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New evidence that Cantor plagiarized Dedekind?

quantamagazine.org

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Re: New evidence that Cantor plagiarized Dedekind?

#61

Post by layer8 »

dkarl wrote: post #53
antasvara wrote: post #33

Earlier quoted context omitted.

Take something like the integers (1,2,3,etc.). They are infinite; given an integer, you can always add 1 and get a new integer. However, there are "gaps" in that number line. Between 1 and 2, there are values that aren't integers. So the integers make a number line that is infinite, but that has gaps. Then we have something like the rational numbers. That's any number that can be expressed as a ratio of 2 integers (s…

I just don't understand why this was disturbing. Prior to the construction of the reals, the existence of irrational and transcendental numbers was disturbing, because they showed that previous constructions (rational numbers and algebraic numbers) were incomplete. If those gaps were disturbing, a construction without gaps should have been satisfying, reassuring, a resolution of tension. Was there some philosophical…

I think the issue was that most irrational/transcendental numbers aren’t finitely representable. This means that they are mathematical objects which, each of them individually, somehow consist of an infinity (e.g. an infinite decimal expansion). They are the result or end point of infinitely many steps (e.g. a converging sequence) that you can’t actually reach the end of in practice, and for most of them can’t even write down a finite description on what steps to perform, and which therefore arguably doesn’t “really” exist.

Another point of contention was the notion that the continuous number line would be formed out of dimensionless points. Numbers were thought of as residing on the line, but it was hard to grasp how a line could consist solely of a collection of points, since given any pair of points, there would always be a gap between them. “Clearly” they can’t be forming a contiguous line.

Re: New evidence that Cantor plagiarized Dedekind?

#62

Post by vessenes »

bhk wrote: post #45
Quekid5 wrote: post #44

Earlier quoted context omitted.

sqrt(2)

That's not a "gap" that you find by "zooming in". And how can it be a gap when it is occupied?

You’re thinking of this with the benefit of dedekind in your schooling - whether or not your calculus class told you about him.

Density - a gapless number line - was neither obvious nor easy to prove; the construction is usually elided even in most undergraduate calculus unless you take actual calculus “real analysis” courses.

The issue is this: for any given number you choose, I claim: you cannot tell me a number “touching” it. I can always find a number between your candidate and the first number. Ergo - the onus is on you to show that the number line is in fact continuous. What it looks like with the naive construction is something with an infinite number of holes.

Re: New evidence that Cantor plagiarized Dedekind?

#63

Post by jacquesm »

tchalla wrote: post #8
dang wrote: post #5

I think we can do without the baity title since most HN readers should know who Cantor and Dedekind are. Edit: okay, maybe not Dedekind. If someone wants to suggest a better title (i.e. more accurate and neutral, and preferably using representative language from the article itself), we can change it again.

> since most HN readers should know who Cantor and Dedekind are. Show up with your hands here if you didn’t know either Cantor or Dedekind.

Then you can just skip this submission and nobody will be the wiser.

Re: New evidence that Cantor plagiarized Dedekind?

#64

Post by tadfisher »

dvt wrote: post #59
wizzwizz4 wrote: post #27

Earlier quoted context omitted.

It's best practice to say something like "Noether's real story is recounted in my book [link]". This both establishes you as a subject matter expert, and stops your comments looking like disingenuous grift.

It's literally cited in his bio, and he's using his real name on HN. It's about as far as grift as it could be. If he's being curt, he's probably (rightfully) frustrated that "journalists" are getting such bottom-of-the-barrel facts wrong.

But surely you would agree that "my book" just wastes less time all around, and doesn't harm the author's message?

Re: New evidence that Cantor plagiarized Dedekind?

#65

Post by moefh »

zeroonetwothree wrote: post #16
mymacbook wrote: post #3

Earlier quoted context omitted.

