Hello, 
I wanted to know that how researchers in mathematics keep updates in their field of interest. 


(original question by Rahul Gupta)



How to be updated with current advances in mathematics 
There are several ways, and it depends on the precise meaning of 'in their field of interest'.


With a narrow definition of this an important and classical way to keep up to date is personal correspondence, people in the same field often know each other and thus people actively inform people of which they know that they are interested in progress on a certain problem directly.
More recently, some people also use blogs for announcments of latest progress.


With a less narrow defintion: As mentioned in a comment, there is a large preprint server
arXiv.org where many researchers post their preprints. One can subscribe to keep daily emails on new postings in specific subcategories.


Attending (specialized) conferences is also an relevant way to keep informed.


Finally, most fields have specialized journals, and one can browse them to see whether one sees an article one wishes to study in more detail.


So, personal communication, preprints, (specialized) conferences, (specialized) journals; and more recently blogs and personal websites, is what comes to mind at the moment.


