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The concepts of “future”, “job stability” or even “location” are quite fuzzy when in Mathematics. I think I don’t know any PhD student who knows what he will be doing in 3 years, what he will be working on (not what he will be researching, but working…) or even where he will be.
1-2 years of Master+Master thesis
2-6 years of PhD thesis (3-4 years PhD grant+maybe some associated professor, 1-4 years)
1-2 years of postdoc, maybe abroad
Who knows? And where?
This is a rough schedule. I’m in step 2: 2 years left in my 4 year PhD grant. Probably with 2 years left for my thesis to finish. The uncertainty about the future feels like Damocles' sword dangling over one’s head. You may not think at all on it, but it is always there. And the days your theorems look impossible to prove, you can feel overwhelmed.