Thank you! After Benj Edwards and Kyle Orland's Ars Technica article they published using AI (while saying they didn't), and all the while their article was about an AI agent publishing a hit piece on Scott Shambaugh (matplotlib maintainer), I feel like I now assume journalists are using AI and things need to be fact-checked just as we do for our AI interactions. I appreciate hearing about details like this and getti…

It’s not like journalists were very accurate before AI. Classic Gell-Mann amnesia

Being "not very inaccurate" is very different from publishing outright fabricated quotes, which is what Ars Technica did and later admitted to: https://arstechnica.com/staff/2026/02/editors-note-retractio...

Re: New evidence that Cantor plagiarized Dedekind?

#66

Post by shermantanktop »

zeroonetwothree wrote: post #16
mymacbook wrote: post #3

Earlier quoted context omitted.

Thank you! After Benj Edwards and Kyle Orland's Ars Technica article they published using AI (while saying they didn't), and all the while their article was about an AI agent publishing a hit piece on Scott Shambaugh (matplotlib maintainer), I feel like I now assume journalists are using AI and things need to be fact-checked just as we do for our AI interactions. I appreciate hearing about details like this and getti…

It’s not like journalists were very accurate before AI. Classic Gell-Mann amnesia

I see what you did there. Turning the page of time, I guess.

Re: New evidence that Cantor plagiarized Dedekind?

#67

Post by rvba »

lich_king wrote: post #10
leephillips wrote: post #2

“Noether, who was Jewish, fled from Germany to the U.S., where she died two years later from cancer” It wasn’t two years, and it wasn’t cancer. These details are unimportant to the (quite interesting) story, but the error is a sign that the author copies information from unreliable secondary sources, which puts the other facts in the article in doubt. I wrote to him about the error when the article first appeared, bu…

I have an opinion about the editorial style of Quanta that I don't think it's popular here (judging by how often they get upvoted), but I think it's a symptom of that. They cover science, but the template they consistently follow is a vague title that oversells the premise and then an article filled with human-interest details and appeals to implications. This makes it easy for everyone to follow along and have an op…

The articles are unreadable fluff

Re: New evidence that Cantor plagiarized Dedekind?

#68

Post by shermantanktop »

renewiltord wrote: post #14

This whole plagiarism thing is too overwrought these days. People discuss stuff and the idea forms in the discussion between the two. Then one writes it up. Oh he plagiarized the other. I don’t know man.

I’ve been in joint discussions where “the idea forming” was really one party thinking out loud and doing almost all the work, and the other providing approximately the same function as a rubber duck.

Sometimes the one doing the heavy lifting is me; sometimes it’s the other person, and I’m happy to make squeaky rubber duck noises that help. And with some people we have switched roles, even during the conversation. And perception will not track with reality because we’re all the hero of our own story.

Very hard to assign credit after the fact without a verbatim transcript, which written letters provide here.

Re: New evidence that Cantor plagiarized Dedekind?

#69

Post by wizzwizz4 »

dvt wrote: post #59
wizzwizz4 wrote: post #27

Earlier quoted context omitted.

It's best practice to say something like "Noether's real story is recounted in my book [link]". This both establishes you as a subject matter expert, and stops your comments looking like disingenuous grift.

It's literally cited in his bio, and he's using his real name on HN. It's about as far as grift as it could be. If he's being curt, he's probably (rightfully) frustrated that "journalists" are getting such bottom-of-the-barrel facts wrong.

> It's about as far as grift as it could be.

Indeed. I don't generally give grifters tips on how to disguise themselves.

Re: New evidence that Cantor plagiarized Dedekind?

#70

Post by fph »

dvt wrote: post #59
wizzwizz4 wrote: post #27

Earlier quoted context omitted.

It's best practice to say something like "Noether's real story is recounted in my book [link]". This both establishes you as a subject matter expert, and stops your comments looking like disingenuous grift.

It's literally cited in his bio, and he's using his real name on HN. It's about as far as grift as it could be. If he's being curt, he's probably (rightfully) frustrated that "journalists" are getting such bottom-of-the-barrel facts wrong.

A bio is not proper disclosure: it is hidden behind a link that you have to click, and it can be changed at any moment without leaving traces.
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