New arXiv policy: 1-year ban for hallucinated references
twitter.com320 points by gjuggler 6 hours ago
320 points by gjuggler 6 hours ago
> The penalty is a 1-year ban from arXiv followed by the requirement that subsequent arXiv submissions must first be accepted at a reputable peer-reviewed venue.
This is incredibly good for science. arXiv is free, but it's a privilege not a right!
I'm not seeing this clearly listed on https://info.arxiv.org/help/policies/index.html so it's possible this is planned but not live yet - or perhaps I'm not digging deeply enough?
As a certain doctor once said: the whole point of the doomsday machine is lost if you keep it a secret!
I bet, since this has been posted, someone here has already vibe coded a reference checker that they plan to put behind a subscription.
This is good for reference checking, but I doubt this will do much for the most likely shoddy science that accompanies hallucinated references.
My take: this seems excessive.
ArXiv doesn't even check the submission closely, so how can they know?
They say "errors, mistakes"
They use an automated system to check if the basic requirements were met, and sometimes papers are flagged for further superficial human review, but there is no way they can possibly do this at scale or check every reference. This would be like trying to do peer review, but for a preprint archive that gets easily 100x more volume than any journal.
Second, there is such a huuuuge gap between publishing on arvix and peer review. I can attest personally that it's not even close. I've gotten probably dozen rejections from peer review and no problems publishing in arxiv math. This is because peer review checks not just for if something is new or correct, but also if it's of "interest to math community," which is inherently subjective, but also makes peer review many magnitudes harder than publishing on arxiv.
Even when a well-known professor in number theory praised the paper when I got an endorsement and a second emailed me and and encouraged me to publish it, it still got rejected 3 times and still waiting.
Being required to publish in a peer reviewed journal will close off arxiv for many researchers for good. It also defeats the point of it being a pre-print.
You could at least filter out hallucinated references which simply don't exist pretty trivially, I'd imagine.
It's more than that. if there are mistakes, then you can also be flagged.
read the whole tweet:
If generative AI tools generate inappropriate language, plagiarized content, biased content, errors, mistakes, incorrect references, or misleading content, and that output is included in scientific works, it is the responsibility of the author(s).
If you'd read the whole series of tweets it's obvious that is not their intention and there needs to be "incontrovertible evidence that the authors did not check the results of LLM generation" for the penalty to apply.
It's not hard to divine their intentions: you are entirely responsible for what you summit and if it's clearly slop(py) you get a ban. In a reply they state that they are seeking to apply this rule fairly and accurately and are mindful of unintended effects.
> This is incredibly good for science.
I disagree. It's just one darn hallucinated citation for heaven's sake, not fraud or something. It doesn't account for the substance or quality of their work at all. A one-year ban seems plenty sufficient for a minor first time mistake like this. People make mistakes and a good fraction of them can learn from those mistakes. There's no need to permanently cripple someone's ability to progress their life or contribute to humanity just because an AI hallucinated a reference one time in their life. That's punitive instead of rehabilitative.
> It's just one darn hallucinated citation for heaven's sake, not fraud or something.
It is fraud.
> It doesn't account for the substance or quality of their work at all.
References are part of the work. If you're making up the references, what else are you making up?
> People make mistakes and a good fraction of them can learn from those mistakes. There's no need to permanently cripple someone's ability to progress their life or contribute to humanity just because an AI hallucinated a reference one time in their life.
A one year ban is not permanent. Having a negative consequence for making poor decisions seems like an inducement to learn from the mistake?
In an ideal world, one would be keeping notes on references used while doing the research that lead to writing the paper. Choosing not to do that is one poor decision.
Having a positive outlook, if asking an AI to provide references that may have been missed, one should at least verify the references exist and are relevant. Choosing not to do that is also a poor decision, even if one did take notes on references used while researching.
> In an ideal world, one would be keeping notes on references used
In a far less than ideal world authors are referencing papers they've at least read the title and abstract of. In an ideal world, authors would be only referencing works they have read in their entirety. I don't think we need to live in the ideal world[0], but let's also not pretend the ideal world is even remotely out of reach. Let's also be honest that in the current setting a lot of citations are being used to encourage a work be accepted more than they are being used because of their utility to the paper. The average ML paper now is 8 pages and has >50 citations. That's crazy[0] References can be entire textbooks, which is potentially too high of a bar
> It is fraud.
