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Math Overflow users resolve PhD thesis crisis

653 points by DarkContinent 6y ago

generationP 6y ago
As far as notational clusterfucks go, crossing numbers (along with the three standard definitions of a ring) are one of the best-known ones to still be biting people on a regular basis. ("Positive" and "natural number" are sufficiently well-known that people are careful.) But imagine how it felt to do group theory back when "group" could mean any of "abstract group", "subgroup of GL(n)", "finite group", "monoid", "semigroup" and combinations thereof.
- OskarS 6y ago
  The way I was taught was that back in the olden days, "group" always referred to groups of permutations (and the operation was always composition), and it was Cayley that introduced the much more general and abstract notion of groups that we use now. He could do that because it's relatively trivial to prove that the the two definitions are basically the same: every group is isomorphic to some group of permutations according to Cayley's theorem: https://en.wikipedia.org/wiki/Cayley%27s_theorem https://en.wikipedia.org/wiki/Cayley%27s_theorem
  - generationP 6y ago
    Sure you can embed any group in a permutation group, but that doesn't mean the two notions behave identically in all respects. For example, two groups being isomorphic is not the same as two permutation groups being isomorphic, as the latter come with their embeddings.
- tgb 6y ago
  The simplest gotcha I know is: is f(x) = 1/x piece-wise continuous?. This is calculus 1 level material and yet author's disagree significantly on this point, sometimes without specifying it! Some say yes, others would require f to have finite left and right limits at every point. This mattered for a point of my thesis and my advisor was very unhappy with me calling these function piece-wise continuous.
  - gowld 6y ago
    f doesn't even have either of a right or left limit at 0. f is maybe (piece-wise) continuous over what pseudo-domain? R or R\{0}? You could axiomitize that an infinite discontinuity is like an unbouned function as x->infinity, but then how would you avoid 1/x being regular continuous? I think you are claimokg that a set being incomplete "at the end" is different from a set having a hole in the middle -- that the question of continuity presumes connected sets. That's not standard but might be an appropriate assumption for the context of your paper. Anyway, arguing over terminology is boring unless it raises conceptual issues. The point is to communicate, which has at least 2 stakeholders. Clarify your terms and move on.
    - Ericson2314 6y ago
      The idea is that what 1/x is is intuitively simple enough, so we should have some standard terminology for it. And saying left and right limits is -infinity or +infinity really also isn't that weird. I'm pretty sure other metric spaces can be likewise extended and end up with similar algebraic laws as the "extended real numbers". Again this isn't very profound, but is good for education and efficient communication, and so should be perused. Finally, it's interesting that measure spaces with infinite measure is already a thing that people. I would like to see more connections with metric and measure spaces; e.g. we can have an n-point metric which is defined using the measure of the (n-1)-simplex. Just as regular metric spaces have a "triangle inequality", 3-point metric spaces should have a "tetrahedron inequality", and n-point metric spaces should have a "(n-1)-simplex inequality". Again, this is not profound, but good for communication, and connections between definitions help one compress everything for better mental storage.
    - tgb 6y ago
      I think you missed the point of the example, which is that people rarely clarify this because to the author their definition seems obviously correct. I made it 90% through a PhD without having considered that there could be more than one possible meaning for "piece-wise continuous". The domain is R in this case. The less-restrictive definition would be that f is piece-wise continuous if there are a discrete set of points .. < x_0 < x_1 < ... with f continuous on each interval (x_i, x_{i+1}). The alternative definition is that, plus requiring that the restriction of f to those intervals have limits at the endpoint. For piecewise smooth function, there's an even larger variety of possible meanings, yet it's often stated without clarification.
lifeisstillgood 6y ago
The walled garden sweet spot Stack overflow and it's cousin sites have many serendipities like this - and I happily conjecture this happens more here than facebook or twitter. I think the reason is that despite being a walled garden (ie proprietary) it still has a promise to open up the content and makes effort to moderate and grow the community - in other words what they are really selling is not the SEO but the sweet spot between "anyone posts anything" of an "ideal" internet where no rentiers exist but no one can find anyone else, and the much more corporate hand of Facebook. I am not sure reddit exists in this sweet spot either - mostly because there is just sooo much reddit.
