> Mathematicians are, indeed, also paid to teach, peer-review, go to conferences and learn mathematics, but all of that better result in some damn good theorems.
As a mathematician who publishes theorems, I think this is mistaken. New theorems in abstract and pure fields of mathematics never had the economic value of what mathematicians are paid. Even creative works of art can be displayed but mathematical papers are unread by nobody except a tiny number of people who wouldn't want to pay all that much for them if they had to.
The economic value of mathematicians is to teach mathematics. Proving theorems is how we build the credentials we need to be trusted to be allowed to teach it. Teaching young and less young people how to navigate through a mathematical problem is how we make ourselves useful.
LLMs coming up with counter examples to obscure conjectures (albeit old and important to a small number of people) is only a threat in that it removes this ritual of belonging.
Many people are excellent teachers (and very competent mathematicians) without publishing new theorems, and many theorem producers are atrocious teachers.
Perhaps the pecking order may change. Or maybe something else will happen. Maybe society will decide to replace all its teachers with AI, or that mathematics is no longer worth learning. I don't know. But what I know is that nobody saw any of the papers I wrote or the theorems I proved and thought "that's money well spent".
I agree that calling someone a bad person for using one of the most common test images is excessive. However, regarding this:
> The subject of the photograph merely went along with it.
The subject of the photograph did ask for it to no longer be used. Here's a quote from her:
> I retired from modeling a long time ago. It’s time I retired from tech, too.
> to defiantly do the opposite.
If the policing comes from third party for virtue signalling, this is fair game. Here, I'd just suggest that respecting her wish is just common courtesy and consider someone who defiantly doesn't as a somewhat rude person.
Because I have personally never seen "jazzes" pluralised and I didn't think of it.
Maths and math are both used, and the reason I used the plural form is not because I insist on anything but because it is the most commonly used of the two. I personally don't mind either forms.
With that said, linguistically using the plural for either is a bit odd, since that would imply you can pick "a" mathematic out of many, or "a" jazz out of many. But linguistic is not math (nor are lingustics maths), logic doesn't always apply.
Actually I think that maths and jazz have something in common in the general public peception that you have to be smart to "get it".
Nobody will try to perform a deep intellectual analysis of Lady Gaga's or Ed Sheeran's work the way they analyse Coltrane or Miles Davis (or Mozart, or Stravinsky). Those musicians are intellectuals of the sort Einstein is, unlike Lady Gaga or Ed Sheeran (in the collective perception). Jazz is intellectual music.
And when they analyse something, "smart" people use maths.
I am putting scare quotes around "smart" here to insist that this is largely a social perception and expected behaviour. However, maths can sensibly be used to analyse art, just like it's used elsewhere. This is not patronising, it is more that maths provides a useful language to talk about patterns.
GP reported on an opinion and called it insane. That's not an ad hominem.
There is a difference between judging an opinion and judging a person. If the response had been something like "what is crazy is to think the world can just switch off its dependence on petrol suddenly", I would not have reacted either.
If your intention is honest engagement with people you disagree with, you should refrain from ad-hominem attacks like this. Work with their arguments, not with their tastes or appearances.
If your intention is to ridicule them and convince yourself they are not worth discussing with, then ad-hominem is fine, but not engaging at all is better.
That the credit for the theorem belongs to Cantor is not under question. This is acknolwedged in the article:
>The revelation about Cantor’s result doesn’t undermine his legacy. He was still the first person to prove that there are more real numbers than whole ones, which is what ultimately opened up infinity to study.
What he is alleged to have plagiarised are the proofs, or at least one of the proofs. The original article by Goos [0] contains a lot more details about this, including a partial transcription of the letter by Dedekind that Cantor is accused of plagiarism. The story is complex.
1. Cantor's paper has two theorems: the countability of algebraic numbers and the uncountability of reals.
2. The proof of the former appears in Dedekind's letter, and Cantor acknowledges this in his response to the letter. Dedekind mentions in his letter that he only thought about proving this because of Cantor's prompt and only wrote it with the hope of helping Cantor. Dedekind felt that the proof by Cantor is "word for word" his, although it is quite the case. It is essentially the same proof though.
Cantor also felt that Dedekind's proof that the set of algebraic numbers is countable is essentially the same as his own proof of the countability of tuples. It remains that he didn't think of adapting that proof himself, and that Dedekind was the first to prove the theorem is not under question.
3. Dedekind was not the first to prove the uncountability of real numbers. However, he gave a number of ideas to Cantor in that same letter. Namely, he suggested proving the uncountability of the interval (0,1), and it seems that gave a pointer towards how to build the diagonalisation argument, although how this statement was useful to Cantor (page 76 of Goos' paper) escapes me.
EDIT: it's not a pointer to the diagonalisation argument, it is an argument why proving the theorem on (0,1) is enough.
4. Cantor proved the uncountability of reals shortly afterwards, and shared his proof with Dedekind. Dedekind simplified the proof in his reply, and Cantor seems to have come up with a similar simplification on his own. None of these letters are analysed in Goos' article.
5. Cantor published the two theorems; the first proof is essentially the same as Dedekin's, and the second proof is possibly the one Dedekind's simplified version of Cantor's. Dedekind is not acknowledged at all in that paper, due to academic politics.
Goos' paper is very detailed and quite readable. I recommend it. The site is pretty annoying and you can't download the article without creating an account, but you can read the article online.
Even if the most important theorem of the two is unquestionably creditable to Cantor, the first one should likewise unquestionably be credited to Dedekind, at least partially. This is where the accusation of plagiarism stems from.
Beyond the question on plagiarism, there is no question that Cantor and Dedekind worked together on this. The lack of acknowledgement by Cantor is certainly quite unfortunate.
