Can You Change Your Speciality After Receiving a PhD in Mathematics or Physics?

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let's say, hypothetically, that i was doing my phd dissertation on only one of the next topics: 1.Metamathmeatics (model logic,proof theory,set theory,recursion theory).
2. Pure Maths (Algebra,Analysis,Geometry/Topology,Combinatorics,Number Theory).
3. Mathematical Physics &/or theoretical physics (cosmology,quantum gravity,chaos).

and I receive my phd diploma, let's say afterwards i would be doing a postdoc, and gradually getting to be a reasercher in academia, would my speciality in one of the above subjects harm any chance of me to also research in other subjects, or when you choose your narrowed speciality you cannot also contribute to other fields, i mean by writing articles etc.

this is only a hypothetical question, i don't think that iv'e even touched the tip of the exciting questions in the above fields, and above all my ignorance is obviously showing, but at least i have a great deal of enthusiasim towards the fields mentioned above, perhaps not to specialise in but at least be of interest to me.

p.s
you may assume I am daydreaming but in hypothetical type of questions you can do so. [;-)].
 
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all sound very interesting! but probably too hard to even write a thesis on these, not to say work as a competent researcher... the dream is over... wake up!
(talking to myself) :smile:
 
Sadly, yo'ure unlikely to be able to change speciality after the PhD. The problem being you have to keep producing results in order to get your next job, and it depends on whether you can spare the time to both produce results on something and learn something else entirely different. Of course, there are lots of overlaps between the subjects, and you may find yourself able to work in some areas that involves all subjects - there is no reason to suppose that research in one area is completely isolated from work in another.

The chance to suddenly switch direction is often restricted to those whose positions are established. This is frequently one of the criticisms levelled at the tenure system: sure, once you have tenure you're not as beholden to meeting publication criteria, but until then you're frequently forced to work in some narrow area tweaking small things in your research.