- Dirlewanger 6y ago
  Both reddit/SO and say, classic forums, each have their own method of content discovery (reddit/SO always prioritize new items, forums push you to long-running threads), but both have their blind spots. With reddit you can end up with a lot of duplicates because a subreddit's dashboard decays stuff pretty fast based on the frequency of posts. It makes long-running discussion impossible. With forums you can have your long-running discussions, but you sometimes have to wade through page after page to find those specials nuggets of info.
  - munificent 6y ago
    I look at this as a fundamentally hard problem of information design. You have a series of posts to present to a reader. Which posts do you give primacy to? If your reader already knows most of the context and has read the previous posts, then "re-posts" are bad, long-running threads are good, and they just want to see the latest updates. If your reader is coming to the material cold, a "re-post" may be completely new to them, and posts that presume pages and pages of existing context are completely impenetrable. You want to lean towards fresh, short threads. The challenge for designing a forum then is balancing the competing needs of those users. You can make some progress by tracking on a per-user basis which comments they've already seen. Reddit does that (maybe just for gold accounts?) where new comments are blue. That makes it pretty easy to skim through a comment thread and see just the new leaves. But there's still the question of how to sort the threads themselves. It might be interesting if that sorting was also user-specific. Maybe deprioritize threads that you've seen but not interacted with, and prioritize "live" threads that you've participated in and are still changing.
oconnor663 6y ago
A neat comment on the accepted answer: > From OP's point of view this could be viewed as glass half-full rather than glass half-empty. Their dissertation results hold unequivocally on the sphere and might hold on the torus, though it is an open problem if they do. It is certainly legitimate to study what follows from a given conjecture being true. It could even be spun as a feature rather than a bug of the dissertation. If the results in fact fail on the torus then you know that the conjecture must be false. Potentially, it could open up a fruitful avenue of attack. Kind of reminds me of Terence Tao's post on what solving big problems looks like: https://terrytao.wordpress.com/career-advice/be-sceptical-of-your-own-work/ https://terrytao.wordpress.com/career-advice/be-sceptical-of...
- finolex1 6y ago
  As an aside, looks like one of the comments in the Math Overflow link above was made by Terence Tao himself
  - oconnor663 6y ago
    Oh neat!
- theossuary 6y ago
  It reminds me of this math overflow answer: https://mathoverflow.net/a/338620 https://mathoverflow.net/a/338620 I suspect the reason OP's thesis worked out okay is because his intuition wrt the problem is correct, even if his formulation was a bit off. Very cool, sounds like a good mathematician to me
- thechao 6y ago
  When Terence Tao writes stuff like this, I'm always very happy that I got to experience the Moore-method for learning math (at UT Austin). A group of us would be dumped into a class with a common topic and we'd just have to prove things (topology, algebra, analysis) ... on the blackboard, in front of everyone. The best work we did was when something started going wrong and then we'd all start arguing about the proof, building count-conjectures on the fly and riffing on the math. The worst work was when someone went and found a proof ahead of time and just showed the answer. There's so much to learning where the sharp bits of math are; proofs are the razor-thin path through the briar patch. It was only later that I found out that history, the study of art & literature, and philosophy can all teach you the same thing. The important part is that you're interested in the topic.
no_identd 6y ago
>"the faculty will not accept asymptotics" the hell does that mean?
- impendia 6y ago
  (Math professor here). Ambiguous and poorly explained. (Note the question immediately afterwards asking for clarification.) But probably something along the general lines of "My advisor said that, if my main theorem is an asymptotic estimate instead of an exact formula, then this would not be judged to be novel/strong enough to earn a Ph.D."
  - mywittyname 6y ago
    If you don't mind, could you explain the practical difference or the reasoning behind such a requirement? Are there situations where boundaries appear to be asymptotic but the exact solution shows this not to be the case?
    - truthwhisperer 6y ago
      (try to be funny) depends if you are on the university where 2+2 can also be 5 depending on your feelings
    - rrobukef 6y ago