We have gone from the industry clamouring that what's being done now is not possible and spending millions of lobbying money against it, to such laws spreading like wildfire.
The next step is the (inevitable) mess up because implementations won't be foolproof, followed by yet more millions of lobbying money being spent to amplify the effect of these mess ups.
Eventually we will come to a new normal. It will take time. But the hope is that the cat is out of the bag and we don't come back to a model that we know hurts children and pretend it's just how it is.
It depends how you define "good writing", which is too often associated with "proper language", and by extension with proper breeding. It is a class marker.
People have a distinct voice when they write, including (perhaps even especially) those without formal training in writing. That this voice is grating to the eyes of a well educated reader is a feature that says as much about the reader as it does about the writer.
Funnily enough, professional writers have long recognised this, as is shown by the never-ending list of authors who tried to capture certain linguistic styles in their work, particularly in American literature.
There are situations where you may want this class marker to be erased, because being associated with a certain social class can have negative impact on your social prospects. But it remains that something is being lost in the process, and that something is the personality and identity of the writer.
The comments suggest to recuse the judges from countries involved, or to remove the lowest or highest scores for each contestant.
If you remove the scores given by the judges from France and the US, the French pair wins. If you remove the lowest and highest score for each contestant, the French pair wins. If you do both of those things the French pair wins.
The individual judges scores can be found here [0].
This really comes across as a smear campaign by sore losers.
Do you have advice on how to use those calculators with modern tooling? For example I remember there were cross-compilers for the hp48 [0], do you use any of that (and how do you transfer data to/from the calculators)?
> The very fact people think they need to read (fiction) books released this year more than ones released before is baffling.
Do they really?
I was comparing rates of production vs consumption. It doesn't follow that what is being consumed on a given year is this year's production.
My guess is that most of the books written are read by hardly anyone. A few authors have a faithful following that will read their books as soon as it's out (which isn't too baffling). Reviewers and critics may indeed be more likely to review new books, which might impact people's decisions (again, not necessarily baffling). Book shops also put new books forward, but all those books tend to be the ones by trendy authors.
Other than the few fashionable books that come out each year you'll find reviewers like the one described in the article who don't seem to focus on new books (e.g. they talk about Dostoïevski), so it is not obvious that people feel that compelled to read new books.
> the backlog of books spread across millennia, not a century.
How much I agree with this! Plus, time does such a great job at filtering out the good from the bad (or the exceptional from the mundane). That's where lists of books entering the public domain, like this one [0], are important. Or the reviews [1].
Ultimately, the fact that there is more available to read than is possible even to the most voracious of readers means that most people will rely on guidance on what to read.
> Can't they figure out what books to get without being told?
Probably not? People are not "being told" what to read, they are given some opinionated advice which they can then decide to follow or not.
According to Wikipedia, 275,000 books are published each year in the US alone [0]. Most people (even excluding the many that don't read) will read well under 0.01% of that. Deciding which books to read without taking advice from someone more informed would not be optimal.
Sometimes it makes a lot more sense to rely of expert advice than to just make all decisions on your own.
This quote explains why the author thinks that it is a problem :
> with string theorists now virtually unemployable unless they can figure out how to rebrand as machine learning experts.
Their issue is (seemingly) not with the paper, but with the claim that these headlines feed a hype that attribute to string theory capabilities it doesn't have.
To be clear this is OP's argument, not mine. I am not sure I buy it, except perhaps for the fact that every other academic is expected to rebrand as an ML expert nowadays. It has more to do with ML hype than with string theory hype.
> Distance education is a tiny percentage of higher education though.
It is about a third of the students I teach, which amounts to several hundreds per term. It may be niche, but it is not insignificant, and definitely a problem for some of us.
> Even for distance education though, proctored testing centers have been around longer than the internet.
I don't know how much experience you have with those. Mine is extensive enough that I have a personal opinion that they are not scalable (which is the focus of the comment I was replying to). If you have hundreds of students disseminated around the world, organising a proctored exam is a logistical challenge.
It is not a problem at many universities yet, because they haven't jumped on the bandwagon. However domestic markets are becoming saturated, visas are harder to get for international students, and there is a demand for online education. I would be surprised that it doesn't develop more in the near future.
A limitation of written exams is in distance education, which simply was hardly a thing for the hundreds of years exams were used. Just like WFH is a new practice employers have to learn to deal with, study from home (SFH) is a phenomenon that is going to affect education.
The objections to SFH exist and are strikingly similar to objections to WFH, but the economics are different. Some universities already see value in offering that option, and they (of course) leave it to the faculty to deal with the consequences.
As a mathematician who publishes theorems, I think this is mistaken. New theorems in abstract and pure fields of mathematics never had the economic value of what mathematicians are paid. Even creative works of art can be displayed but mathematical papers are unread by nobody except a tiny number of people who wouldn't want to pay all that much for them if they had to.
The economic value of mathematicians is to teach mathematics. Proving theorems is how we build the credentials we need to be trusted to be allowed to teach it. Teaching young and less young people how to navigate through a mathematical problem is how we make ourselves useful.
LLMs coming up with counter examples to obscure conjectures (albeit old and important to a small number of people) is only a threat in that it removes this ritual of belonging.
Many people are excellent teachers (and very competent mathematicians) without publishing new theorems, and many theorem producers are atrocious teachers.
Perhaps the pecking order may change. Or maybe something else will happen. Maybe society will decide to replace all its teachers with AI, or that mathematics is no longer worth learning. I don't know. But what I know is that nobody saw any of the papers I wrote or the theorems I proved and thought "that's money well spent".