At which point in your PhD should you feel like you're in the edge of human knowledge/ know exactly what is your contribution?

Question

I am a first semester PhD student. The standard time for finishing a PhD is 3 to 5 years in the part of the world I'm in. I have to defend a thesis proposal or project by the end of the second year. I have changed my area of research since my master's, so I only have conference papers in my current field.

I feel like my research proposal was a little open, a bit too general. I have an idea of where the current state of the art is in my field (let's say I read a few tens of articles in my field to write my proposal). However, i don't think I "am" at the state of the art. My coursework, experiment planning and helping the research group in other tasks are taking a lot of time, and I haven't evolved much on this for the first 3 months.

How far in the PhD should I be when (in parentheses when I think I can manage to accomplish these phases):

• I am able to understand to a very detailed degree state of the art work (15 months)?
• I am able to reproduce state of the art results with my models (18 months)?
• I publish in a journal something related to my work (21 months)?
• I know very well where I intend to "push" the boundary of knowledge in my field and the methods I will use for that (24 months)?

Answer 1

You may never "feel" it. But you might be there. You might "feel" it always, but not be even close. Results will tell you that you were there. Especially if others (reviewers) find your results and methods to be "interesting".

Human knowledge is sometimes viewed as a vast sphere with researchers chipping away at the "edge of the known" to make advances and push out the boundaries. That is probably more or less accurate. But imagine, instead, that human knowledge is fractal instead. With the boundary everywhere about us. The edge isn't smooth. You can be at the edge no matter where you are.

But you have to be able to look beyond the edge, into the unknown. You have to be able to formulate questions about the unknown for which you don't have the answer. In some fields (math, physics) there may not even be an answer to some questions. But to be "at the edge" you need to also have ideas about how to go about answering those questions or showing that the answers are impossible.

Note, for example, that few would question whether Einstein was at the edge. But note also that he was very tentative about some things. And he backtracked a few times. He posed big questions, interesting questions. He sought ways to answer them. He proposed ways to answer them that were beyond the state of knowledge and technology at the time.

But if you want to get a good sense of whether you are there or not get feedback on your ideas. Two good ways are to submit papers and get reviewer feedback and to form a circle of collaborators with whom you can propose questions and evaluate them. In most fields, unless they are very new, it isn't possible to know everything about the field. In mathematics that was last possible about a hundred years ago. But a collaborative group will have a better overall grasp of what is known and what is not and what is an "interesting" direction in which to push.

But the unknown is unknown. At least until you make part of it known.

---

Personal note: I guess I learned I was there in about the fifth year of a graduate program. But only in a couple of very narrow (fractal, again) areas.

Answer 2

There may or may not be a breakthrough moment during your PhD, but if there is one it will not happen “on cue”. Indeed if research is so linear as to be planned months in advance, it’s unlikely to lead to breakthrough and “ha!ha!” moments, which are in my experience always unscripted. The most interesting part of research is when things don’t quite work out.

It doesn’t mean there should be no plan: luck favours the well-prepared. It does mean keeping an open mind and be willing to deviate from “the plan” when needed and justified is more likely to provide you with magical moments than rigidly following a script.

Speaking for myself I realized I was at the edge on a January Sunday afternoon, when I totally unexpectedly reproduced by hand a calculation that had previously been done only by computer. It took 5 minutes to confirm my insight on the computer, and approximately 90 seconds to convince my thesis director the following day. This followed weeks of long and highly technical manipulations trying to simplify some expressions: only once I had abandoned this path as overly tortuous was I properly prepared to contemplate a simpler more elegant solution. I was in the 2nd year of my PhD. It took me 3 years to finish the job, getting additional insights along the way. The final product rather different from what was initially envisaged.

I give immense credit to my thesis director for recognizing the good parts of my argument from the jumble of my original explanation. My office neighbour never had such moments, but he didn’t an advisor half as open-minded as mine.