      I re-implemented a quasi-polynomial algorithm. Experimentally, it shows exponential behaviour. Back-of-the-envelope calculation shows this behaviour can continue until the input size is >>10^21 before the asymptotic bound asserts itself. (For comparison, input size 30 is unfeasible)
      - Ragib_Zaman 6y ago
        Which algorithm?
        rrobukef 6y ago
wenc 6y ago
This reminds me of my Ph.D. crisis. (which I'm sure many former grad students can relate to) I was in my 6th year. All my friends had graduated, and my stipend had run out. I was 2 weeks away from submission and discovered that one of my assumptions was wrong, which potentially distorted/invalidated all my studies -- to fix these studies would have potentially delayed submission for months. It was a very subtle assumption violation (and it wasn't even that wrong) and my committee probably wouldn't even have noticed. I was tempted to sweep it under the carpet and not let it keep me from graduating. But I knew it was wrong. I felt that if I sacrificed my integrity then, the moral failure would mark me for life. No one would know -- but I would know. So I decided to fix the issue, re-do the studies and live with the reality that I would have to delay my defense. Turns out when you're desperate -- and many grad students can attest to this -- a resourcefulness that you never thought you had kicks in ("where were you during all my years of grad school?"). I don't remember how, but I somehow managed to wrangle new studies out in 3 days (which would have previously taken me months). I made the deadline in the end. The lesson I learned was that committing to doing the right thing has its costs, but in some cases it also forces one to explore attacks never previously considered. Asking on MathOverflow is one such attack.
- sadfev 6y ago
  Your comment is a lifeline to me in this difficult time. Why are we not resourceful in normal time?
  - YeGoblynQueenne 6y ago
    Because in normal time we spend most of our time reading HN rather than working on our urgent stuff.
    - infogulch 6y ago
      Whelp that's my signal to get back to work.
  - dleslie 6y ago
    It's not typically sustainable to operate at such high levels of stress, but the stress brings with it a myriad of hormones and behavioural adaptions that, for some people, aid in sustaining focus and effort.
thaumasiotes 6y ago
I was contacted by someone in a PhD thesis crisis who wanted me to provide speech samples they were apparently missing. The thesis was due imminently. As far as I could tell, the analysis was already done -- but my samples were needed for some other reason. I was kind of bemused by the idea that the analysis would be invalid with nothing behind it, but valid with unrelated data behind it.
truthwhisperer 6y ago
Maybe I don't understand but he should have been now in the position to have already a few accepted publications. I'm mean this seems strange to me a few weeks before due date or is his supervisor on covid break? Don't get this honestly. Or is this a paid phd?
supernova87a 6y ago
I have to say also that this type of crisis is not surprising (unfortunately) for math, or similar highly theoretical, loner fields. I can guess that the student asking the question is not being very open with his/her advisor, has worked and struggled for long hours alone, thinking they have to solve it on their own, and is not super communicative and checking in about important aspects of the thesis. Because he/she thinks it has to be a surprise "breakthrough" result -- a heavy obligation of the field's expectations. No responsible advisor would let the work get to such a state, so late in the game. Major fault of the advisor too, here.
- jfkebwjsbx 6y ago
  Advisors are also very much at fault, not just students. The last year of my PhD I ended up being pretty much alone because my advisor had changed research topics a year before and therefore was not interested nor up to date, so any of her inputs were not very useful. A couple friends of mine also struggled with their advisor because he actively avoided communication for some reason. I guess he had a personal or health issue. So even on good faith, advisors can end up making students life quite stressful for one reason or another
leokennis 6y ago
Low quality comment, but this once again confirms what I already knew: I suck at math.
- deleted 6y ago
  [deleted]
jb775 6y ago
Wisdom of the crowd in action. I feel like this wisdom isn't tapped into enough. We're often burdened with individual tasks and challenges while utilizing crowd knowledge is looked down upon or seen as an inferior solution finding mechanism. e.g. Imagine if companies worked together to figure out self-driving cars rather than compete?
- alentist 6y ago
  There’s the Autonomous Vehicle Computing Consortium (AVCC): https://www.avcconsortium.org/aboutus https://www.avcconsortium.org/aboutus
ReedJessen 6y ago
This kind of "social media" gives me faith in the ability of humanity to survive and thrive in the future.
fizixer 6y ago
OP is incredibly fortunate. Or maybe mathoverflow is that active/supportive. As a STEM grad student (not in math), I had more than a couple such moments of crises, when I posted my questions on various stackexchange websites. I got either useless replies, or no replies.
