Writing a Master's thesis for 2 years ... is that appropriate? I am currently three months into writing a Master's thesis for a Master's degree in Mathematics, and the school I am currently attending is a California state university. I was asking my thesis advisor if I can expand the scope of the topic of my thesis, which means I would have to anticipate 2 years of working on the thesis (instead of 1 year). 

However, as I am also applying to various math Ph.D programs after completing my Master's thesis and degree, my thesis advisor is not keen to the idea of working on a larger scope of my thesis for 2 years. My advisor says that this would be "inappropriate", that he thinks the faculty on admissions committees would be confused and that my advisor would "not be doing his job" (in having me finish in 1 year, or "soon enough").

I for one disagree with my advisor personally, because I thought that expanding the scope of my thesis, even if it would take longer for me to complete and defend, would look even better on my Ph.D applications. I thought this would actually impress the committee rather than confusing them. I wanted to demonstrate that my finished thesis would reflect my having looked into more mathematical papers in research literature, as opposed to only two papers, which were chosen by my advisor, that I'm reading currently for my thesis topic. 

So I'm asking here simply for more thoughts on this matter. I do hope my point is valid, but if it seems most of the people here are agreeing with my thesis advisor, then I'll understand either way. 

tl;dr: I want to write more to my Master's thesis and plan to take 2 years instead of 1 year. My advisor disagrees and thinks the Ph.D admissions committees won't like this. Is this true?
Of course it's hard to say without knowing a lot about your specific situation, but I doubt spending an extra year on your master's thesis would be worthwhile.  In particular, if your advisor doesn't think another year is a good use of time, then I'd bet he is right.

Completing a master's degree is not necessary before applying to Ph.D. programs in mathematics in the U.S., and the primary purpose is to make up for a weak background or to shift fields.  From this perspective, the main goal is to do good work and move on, not to spend extra time trying to accomplish even more.  That comes across as eccentric, like you are wasting time on a side track rather than moving on with your academic career.

Two years in a master's program is the upper limit for what's normal in mathematics in the U.S., and this includes coursework.  Spending two full years working on a master's thesis would be unusual.  If you spend an unusually long time on your master's thesis, it may look like you just weren't able to write one more quickly, either because you weren't adequately prepared or you aren't good at getting things done.


  I thought that expanding the scope of my thesis, even if it would take longer for me to complete and defend, would look even better on my Ph.D applications.


If you write a much better thesis, it could be worthwhile, but it needs to be dramatically better even after normalizing for the time spent.  Linear scaling can't help you: if you spend twice as long writing a thesis that looks like it involves twice as much work, then it won't end up being a significantly better demonstration of your abilities.  The only real benefit is if your thesis is much better than twice as good.  (For example, if you have almost proved a significant new theorem, you might be better off taking longer and actually proving it.)