Is there any disadvantage from non-academic job turn to academic job in math If you get your PhD in math , and then work for 1 or 2 years in a non-academic institution and then turn to apply for postdoc or tenure-track position in math like usual, is there any disadvantage (I mean for your application for postdoc or tenure-track position)?
An appendix: I just want to make sure whether or not I can't or it is difficult to get reference letter, take conference or give talks (in the future) because you are not in academic institution. This is the most important for someone (like me) who will returen to academic job.(but for some reasons he can't now)
 A: My personal opinion is that such a career path can contribute a lot to mathematics, because such candidates can often be informed by a more practical or utilitarian focus in their mathematical research, providing an important and invigorating perspective. For example, for someone to arrive at hard-core mathematical research in financial mathematics after having actually worked in investment banking would be extremely useful. And surely there is a similar situation with many other areas of applied mathematics. In areas tending towards pure mathematics, however, probably it becomes more difficult to make the case that the time spent away from research mathematics was beneficial. 
In any case, a person applying for a position from such a situation would naturally have a disadvantage in terms of publications and research accomplishments in comparison with the competing candidates. If the idea were to take a non-academic position with the goal of eventually returning to academic research, therefore, then it would seem advisable to keep up one's research as best as one can. Even a publication or two would be fairly convincing evidence of one's true mathematical nature. 
I do know several examples of people who spent a long time away from academic mathematics and then returned to a successful academic career in pure mathematics (even in set theory!). I know of several mathematians who had entire careers in business or computer software before returning to academic research and becoming tenured professors. So indeed it is possible. But surely this is far from usual, and certainly the more typical pattern is that once someone leaves mathematical research, unfortunately, they do not return.
A: It's indeed possible [I spent many years in industry building math software, and now I'm a tenured prof, albeit in computer science and software engineering department rather than math; although my research involves building mechanized mathematics systems...].  I started my academic career having previously 'published' 0 academic papers!  I was, however, already well-known within the computer algebra community, and my work was known [so I was able to get many good academic reference letters].  The reason for me to report this is that it is important to be able to convince the academic community that you really have something to contribute, else why would they hire you?  So, if you intend to move back to academia, either write papers or make sure that somehow the community 'knows' you and appreciates your work.
From my experience, I would say that the hardest part is to go from having well-defined goals with precise deadlines, often driven by external pressures, to writing research papers with no deadline.  Getting up to speed on producing papers while being on the 'tenure clock' was most unpleasant.  And, of course, at the beginning teaching courses can (and likely will) swallow all available time.  Unless you're in an enlightened department (I wasn't) where untenured faculty are given a lighter teaching load to allow them the time to get settled into their research career.
If at all possible, get a post-doc in between a non-academic job and a tenure-track position.  This will give you the time needed to 'switch gears'.  I probably would not have done that myself (the salary cut was already substantial enough as it is, I didn't want to make it even worse).  It depends on your personal situation.