I think we are talking semantics here.
While fraud does require intention to deceive, I get the sentiment that hallucinated citations shouldn't be dismissed as simply carelessness. It should be something stronger than that: gross negligence or something MUCH stronger! There should absolutely be repercussions for this.
But let's not call it fraud. That word is reserved for something specific.
EDIT: someone else said "reckless disregard" equals intent or something to that effect. So I looked it up.
It appears so that is the case. "Reckless Disregard Equals Intent" in legal language.
But I am not sure if this particular clause should apply here. Perhaps it depends on what kind of research is being published? For e.g., if it is related to medical science and has a real consequence on people's health, we can then apply this?
The intent to deceive is there. The deception is lying when you submit it that it is a scholarly piece of work in which amongst many other things you know the citations are accurate. This false representation was knowingly and intentionally made at the time of submission.
The citation being incorrect is merely the proof of deception not the (relevant) deception itself.
Fraud is the correct description provided (and this is practically a guarantee) you intended to benefit from the submission of the paper (e.g. by bolstering your resume).
If I violate the letter of the ToS when clicking submit you can correctly argue that I have technically committed fraud! Yet that is almost never what anyone actually means when having discussions like this one.
Fraud in a scientific context generally refers to fabricated research results. At least personally I agree with GP that hallucinated citations are generally something akin to laziness thus not fraud but rather some sort of professional negligence.
> It is fraud.
No, it is emphatically not. Fraud requires intent to deceive.
> A one year ban is not permanent.
...what text are you reading? Nobody was calling the one-year ban permanent, or even against it. I was literally in favor of it in my comment. I explicitly said it is already plenty sufficient. What I said is there's no need to go beyond that. My entire gripe was that they very much are going beyond that with a permanent penalty. Did you completely miss where they said "...followed by the requirement that subsequent arXiv submissions must first be accepted at a reputable peer-reviewed venue"?
Fraud requires intent to deceive _or_ reckless disregard, sometimes called, “conscious indifference” for the veracity of the statement asserted.
No. One single hallucinated citation on a document with you as an author is not evidence of your reckless disregard for anything. These exaggerations are crazy and you would absolutely deny such accusations if you missed your co-author's AI hallucinating a citation on your manuscript too. At best it would be careless, if you really relish extrapolating from one data point and smearing people's character based on that. Not reckless. It's quite literally the difference between going five miles per hour over the speed limit versus fifty.
If your co-author inserted the fradulent reference, I agree that you may not have committed fraud. But your co-author did, and you didn't check their work. and knowing that you didn't check their work, you signed off on it.
You didn't pick your co-author very well, but arXiv lacks investigative powers to determine which co-author did the bad, so they all get the consequence.
I’ve disagreed with some of your other stances in this thread, but I want to acknowledge the validity of your take here.
You’re right that a single hallucinated line is not evidence of reckless disregard - because that could have happened on a final follow-up pass after you had performed due diligence. It’s happened to me. I know how challenging it can be to keep bad patterns out of LLM generated output, because human communication is full of bad patterns. It’s a constant battle, and sometimes I suspect that my hard-line posture actually encourages the LLM to regularly “vibe check” me! E.g. “Are you sure you’re really the guy you’re trying to be? Because if you are you wouldn’t miss this.” LLMs are devious, and that’s why I respect them so much. If you think they’re pumping the breaks then you should check again, because they probably just put the pedal to the metal.
That being said, I regularly insist on doing certain things myself. If I were publishing a paper intended to be taken seriously - citations would be one of the things I checked manually. But I can easily see myself doing a final follow-up pass after everything looks perfect, and missing a last minute change. I would hope that I would catch that, but when you’re approaching the finish line - that’s when you expect your team to come together. That’s when everything is “supposed to” fall into place. It’s the last place you would expect to be sabotaged, and in hindsight, probably the best place to be a saboteur.
You're saying it as if the poor author just had no choice but to let LLM write their bibliography. To avoid hallucinations, maybe just don't let an LLM write any part of your paper?
You can only get in this situation if you let a bullshit generator write your paper, and the fraud is that you are generating bullshit and calling it a paper. No buts. It's impossible to trigger this accidentally, or without reckless disregard for the truth.
arXiV is not intended to be your blog. You should be held to a zero-mistake standard when publishing academic work.
