What to do when you discover a mistake in the archived copy of your PhD thesis?

Question

I've just defended my PhD in mathematics and started a postdoc. While working on an improvement of one of the results of my thesis, I realized that there are several minor mistakes and a big bug in a proof that invalids a minor result in the thesis (about 3-4 pages out of 110). Unfortunately neither I nor my advisor or referees figured it out the mistake. Though the result is minor, it is announced in the introduction and the manuscript is on-line on an ArXiv-like server, so that I could publish a new version but not cancel the one on-line.

What is the best thing to do? Upload an errata? Upload a "revised" version of the thesis? Publish a "revised version" of the thesis on my web-page?

Can this damage my future career, making me look not "reliable" as a researcher?

Answer 1

Though I am not in mathematics (I'm a philosopher), I would only add that generally speaking, the PhD dissertation should be one of the worst papers you ever publish. That doesn't mean it should be terrible...it only means that it's the start of your career, and your writing--and your research--will get better with experience.

You could still go ahead and submit a correction, but at the same time, don't stress yourself out over it. So many doctorandi today think the dissertation has to be flawless, and that they have to make some ground-breaking, Nobel-prize-worthy advancement in their field for the thesis to be any good. This is simply not true. Look--you have a postdoc, the results of which will no doubt be more influential on your future than your dissertation.

Again, I'm not saying to not submit the errata. Rather, I just don't want you to lose sleep over the mistake. Don't be too hard on yourself.

Answer 2

This question actually reminded me that I had made some (minor) addenda/errata notes on my own thesis but somehow forgot to ever post them. I should get to that!

Anyway, you definitely should correct the error; it's bad for mathematics if serious errors propagate. It's a little embarrassing, yes, but it's not at all uncommon. It will be more embarrassing if someone else finds the error first, and extremely embarrassing (and maybe starting to be career-damaging) if you have to say "Oh yeah, I knew about that, but never corrected it because I was embarrassed."

Before doing anything, I would suggest you spend a few days seeing if you can fix the error. Maybe you can find a way to work around the gap in the proof. Maybe you can adjust the hypotheses so that you still have a theorem, though a weaker one. (Or maybe you can find a counterexample.) Figure out what other parts of the thesis are affected by this error, and if they need fixing as well.

It can get confusing if there are multiple versions of your thesis floating around, so rather than trying to revise it, I would write up a short erratum note, explaining whatever you have learned about the error and its fix (if any). You might as well also list any other typos or errata that you have found, references to relevant work that's been published (or discovered by you) since your thesis was written, and anything else you would like to add.

Post the addendum on arXiv. Then, wherever your thesis is posted (your web site, the alternative preprint server you mention, the university's official site if possible), post a note saying "Addendum posted at arXiv:1234.5678". If you can't add notes or comments on the site itself, but can upload a revised version of the thesis, just add a page at the beginning with a reference to the addendum.

(And I'll echo JeffE's suggestion: it would be nice to post your thesis on arXiv itself as well. The "Comments" field would be a good place to reference the addendum.)

Answer 3

Mathematics has a great tradition of making mistakes and then fixing them yourself. Having other people find your mistake is a little embarrassing, but fixing them yourself shows that you are dilligent, so stop worrying.

Whether you upload an erratum or a revised thesis doesn't really matter, as long as both the old and new versions are available. (It's useful to see how things have been corrected, since mistakes are a good source of learning.)

Before you upload the new content, please double check that you really got it right this time. If it is wrong a second time (or was right and now you made it wrong), you can start to look a little foolish.

Answer 4

If anyone would care, there would be a mechanism for erratas... Even now, majority of the thesises is not available for the public. It is true for most science and most (even prestigious) universities. In short: no one reads them and no one cares.

If the mistake is something you published, I would care more about fixing the actual paper.

Answer 5

I had at least one error in my thesis (that I know of). As with yours, it was minor and affected even less of the paper. I found it when I was preparing a paper for publication. Fortunately, I was able to correct it, and the correct version was actually more interesting than the original erroneous one. I never corrected my thesis because the correct result was actually put in a journal article.

I've also had errors in print, a much more embarrassing affair. The mathematician who corrected it was very kind about it. I have not yet issued a correction, but it will appear in a forthcoming article, and quite a while after the initial error.

In my opinion, shared by some other responders, your publication record is more important than your thesis (unless you're a stratospheric talent). So don't sweat it too much. And, don't be reluctant to ask your advisor for advice (that's one of the reasons why he's called an advisor).