I am a first year PhD student in mathematics (complex differential and Kahler Geometry) and the other day I had a thought about the difficulty of starting to do research. This is my first post here but I have some in Math Stack-exchange.
First of all I hope this is the right place to post such a question, if it isn't let me know and I will move the post immediately.
Being in the first year of my PhD I am in an intensive study phase in order to get to the limits of research and start working on a project with my supervisor. I am noticing, however, that in order to be able to truly understand a problem (which is within the reach of a doctoral student, so excluding complicated problems that have been unsolved for many years e.g. the existence of a complex structure on the six-sphere) it really takes a lot of study and above all a good knowledge of the basics in other nearby fields of mathematics. Just think of Kahler geometry in which you must have good bases of analysis and geometry (sometimes even algebraic if you want to focus on the various notions of stability), or for example also in the low-dimensional differential topology in which you need to have good basics of algebraic topology and differential geometry. Obviously the more one goes on with the years the more this phenomenon, in my opinion, becomes more and more accentuated. On the other hand, however, thanks to technology we have new tools from which to draw/spread the culture and knowledge in pure mathematics (just think of this site), tools that the researchers of 30 years ago did not have.
At this point, thinking in this light, I asked myself a question: how difficult will it be for a master's degree student to start a PhD in 2050, say? The problems could be two: the first that obviously the research from today to 30 years has gone on and we have gone further and further with knowledge; the second is that university exam programs, to try to cope with the first problematic, are weighed down more and more. The most obvious consequence is that only a few people (the most determined and brilliant) will be able to go ahead and start a research program, or that they will dedicate themselves exclusively to a super specialized topic ignoring everything else (even if I don't see how it is possible in a subject like mathematics, moreover it would be a real shame).
This talk I am giving is exclusive to pure mathematics research, thus excluding the use of a computer as a means to be able to do research in the strict sense of the term (as for example a particle physicist or an applied mathematician can use it to do numerical simulations).
Having said that, I wanted to know what you thought about it and above all what researchers and/or university professors who have been in this field for many years think about it. I hope I have not asked a question that may be trivial, but rather a food for thought. Thanks for reading.