The people I worry for are the junior researchers who are going to be splash damage for dishonest PIs. The PIs, though, deserve everything that’s coming for them.
Allowing hallucinated content or citations into your work is an act of carelessness and disregard for the time of people that are going to read your paper and it should be policed as such.
And flatly, if a person can't be bothered to check their damn work before uploading it, why should anyone else invest their time in reading it seriously?
How are you suggesting the fake citation came about? Why are you writing papers and not having actually read the source you took the material from?
If you are using AI-hallucinated references in scientific papers then there is some obvious intent to deceive there
> No, it is emphatically not. D Fraud requires intent to deceive.
I'm about as pro AI-as-a-research--and-writing-assistant and anti AI-witchhunt as they come, but I simply cannot parse what I've quoted here.
Posting slop to arxiv is blatant deception. Posting an article is an attestation that the article is a genuine engagement with the literature. If you're posting things to arxiv that are not sincere engagements with the literature, you are attempting to deceive.
>I'm about as pro AI-as-a-research--and-writing-assistant and anti AI-witchhunt as they come, but I simply cannot parse what I've quoted here.
Ditto. And its only 1 year. Like its about the most reasonable thing they could have done.
> followed by the requirement that subsequent arXiv submissions must first be accepted at a reputable peer-reviewed venue"?
This part seemed reasonable too. I'm not in academia, but my understanding is most people writing papers intend for them to be accepted by reputable peer-reviewed venues, but post to arXiv because those venues don't always allow for simple distribution.
If your papers aren't going to be accepted at reputable venues and you posted slop to arXiv before (and they noticed it!), seems reasonable that they only want reputable stuff from you in the future?
it's very silly, but not a big deal. Arxiv is becoming irrelevant these days anyways.
In fact would be better if they just banned AI, so we could just get off the luddite platforms.
Automated research is the future, end of story. And really it couldn't have come out at a better time, given the increasingly diminishing returns on human powered research.
If automated research is the future, it has to be research, not making stuff up.
Which of those two does "hallucinated references" fit into?
A "mistake" would be a typo in a real citation. A hallucinated citation is evidence of just plain laziness and negligence, which taints the entire submission.
No it is not. Seriously. All you need for this to happen is for your lab partner to ask AI to add a missing citation that they are already familiar with at the last minute before a midnight submission deadline, and for the AI to hallucinate something else, and for them to honestly miss this. It does not even imply any involvement on your part, let alone that either of you were lazy or negligent on the actual research or substance of the paper. The lack of any sympathy or imagination here is astounding.
There are no deadlines for journal submissions. Even if you felt you were running close to your revisions being due, an email to an editor will probably fix this for you. And what you described is still negligent, not verifying the garbage output bot did not in fact output garbage.
Even more, there are no deadlines for arXiv submissions.
Kinda. There is a deadline to appear in the next days posting and this can be important if e.g. you want to get something on the arxiv before a talk or a proposal deadline.
In other words: all it needs for your paper to have fraud is for your lab partner to add fraud to your paper.
I'm not seeing the problem here. The only problem is that your lab partner should be banned and not you. But being incentivised to check your co-author's work before submission isn't a bad thing.
You’re confusing the issue here by saying it’s not your fault, it’s your lab partner’s. We’re talking about why your lab partner did something wrong. You can assign blame for the wrong thing separately.
The citation is part of the substance of the paper. If you YOLOed in a citation without checking it, seems justified to suspect that you may have YOLOed in some data, or some analysis, or maybe even the conclusion.
Your constructed hypothetical makes it even worse. If there are 2+ people in this scenario who have good intentions, this should especially never happen. When you sign your name on a paper, you are nonetheless vouching for everything written in it, including the things you didn't personally write. You should absolutely be checking every single reference your co-author included and verifying that it says what your co-author claims it says. This is something you should have been doing completely independent of LLMs existing. This is something you're publishing publicly, something that may be associated with you and your career for the rest of your life, it is insanely negligent to not even read and verify what your co-author is adding.
The lack of understanding that you are responsible for the content you create, no matter what tools you use, is what's astounding.
If you cannot be bothered to check your references when writing academic quality papers then you have no place writing them in the first place. The punishment is not chopping off a finger, it is a polite reminder to do the bare minimum.
Well, in the good old days, when we have refereed journals, it would be part of the publishing process.
