REPLY [7 votes]: If you have an idea that you think or hope might be true, then don't just look for reasons to believe it. (It is amazing how strong and how wrong is this instinct.) Look for reasons that your idea might be wrong. If it is wrong, you will save yourself a lot of time and possible embarrassment. If it is right, you will learn a lot about why and have probably found some new reasons to believe it anyway.