How to address impossible “minor” corrections in the UK?

Question

I passed my PhD defense a few weeks ago with minor corrections (in the UK) in a particular field within applied mathematics. Although the corrections were supposed to be minor, the external examiner is making some requests I can’t address. Some of said requests include the attainment of new results that I tried to obtain but couldn’t during my PhD, as well as some additional results that make no sense (and which are being requested simply because said external did not understand the Thesis). Right now I am at a loss, because I do not know what to do. So, my questions are as follows:

1. Can I submit the corrections simply stating that I tried to address a certain comment but didn’t succeed?
2. What happens if I submit the corrections and the examiners are not satisfied with my work?
3. Can I be denied the PhD on the basis that I did not successfully address the external examiner’s comments?

Answer 1

The only formal requirement is that you reach a point where the examiners are happy to sign the paperwork stating that the thesis is now acceptable to them. The usual convention is that the examiners agree that the task of checking corrections can be completed by the internal examiner acting alone, although the external has the right to insist on checking the revised thesis themselves. It may turn out that the examiners are willing to sign off on your corrections even if you do not complete everything on the list.

As such, the starting point is to go and talk to the internal examiner about the situation, and ask their advice on how to proceed. This is entirely acceptable, and quite common. They may wish to discuss the matter with the external examiner, or they may give you some hints about what they think would be sufficient. You should obviously also talk to your supervisor.

If you submit corrections, and the examiners aren't happy, their first response will simply be to send the thesis back to you with (hopefully) guidance on what they think you still need to do.

In theory, it is possible for you to reach an impasse where the examiners are unwilling to sign your paperwork. In that case, you would probably need to investigate the specifics of your university's procedures. Formally, the examiners do not themselves make the decision about whether you pass or fail, but they make a recommendation to a university/faculty committee. As such, you would likely have the right to make representations to that committee, and they could decide to (e.g.) seek an independent opinion from an additional examiner. However, I would be incredibly surprised if the issue got that far - nobody benefits.