Interesting that the folks who wrote a proof based on the 4Chan user's post listed him as a first author. In all of my experience, Mathematics truly seems to be the field with the highest integrity.
Mathematician here. I'd like to think we have high (not sure about highest) integrity. But I should also point out that the custom in the field is to list authors alphabetically by family name, and the paper in question (https://oeis.org/A180632/a180632.pdf) does not break with custom if you view "anonymous" as "family name"...
That's when she had to sit me down and explain that first author is super mega important in her field, not just who is literally listed first.
Perhaps ironically, the convention would then imply that newfag comes before oldfag.
This is only true in some fields of mathematics; many areas of mathematics do not follow this rule. (Also mathematician, and none of the papers I've been involved with have done the alphabetical thing.)
On the converse, psychology and economics seem to have the most problems in terms of reproducibility and fraud. This is because they are the easiest to falsify, and their results are interpreted according to less precise epistemology.
There’s no ‘Austrian school’ vs ‘Chicago school’ in maths (to my knowledge).
Also, the general public isn’t interested in pure maths, so there are less incentives to fake data so you can get a nice press release, or so you can publish your new book, or so that the government bureaucrat will subsidise your ‘research.’
If you think that psychology and economics have problems with reproducibility and fraud, you haven't seen the social sciences!
After all, Mathematics is not a natural science and hereby consensus must be reached.
I may well be wrong, would love some examples.
Don’t all roads lead to Rome? It’s like an engineer deciding to use SI or Imperial units, people have their opinions but at the end of the day both work.
In theoretical maths, yes.
In the same way some heterodox political philosophies may result in new moral systems, but it doesn’t really matter that these moral systems are different to the status quo, until someone uses it as an ideology for their revolution.
It’s probably good to have a variety of theory to choose from, except when your different theories result in different practical outcomes.
In mathematics you might compare groups that work with Vs without the Axiom of Choice, you can can have one group satisfied by an existence proof that asserts X exists otherwise a contradiction must exist and another group that only accept existence proofs that demonstrate a means to construct an example of X.
The habeas corpus divide :-)
If a proof is used by 3 people it won't have much scrutiny, but once major results start to be based on the proof, it'll get reviewed more carefully and either accepted or rejected in the long run. The ABC conjecture is probably the biggest example.
see Brouwer–Hilbert controversy ?
Later, he argued he found mathematical proofs of counterexamples of LEM. From above source:
> “Intuitionist Reflections on Formalism” of 1928 identifies and discusses four key differences between formalism and intuitionism, all having to do either with the role of PEM or with the relation between mathematics and language. Brouwer emphasises, as he had done in his dissertation, that formalism presupposes contentual mathematics at the metalevel. He also here presents his first strong counterexample, a refutation of PEM in the form ∀x∈R(Px∨¬Px), by showing that it is false that every real number is either rational or irrational. See the supplement on Strong Counterexamples.
To prove that I'm not just making this up out of my ass, here[1] is a statement from the American Mathematical Society that talks about it. I'll quote the meat of it here:
> In most areas of mathematics, joint research is a sharing of ideas and skills that cannot be attributed to the individuals separately. The roles of researchers are seldom differentiated (in the way they are in laboratory sciences, for example). Determining which person contributed which ideas is often meaningless because the ideas grow from complex discussions among all partners. Naming a "senior" researcher may indicate the relative status of the participants, but its purpose is not to indicate the relative merit of the contributions. Joint work in mathematics almost always involves a small number of researchers contributing equally to a research project.
> For this reason, mathematicians traditionally list authors on joint papers in alphabetical order. An analysis of journal articles with at least one U.S. based author shows that nearly half were jointly authored. Of these, more than 75% listed the authors in alphabetical order. In pure mathematics, nearly all joint papers (over 90%) list authors alphabetically.
Exceptions do exist, as alluded to by the "over 90%" number mentioned in the AMS statement. But, many of those are caused by transliteration artifacts (e.g. Author1 and Author2 are in alphabetical order in the language the paper was originally published in, but the English transliterated versions of their names are not).
See this Math Overflow post for all the gory details: https://mathoverflow.net/questions/19987/math-paper-authors-...
---
[0]: https://en.wikipedia.org/wiki/Odd_Aalen
[1]: http://www.ams.org/profession/leaders/CultureStatement04.pdf
For example, the recent papers on aperiodic monotiles have Dave Smith as the first author, even though his name doesn't come first alphabetically.
(I can also think of another recent example, which modesty forbids me to detail.)
In the case at hand, we did deliberately intend anon to be the lead author. (I was one of the ‘coauthors’ who helped to write it up.)
You know how the joke goes, right? “The axiom of choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn’s lemma?” [0]
I'm honestly not sure I could have resisted the temptation to ask him "What's yellow and equivalent to the axiom of choice?"[1] one day.
Okay, nevermind. I would have resisted, but I'd be chuckling about it off and on the whole time when I was sure he wasn't around, while I was doing my degree.
In all seriousness, though, proving the equivalence of AC, ZL, and WO was probably my first venture into "real" abstract mathematics in undergrad. For essentially the first time, there was no picture I could draw that would have any semblance of accuracy or utility, and yet at the end, the result popped right out just the same.
Unfortunately, I didn't make it to the independence of the Continuum Hypothesis that year, and had to move on to other courses. :/
---
[0]: AC, ZL, and WO are also equivalent to the Hausdorf maximal principle: in any poset (P, ≤), every totally ordered subset S is contained in some maximal totally ordered subset T. In some ways, HM is kind of the "dual" of ZL by swapping totally ordered subsets for elements, ⊆ for ≤, and push the whole thing up into the power set realm, I think you just get ZL trivially. Of course, I always found HMP much more intuitive than ZL... basically, AC > HM > ZL > WO in my mind, in descending order of intuitiveness.
[1]: Zorn's Lemon
When I visited IU in the '90's there was a new stoplight on E 3rd. Max got hit by a car when trundling into his office every day in Swain Hall East and his colleagues somehow convinced the city of Bloomington to put one up.
While misspending my youth playing 5-minute chess at Bear's Place up the street, Raymond Smullyan showed up and asked if he could kibitz. I can write a very short book titled "What is the Answer to that Question?" It would be much shorter than https://www.amazon.com/Million-Zeros-Douglas-Crockford/dp/19.... Bjarne told me the guy had gone crazy. He is right.
When I'm not yelling at clouds I write some things at https://keithalewis.github.io/math/.
Neat. I'll check that out.
I actually picked up a copy of Cohen's book [0] on CH a few weeks ago. It's in my "actually going to read this" pile right now. Looks pretty accessible, even for an ersatz graph theorist/combinatorialist such as myself.
In math, it's primarily because they want credit for the paper to go to the collaboration. This has the secondary effect of eliminating arguments about whose names go where. Is it the same way in those fields?
It may actually be professional golf, famous for players imposing penalties on themselves.
I said professional golf, not your father-in-law's scorecard.