- iflp 6y ago
  Mathoverflow is different from most of the other SE sites in that it's only for research level questions. There is a separate site, math.stackexchange, for other math-related questions.
thom 6y ago
This seems like a deeply flawed qualification, that smart people, noticing interesting properties of deep problems, are forced to panic in such ways.
- omginternets 6y ago
  On the surface, I agree: there's an interesting problem that's worth solving, and a purely artificial limit is forcing people to do a bang-up job at solving it. But if you dig a bit deeper, I can see two counter-arguments: 1. The real risk -- by which I mean "the risk I have most often observed in the wild" -- is that a Ph.D expands to fill the time it's given, without ever wrapping up and producing a publishable result. This happens so often that it's practically expected in some places. 2. Having a deadline, oddly enough, also serves as a catalyst for birthing an idea... for "pinching it off" as the expression goes. At some point you have to stop planning and start executing. You can see the deadline as a forcing function. Ph.Ds are needlessly traumatic and procedural in many ways, but I'm no longer sure that hard deadlines are a net negative.
ggm 6y ago
My insight was an eng. student whose novel outcome of a maths model in Fortran on a mainframe depended on his not understanding what uninitialised arrays were. This was in the 80s. There was no interesting novel outcome: he was random-sampling prior states of memory. I felt very bad for him, it was mid-stage. I didn't hear how he resolved it. The other side of this is the crisis which only emerges in the viva. I was working in Leeds uni in the 80s and overheard an external discussing a case he had: it was obvious the results were fraud. They made the student and his supervisor to the sums in the room, on the blackboard. He didn't get his thesis.
noumantariq477 6y ago
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blickentwapft 6y ago
You don’t often see mathematics emergencies.
deleted 6y ago
[deleted]
benibela 6y ago
I was in a PhD crisis, but I did not post it anywhere. Not sure if it is allowed to ask for outside help. Although now I have finished the thesis without that part (it should have become an additional chapter). Perhaps I should post it around (although that might spoil it for a paper) Consider n polynomial equations in variables x_1, .., x_n, with constants a_1,..,a_n, b_1,..,b_n, c_1,...,c_n: p_1 := a_1 x_1 x_2 + b_1 x_1 + c_1 x_2 + d_1 = 0 ... p_{n-1} := a_{n-1} x_{n-1} x_n + b_{n-1} x_{n-1} + c_{n-1} x_n + d_n = 0 p_n := a_{n} x_{n} x_1 + b_{n} x_{n} + c_{n} x_1 + d_n = 0 Under which circumstances exists a (unique) solution for x_1,..,x_n in terms of the constants? I have found a recursive approach that results in a quadratic equation, containing only a single variable x_i (and the constants). (It is too much for a comment, here is a PDF: http://benibela.de/tmp/quadratic-equations-recursion.pdf http://benibela.de/tmp/quadratic-equations-recursion.pdf ) For example for n = 2, it is very simple: x^2_1 (a_2 b_1 - a_1 c_2) + x_1 (a_2 d_1 + b_2 b_1 - a_1 d_2 - c_1 c_2) + b_2 d_1 - c_1 d_2 This gives 2 solution. But I do not know what happens if the terms cancel each other out. Like if a_2 b_1 - a_1 c_2 = 0, there would only be one solution. But since the full solution in the pdf is so complex, I do not see which constraints would lead to cancellation there. --- And that is not the full problem I was trying to solve. In the full problem there are constraints on the a, b, c, d. There is a given graph, and depending which nodes are connected in the graph, the constants are the same. Like if node 3 and node 7 are connected, then b_3 = c_7 und c_7 = b_3. (even more complex though). And then the question is, do these constants cancel in the solution of those equations? And the final problem we want to solve: which graphs lead to exactly one solution, and which graphs lead to no solution of the equations?
miqarifa 6y ago
This rings so true to me. I got engaged during the last 6 months of my PhD student tenure, and lo and behold, I defended my thesis in the same month we got married. https://pornogratisaqu.com/es/category/33/Garganta%20profunda/popular/1/ https://pornogratisaqu.com/es/category/33/Garganta%20profund... In the same vein as above, the added perspective and fire under me resulted in a number of novel solutions to problems that probably would have been major issues in the past, including a full change in direction of my research conclusions after realizing a substantial issue in the practical application of the technology.
rvieira 6y ago
I'm totally sympathetic with feeling the clock ticking for a PhD thesis submission (been there), however: I knew I could take this route but never did it. This is a bit of a mockery of the whole purpose of a PhD thesis (it has to be your work primarily). This is just an advanced version of posting homework questions on the internet.