It's not the kind of mistake that is possible unless you're engaging in fraud anyway.
> It's not the kind of mistake that is possible unless you're engaging in fraud anyway.
Seriously? You can't fathom an honest researcher asking for AI to find a citation they know exists, and the AI inserting or modifying a citation incorrectly without them realizing?
If you find evidence of fraud by all means lay down the hammer. Using a single hallucinated citation like it's some kind of ironclad proxy just because you think they must be committing fraud is insane.
if you're not checking citations in the paper youre publishing AND trusting a non SOTA, hallucination prone ai model to come up with sources for it, its probably for the best of everyone that this paper isn't published.
yes there will be rare exceptions but in general i feel like this is a really good addition.
Why would you ask the ai to find a citation you know exists? Just reach for that citation.
if an llm does the work, you did not write it or research it, the llm did. you have no business crediting yourself as an author.
if someone writes a paper and an entirely different person takes credit for it without even bothering to check if the actual writer just made shit up, they deserve a lifetime ban. seems like a year is a very light punishment.
Yes, having AI write something and not checking it yourself is sure to lead to hallucination, hence, it is a fraudulent way to write.
>Seriously? You can't fathom an honest researcher asking for AI to find a citation they know exists
Assumptions:
1. The entire document is loaded into an AI editor
2. The researcher is asking an AI editor to work on his references
3. The researcher has not checked his own references.
This could be avoided at 1, 2 or 3. But even just 1 implies that the researcher knows that they have a hot potato and might critically fuck up and lose all credibility. Being in that scenario and committing to 2 and 3 is at least extreme negligence.
If you are citing a work you paste a citation to that work. If you are bullshitting you ask an AI to come up with a citation. Jesus, there is zero reason to ever "generate a citation" if you are not, in fact, commiting fraud.
I much agree. But I wonder shouldn't the citations all be hyperlinks and thus easy to verify?
How specific are the citations? If it's “Sentence 4 on page 97 supports” or “Paper says ‘___’” then I imagine it would be fairly easy. If it's “(__ page long) paper supports x”, then very difficult?
Verifying that the reference you cite actually exists is the absolute minimum standard for academic work. It is not optional, not something to skip because of a deadline, and not something to outsource blindly to hallucination-prone AI.
If someone cannot meet that bar, they have no business publishing research papers. I have written academic papers myself, and I find it astonishing that people are trying to justify this as if it were some understandable workflow mistake. At that point it is simply slop with academic formatting. Post it on a blog or somewhere else, but do not put it into the scientific record.
A one-year ban is not a lifetime ban. Maybe six months would also have been enough, but the author can use that time to think about whether they should verify references next time — and to manually check every other citation.
I would not necessarily go as far as calling it fraud, but if you cannot even verify that the reference you are citing actually exists, you are not ready to publish research papers.
Deadlines are not an excuse here. Checking whether a cited book, paper, or passage exists is the absolute minimum standard for scientific work, not an optional extra. I have written academic papers myself, and I find it astonishing that people are trying to justify this as if it were some understandable workflow mistake. At that point it is simply slop with academic formatting.
A one-year ban is not a lifetime ban. Maybe six months would also have been enough, but the point is that the author gets time to think about whether they should verify references next time. They can also use that time to manually check every other citation.
What's the difference between a "hallucinated" citation and consciously inserting reference to a non-existent paper and hopping it goes unnoticed? How do we determine which one was done consciously and which was "a minor first time mistake"?
Your standards are lower than what they would accept at my high-school. Seriously.
And generally, if you are generating papers with LLMs, let other LLMs read them. Why would we waste human hours considering something that was generated? At this point publish your prompt because that's the actual work you're doing.
A citation is where you derived knowledge... If you haven't checked it and you are submitting something that should represent a ton of labour (and which will consume labour to review), you don't understand what you're doing. It is not just crossing T's and dotting I'd.
Your being set behind is less important than the fact that your publishing is setting everyone else behind.
Such a banned person is being helped to "step out of the way", and someone more competent will assuredly step forward to consume the limited maintenance labour more thoughtfully
> Your being set behind is less important than the fact that your publishing is setting everyone else behind
One hallucinated citation does not in any way imply anyone is being left behind. All it means nobody is checked that particular line of the manuscript after it was written. The rest of the paper could still be solid and treated accordingly. If you find evidence of the contrary, of course treat it accordingly, but this is so obviously not that.
