It is said that Yitang Zhang obtained his key insights by relaxing and putting the problem away. With this said, is meditation a task that mathematicians often do when they are stuck in a rut? Meditation has been linked with increased working memory and creative insight. I apologize if this is off topic, but I do not know where else to post this.
Even though this may not have any scientifical support, it's what I believe, each person can make a different meditation, not just that kind mentioned in your question, that is, each human being finds its own "clearing mind" moment, it can be sleeping, praying, talking, and going to a pub drinking with friends. The fact is, math requires a lot of intelectual work, it can be stressful and nothing better than take a time leave your work and do somerhing else. Riemman found out that leaving his table and go to the garden and talk to others helped him. Just find your method.
Actually it should not be mdeitation but any type of other positive brain activity that cancels the math problem to subconsciousness see>>>
While I can only really speak from experience (and I don't know if you would consider a student in mathematics to be a "mathematician"), while I don't meditate at all, I find that either going to bed or just doing something other than maths can help a lot for either coming up with ideas for how to do things, or even for finding out where they've went wrong on something (there's been times where half a week will have passed and I've found that there was something wrong with a solution for a question we got asked on an example sheet). If you can find something for you which helps to "reset" your mind and it helps you to get a fresh perspective on problems, then go for it; I honestly think they would differ from person to person.
However, I can't say that doing these "mind clearing" activities are a guaranteed way of thinking of a solution to a problem - sometimes you can only solve a problem by hours of thought and experimentation, using several trees worth of paper in the process. If there were an easy way of coming to solutions in mathematics, it would be an easy subject, but (thankfully?) there isn't an easy way (or at least, if you find everything you do easy, you're not doing hard enough maths).
If you suspect that you are wrong about your approach to a math problem. it is essential to step back and start over. Insofar as meditation helps to reset your emotional state then it is, at the very least, effective in that. although nothing, in my experience, beats sleeping for this.