653 points by DarkContinent 6y ago

As far as notational clusterfucks go, crossing numbers (along with the three standard definitions of a ring) are one of the best-known ones to still be biting people on a regular basis. ("Positive" and "natural number" are sufficiently well-known that people are careful.) But imagine how it felt to do group theory back when "group" could mean any of "abstract group", "subgroup of GL(n)", "finite group", "monoid", "semigroup" and combinations thereof.

OskarS 6y ago
The way I was taught was that back in the olden days, "group" always referred to groups of permutations (and the operation was always composition), and it was Cayley that introduced the much more general and abstract notion of groups that we use now. He could do that because it's relatively trivial to prove that the the two definitions are basically the same: every group is isomorphic to some group of permutations according to Cayley's theorem: https://en.wikipedia.org/wiki/Cayley%27s_theorem https://en.wikipedia.org/wiki/Cayley%27s_theorem
- generationP 6y ago
  Sure you can embed any group in a permutation group, but that doesn't mean the two notions behave identically in all respects. For example, two groups being isomorphic is not the same as two permutation groups being isomorphic, as the latter come with their embeddings.
tgb 6y ago
The simplest gotcha I know is: is f(x) = 1/x piece-wise continuous?. This is calculus 1 level material and yet author's disagree significantly on this point, sometimes without specifying it! Some say yes, others would require f to have finite left and right limits at every point. This mattered for a point of my thesis and my advisor was very unhappy with me calling these function piece-wise continuous.
- gowld 6y ago
  f doesn't even have either of a right or left limit at 0. f is maybe (piece-wise) continuous over what pseudo-domain? R or R\{0}? You could axiomitize that an infinite discontinuity is like an unbouned function as x->infinity, but then how would you avoid 1/x being regular continuous? I think you are claimokg that a set being incomplete "at the end" is different from a set having a hole in the middle -- that the question of continuity presumes connected sets. That's not standard but might be an appropriate assumption for the context of your paper. Anyway, arguing over terminology is boring unless it raises conceptual issues. The point is to communicate, which has at least 2 stakeholders. Clarify your terms and move on.
  - Ericson2314 6y ago
    The idea is that what 1/x is is intuitively simple enough, so we should have some standard terminology for it. And saying left and right limits is -infinity or +infinity really also isn't that weird. I'm pretty sure other metric spaces can be likewise extended and end up with similar algebraic laws as the "extended real numbers". Again this isn't very profound, but is good for education and efficient communication, and so should be perused. Finally, it's interesting that measure spaces with infinite measure is already a thing that people. I would like to see more connections with metric and measure spaces; e.g. we can have an n-point metric which is defined using the measure of the (n-1)-simplex. Just as regular metric spaces have a "triangle inequality", 3-point metric spaces should have a "tetrahedron inequality", and n-point metric spaces should have a "(n-1)-simplex inequality". Again, this is not profound, but good for communication, and connections between definitions help one compress everything for better mental storage.
  - tgb 6y ago
    I think you missed the point of the example, which is that people rarely clarify this because to the author their definition seems obviously correct. I made it 90% through a PhD without having considered that there could be more than one possible meaning for "piece-wise continuous". The domain is R in this case. The less-restrictive definition would be that f is piece-wise continuous if there are a discrete set of points .. < x_0 < x_1 < ... with f continuous on each interval (x_i, x_{i+1}). The alternative definition is that, plus requiring that the restriction of f to those intervals have limits at the endpoint. For piecewise smooth function, there's an even larger variety of possible meanings, yet it's often stated without clarification.

lifeisstillgood 6y ago

The walled garden sweet spot Stack overflow and it's cousin sites have many serendipities like this - and I happily conjecture this happens more here than facebook or twitter. I think the reason is that despite being a walled garden (ie proprietary) it still has a promise to open up the content and makes effort to moderate and grow the community - in other words what they are really selling is not the SEO but the sweet spot between "anyone posts anything" of an "ideal" internet where no rentiers exist but no one can find anyone else, and the much more corporate hand of Facebook. I am not sure reddit exists in this sweet spot either - mostly because there is just sooo much reddit.