> One hallucinated citation does not in any way imply anyone is being left behind.
The parent said “setting” others behind, which refers to lost time.
Being “left” behind implies a degraded trajectory, which is defined not by time lost, but by the final destination.
Different but related things (e.g. lost time can indeed affect your final destination, for instance, after growing old correcting a scourge of hallucinated citations - which should have been table stakes all along).
You clearly misunderstand. You cite a work in your paper because you have read that work, and build upon it or want to refer to it to back up a specific claim. Generating references is fraud period, because you are implying that you have read a work when in fact you just asked an AI "please insert some reference-shaped text here" to make it look like a proper paper. It is sadly not a necessary, but certainly a VERY sufficient, reason to conclude a paper is fraudulent.
> There's no need to permanently cripple someone's ability to progress their life or contribute to humanity
I don't think you need to publish on arXive to contribute meaningfully to humanity.
> That's punitive instead of rehabilitative.
Unfortunately science is competitive. Yours is a race to the bottom where the people who can afford the most expensive models and who are least concerned with the truth can publish the most papers and benefit financially and professionally by doing so. This is not a zero sum arena, grant money and opportunities will possibly be rewarded to them, and not to another team who is producing more careful and genuine output.
While this is certainly a welcome step, I hope there is more work done to fix the underlying problem of easily creating correct BibTeX entries for the cited papers. Citations for any given paper can come from a wide range of journals with various publishers, conferences, and preprints. The same paper can be available from multiple sources with varying details, e.g. arXiv and the conference website. Tools like Zotero have certainly made it significantly easier to extract citations from webpages of publication, but I still find issues with the extracted BibTeX details. While author names and titles are often extracted correctly, I still have to manually ensure that details like publication venue, year, volume number, page number, URL, etc. are extracted correctly and also shown correctly in LaTeX format. Different publications can use different citation styles. This can unfortunately lead to taking shortcuts with AI-generated citation data due to the lack of an easy and unified approach to extract consistent citation data. I am not sure whether hallucinated citations are being generated in the main manuscript or in a separate BibTeX file, so I may be a bit off in my understanding.
> Our Code of Conduct states that by signing your name as an author of a paper, each author takes full responsibility for all its contents, irrespective of how the contents were generated (Dieterrich, T. G.)
Good.
If it’s not worth your time to check the output of your LLM carefully, it’s not worth my time to read it.
Unfortunately, it's probably not worth your time to read 99% of arxiv papers, LLM generated or otherwise.
Ever pick a random one and really dive in?
Agreed. There was already too much human generated slop in academia.
And I’m not talking about good faith research that didn’t pan out, I mean research that is completely useless for any other purpose other than convincing a casual observer that the authors are doing research.
There needs be to a careful vetting before such adverse actions. If somebody includes a name and pushed it without express permission, does everyone get the ban? I agree that implemented the right way, this is good.
Plus afaik you can add any co-author you want without validation. So you can ban everyone on arxiv with one paper with one sentence.
Seeing the usual LLM hypers angry replying to this on twitter is such a tell. Just like the comments on the LLM poisoning articles, some people just can't accept that some people don't like LLMs and get upset when you put any amount of hindrance to their rapid acceptance.
Crazy that this is graytexted. So basically HN consensus is that we need to be hyper and accelerate llm adoption everywhere.
Bonkers. At the same time peak hn
Good; academic literature is in crisis because of all of the slop. Forcing some consequences on easily-detectable hallucinations can only be a good thing
It's not just AI, though. I did a doctorate in physics about 40 years back, and bad references were a problem back then.
Doesn't matter if it is AI hallucinations or entirely human scientific fraud, the problem is the same, and the solution works fine for both cases.
If you can't validate that your bibliography is full of real articles, you shouldn't get published.
LLMs have just poured gasoline on the fire.
In what way? Surely something like the source not quite saying what was cited, or mixing up citations, rather than inventing them outright?
That, and mixing reference details from multiple sources and messing it up.
Let's say you read a paper on Arxiv but cite the version that was submitted to a journal or conference, without realizing that the authors made changes to the version they submitted and forgot to upload them to Arxiv.