Dirlewanger 6y ago
Both reddit/SO and say, classic forums, each have their own method of content discovery (reddit/SO always prioritize new items, forums push you to long-running threads), but both have their blind spots. With reddit you can end up with a lot of duplicates because a subreddit's dashboard decays stuff pretty fast based on the frequency of posts. It makes long-running discussion impossible. With forums you can have your long-running discussions, but you sometimes have to wade through page after page to find those specials nuggets of info.
- munificent 6y ago
  I look at this as a fundamentally hard problem of information design. You have a series of posts to present to a reader. Which posts do you give primacy to? If your reader already knows most of the context and has read the previous posts, then "re-posts" are bad, long-running threads are good, and they just want to see the latest updates. If your reader is coming to the material cold, a "re-post" may be completely new to them, and posts that presume pages and pages of existing context are completely impenetrable. You want to lean towards fresh, short threads. The challenge for designing a forum then is balancing the competing needs of those users. You can make some progress by tracking on a per-user basis which comments they've already seen. Reddit does that (maybe just for gold accounts?) where new comments are blue. That makes it pretty easy to skim through a comment thread and see just the new leaves. But there's still the question of how to sort the threads themselves. It might be interesting if that sorting was also user-specific. Maybe deprioritize threads that you've seen but not interacted with, and prioritize "live" threads that you've participated in and are still changing.

oconnor663 6y ago

A neat comment on the accepted answer: > From OP's point of view this could be viewed as glass half-full rather than glass half-empty. Their dissertation results hold unequivocally on the sphere and might hold on the torus, though it is an open problem if they do. It is certainly legitimate to study what follows from a given conjecture being true. It could even be spun as a feature rather than a bug of the dissertation. If the results in fact fail on the torus then you know that the conjecture must be false. Potentially, it could open up a fruitful avenue of attack. Kind of reminds me of Terence Tao's post on what solving big problems looks like: https://terrytao.wordpress.com/career-advice/be-sceptical-of-your-own-work/ https://terrytao.wordpress.com/career-advice/be-sceptical-of...

finolex1 6y ago
As an aside, looks like one of the comments in the Math Overflow link above was made by Terence Tao himself
- oconnor663 6y ago
  Oh neat!
theossuary 6y ago
It reminds me of this math overflow answer: https://mathoverflow.net/a/338620 https://mathoverflow.net/a/338620 I suspect the reason OP's thesis worked out okay is because his intuition wrt the problem is correct, even if his formulation was a bit off. Very cool, sounds like a good mathematician to me
thechao 6y ago
When Terence Tao writes stuff like this, I'm always very happy that I got to experience the Moore-method for learning math (at UT Austin). A group of us would be dumped into a class with a common topic and we'd just have to prove things (topology, algebra, analysis) ... on the blackboard, in front of everyone. The best work we did was when something started going wrong and then we'd all start arguing about the proof, building count-conjectures on the fly and riffing on the math. The worst work was when someone went and found a proof ahead of time and just showed the answer. There's so much to learning where the sharp bits of math are; proofs are the razor-thin path through the briar patch. It was only later that I found out that history, the study of art & literature, and philosophy can all teach you the same thing. The important part is that you're interested in the topic.

no_identd 6y ago

>"the faculty will not accept asymptotics" the hell does that mean?

impendia 6y ago
(Math professor here). Ambiguous and poorly explained. (Note the question immediately afterwards asking for clarification.) But probably something along the general lines of "My advisor said that, if my main theorem is an asymptotic estimate instead of an exact formula, then this would not be judged to be novel/strong enough to earn a Ph.D."
- mywittyname 6y ago
  If you don't mind, could you explain the practical difference or the reasoning behind such a requirement? Are there situations where boundaries appear to be asymptotic but the exact solution shows this not to be the case?
  - truthwhisperer 6y ago
    (try to be funny) depends if you are on the university where 2+2 can also be 5 depending on your feelings
  - rrobukef 6y ago
    I re-implemented a quasi-polynomial algorithm. Experimentally, it shows exponential behaviour. Back-of-the-envelope calculation shows this behaviour can continue until the input size is >>10^21 before the asymptotic bound asserts itself. (For comparison, input size 30 is unfeasible)
    - Ragib_Zaman 6y ago
      Which algorithm?
      - rrobukef 6y ago