In physics, references which just didn't exist. That could be that the author made it up, but often it's because they transcribed the reference from another paper without reading it - we know because a few people have deliberately introduced fake references to trace how far they would go. The reasons are not the same as for AI, but the problem they produce is the same.
References which don't accurately reflect the quoted material seem more common in other subjects.
"Bad", like, you literally just made them up? I hope that would have been a problem.
Well, I certainly didn't make them up. But it was common to follow a reference and find that there was no paper on the other end.
Which is why the angry replies on Twitter from AI hype accounts is so funny. You should get penalised for fake references and profanity in your submissions, even if you wrote your slop longhand. I don't know why anyone would have an issue with this policy.
Yes and ffs arrows kill people too but we don't bring that up every time we talk about what to do with guns.
It's been pretty eye opening watching Craig Wright (of bitcoin fakery fame) flooding out LLM generated 'academic' papers and even having some of them accepted.
He's toast if SSRN were to adopt a similar policy.
Had a colleague submit a paper with literal AI slop left in the text, got hit with a nasty revision request. Check your drafts before you submit, people. The reviewers will find it.
Also check your LaTeX comments, Arxiv makes those publicly visible!!!
I'm a screen reader user and usually read papers as raw TeX. I've seen everything: slurs, demeaning comments towards reviewers and professors, admissions of fraud, instructions to coauthors to commit further fraud before paper submission to mask the earlier fraud... it's all there. There's far less of it than I would think, definitely <1% of papers, but it's there.
I think it would be useful to run an LLM anti-fraud pass on the TeX source of all new arxiv papers. It wouldn't catch everything, but it would catch some of the dumbest fraudsters.
On the positive side, you can also find stronger claims that didn't survive review, additional explanations that didn't make the cut due to the conference's page limit, as well as experimental results that the authors felt weren't really worth including. Those need to be approached with an abundance of caution, but are genuinely useful sometimes.
Sad the suggestion here is to just disguise the slop to make it harder for reviewers to spot rather than not submitting slop to begin with.
Should be more harsh in my opinion.
[flagged]
It seems a good idea to ban cheating, but how hard is it, especially in new reasoning/agents contexts to validate references?
The deeper question is whether legitimate AI generated results are allowed or not? Test - In the extreme - think proof of Riemann Hypothesis autonomously generated (end to end) formally proven - is it allowed or not?
This is not about banning cheating, it’s about banning inaccurate information.
You don’t need to solve everything, catching a few thousand non existent citations with such a policy is on its own a net benefit.
It is allowed as long as it’s verified.
The thread specifically points out that if authors can’t be arsed to simply proofread their text the rest can not be trusted either.
It’s a simple heuristic against low quality submissions, not an anti-ai measure.
In that case, you would just not do a reference. End to end autonomous science might have fewer concrete citations as the contributing knowledge is just the sum of the training data of the model.
If you use AI correctly, nobody should be able to tell that it was used at all.
There already exists multiple tools for automatically verifying references. This measure will likely only filter out the laziest and most incompetent of AI slop submissions. It's a very modest raising of the bar, but comes at zero cost to honest researchers.
I expect arXiv will still have problems with slop submissions but, at least, their references should actually exist going forward.
It isn't "cheating" they're concerned with, it's sloppiness. This dictum isn't some sort of AI ban, but instead simply that if there is evidence that it was so low effort that the work includes such blatant problems, it's just adding noise.
> think proof of Riemann Hypothesis autonomously generated (end to end) formally proven - is it allowed or not?
Sorry to be rude, but this seems like a dumb question. I want science to progress. A primary purpose of these journals is to progress science. A full proof of the Riemann Hypothesis progresses science. I don't care how it was produced, if Hitler is coauthor, etc, I just care that it is correct. Whether the authors should be rewarded for whatever methods they used can be a separate question.
Terence Tao had a nice talk from the Future of Mathematics conference posted yesterday [0] that shapes a lot of my own feelings on this matter.
The short of it is he argues how first to correctness shouldn't be the only goal / isn't a great optimisation incentive. Presentation and digestibility of correct results is a missing 1/3 when you've finished generation and verification. I completely agree with him. You don't just need an AI generated proof of the Reimann Hypothesis. You would really like it to be intentional and structured for others to understand.
A really beautiful quote I learned of in the talk is this:
> "We are not trying to meet some abstract production quota of definitions, theorems, and proofs. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about math." - William Thurston