wenc 6y ago

This reminds me of my Ph.D. crisis. (which I'm sure many former grad students can relate to) I was in my 6th year. All my friends had graduated, and my stipend had run out. I was 2 weeks away from submission and discovered that one of my assumptions was wrong, which potentially distorted/invalidated all my studies -- to fix these studies would have potentially delayed submission for months. It was a very subtle assumption violation (and it wasn't even that wrong) and my committee probably wouldn't even have noticed. I was tempted to sweep it under the carpet and not let it keep me from graduating. But I knew it was wrong. I felt that if I sacrificed my integrity then, the moral failure would mark me for life. No one would know -- but I would know. So I decided to fix the issue, re-do the studies and live with the reality that I would have to delay my defense. Turns out when you're desperate -- and many grad students can attest to this -- a resourcefulness that you never thought you had kicks in ("where were you during all my years of grad school?"). I don't remember how, but I somehow managed to wrangle new studies out in 3 days (which would have previously taken me months). I made the deadline in the end. The lesson I learned was that committing to doing the right thing has its costs, but in some cases it also forces one to explore attacks never previously considered. Asking on MathOverflow is one such attack.

sadfev 6y ago
Your comment is a lifeline to me in this difficult time. Why are we not resourceful in normal time?
- YeGoblynQueenne 6y ago
  Because in normal time we spend most of our time reading HN rather than working on our urgent stuff.
  - infogulch 6y ago
    Whelp that's my signal to get back to work.
- dleslie 6y ago
  It's not typically sustainable to operate at such high levels of stress, but the stress brings with it a myriad of hormones and behavioural adaptions that, for some people, aid in sustaining focus and effort.

thaumasiotes 6y ago

I was contacted by someone in a PhD thesis crisis who wanted me to provide speech samples they were apparently missing. The thesis was due imminently. As far as I could tell, the analysis was already done -- but my samples were needed for some other reason. I was kind of bemused by the idea that the analysis would be invalid with nothing behind it, but valid with unrelated data behind it.

truthwhisperer 6y ago

Maybe I don't understand but he should have been now in the position to have already a few accepted publications. I'm mean this seems strange to me a few weeks before due date or is his supervisor on covid break? Don't get this honestly. Or is this a paid phd?

supernova87a 6y ago

I have to say also that this type of crisis is not surprising (unfortunately) for math, or similar highly theoretical, loner fields. I can guess that the student asking the question is not being very open with his/her advisor, has worked and struggled for long hours alone, thinking they have to solve it on their own, and is not super communicative and checking in about important aspects of the thesis. Because he/she thinks it has to be a surprise "breakthrough" result -- a heavy obligation of the field's expectations. No responsible advisor would let the work get to such a state, so late in the game. Major fault of the advisor too, here.

jfkebwjsbx 6y ago
Advisors are also very much at fault, not just students. The last year of my PhD I ended up being pretty much alone because my advisor had changed research topics a year before and therefore was not interested nor up to date, so any of her inputs were not very useful. A couple friends of mine also struggled with their advisor because he actively avoided communication for some reason. I guess he had a personal or health issue. So even on good faith, advisors can end up making students life quite stressful for one reason or another

leokennis 6y ago

Low quality comment, but this once again confirms what I already knew: I suck at math.

deleted 6y ago
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jb775 6y ago

Wisdom of the crowd in action. I feel like this wisdom isn't tapped into enough. We're often burdened with individual tasks and challenges while utilizing crowd knowledge is looked down upon or seen as an inferior solution finding mechanism. e.g. Imagine if companies worked together to figure out self-driving cars rather than compete?

alentist 6y ago
There’s the Autonomous Vehicle Computing Consortium (AVCC): https://www.avcconsortium.org/aboutus https://www.avcconsortium.org/aboutus

ReedJessen 6y ago

This kind of "social media" gives me faith in the ability of humanity to survive and thrive in the future.

fizixer 6y ago

OP is incredibly fortunate. Or maybe mathoverflow is that active/supportive. As a STEM grad student (not in math), I had more than a couple such moments of crises, when I posted my questions on various stackexchange websites. I got either useless replies, or no replies.

iflp 6y ago
Mathoverflow is different from most of the other SE sites in that it's only for research level questions. There is a separate site, math.stackexchange, for other math-related questions.

thom 6y ago

This seems like a deeply flawed qualification, that smart people, noticing interesting properties of deep problems, are forced to panic in such ways.

omginternets 6y ago
On the surface, I agree: there's an interesting problem that's worth solving, and a purely artificial limit is forcing people to do a bang-up job at solving it. But if you dig a bit deeper, I can see two counter-arguments: 1. The real risk -- by which I mean "the risk I have most often observed in the wild" -- is that a Ph.D expands to fill the time it's given, without ever wrapping up and producing a publishable result. This happens so often that it's practically expected in some places. 2. Having a deadline, oddly enough, also serves as a catalyst for birthing an idea... for "pinching it off" as the expression goes. At some point you have to stop planning and start executing. You can see the deadline as a forcing function. Ph.Ds are needlessly traumatic and procedural in many ways, but I'm no longer sure that hard deadlines are a net negative.

ggm 6y ago

My insight was an eng. student whose novel outcome of a maths model in Fortran on a mainframe depended on his not understanding what uninitialised arrays were. This was in the 80s. There was no interesting novel outcome: he was random-sampling prior states of memory. I felt very bad for him, it was mid-stage. I didn't hear how he resolved it. The other side of this is the crisis which only emerges in the viva. I was working in Leeds uni in the 80s and overheard an external discussing a case he had: it was obvious the results were fraud. They made the student and his supervisor to the sums in the room, on the blackboard. He didn't get his thesis.

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blickentwapft 6y ago

You don’t often see mathematics emergencies.

deleted 6y ago

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benibela 6y ago

I was in a PhD crisis, but I did not post it anywhere. Not sure if it is allowed to ask for outside help. Although now I have finished the thesis without that part (it should have become an additional chapter). Perhaps I should post it around (although that might spoil it for a paper) Consider n polynomial equations in variables x_1, .., x_n, with constants a_1,..,a_n, b_1,..,b_n, c_1,...,c_n: p_1 := a_1 x_1 x_2 + b_1 x_1 + c_1 x_2 + d_1 = 0 ... p_{n-1} := a_{n-1} x_{n-1} x_n + b_{n-1} x_{n-1} + c_{n-1} x_n + d_n = 0 p_n := a_{n} x_{n} x_1 + b_{n} x_{n} + c_{n} x_1 + d_n = 0 Under which circumstances exists a (unique) solution for x_1,..,x_n in terms of the constants? I have found a recursive approach that results in a quadratic equation, containing only a single variable x_i (and the constants). (It is too much for a comment, here is a PDF: http://benibela.de/tmp/quadratic-equations-recursion.pdf http://benibela.de/tmp/quadratic-equations-recursion.pdf ) For example for n = 2, it is very simple: x^2_1 (a_2 b_1 - a_1 c_2) + x_1 (a_2 d_1 + b_2 b_1 - a_1 d_2 - c_1 c_2) + b_2 d_1 - c_1 d_2 This gives 2 solution. But I do not know what happens if the terms cancel each other out. Like if a_2 b_1 - a_1 c_2 = 0, there would only be one solution. But since the full solution in the pdf is so complex, I do not see which constraints would lead to cancellation there. --- And that is not the full problem I was trying to solve. In the full problem there are constraints on the a, b, c, d. There is a given graph, and depending which nodes are connected in the graph, the constants are the same. Like if node 3 and node 7 are connected, then b_3 = c_7 und c_7 = b_3. (even more complex though). And then the question is, do these constants cancel in the solution of those equations? And the final problem we want to solve: which graphs lead to exactly one solution, and which graphs lead to no solution of the equations?

miqarifa 6y ago

This rings so true to me. I got engaged during the last 6 months of my PhD student tenure, and lo and behold, I defended my thesis in the same month we got married. https://pornogratisaqu.com/es/category/33/Garganta%20profunda/popular/1/ https://pornogratisaqu.com/es/category/33/Garganta%20profund... In the same vein as above, the added perspective and fire under me resulted in a number of novel solutions to problems that probably would have been major issues in the past, including a full change in direction of my research conclusions after realizing a substantial issue in the practical application of the technology.

rvieira 6y ago

I'm totally sympathetic with feeling the clock ticking for a PhD thesis submission (been there), however: I knew I could take this route but never did it. This is a bit of a mockery of the whole purpose of a PhD thesis (it has to be your work primarily). This is just an advanced version of posting homework questions on the internet.