> In their 1872 papers, though, Cantor and Dedekind had found a way to construct a number line that was complete. No matter how much you zoomed in on any given stretch of it, it remained an unbroken expanse of infinitely many real numbers, continuously linked.
> Suddenly, the monstrosity of infinity, long feared by mathematicians, could no longer be relegated to some unreachable part of the number line. It hid within its every crevice.
I'm vaguely familiar with some of the mathematics, but I have no idea what this is trying to say. The infinity of the rational numbers had been known a thousand years prior by the Greeks, including by Zeno whom the article already mentioned. The Greeks also knew that some quantities could not be expressed as rational numbers.
I would assume the density of irrational numbers was already known as well? Give x < y, it's easy to construct x + (y-x)(sqrt(2))/2.
I don't get what "suddenly" became apparent.
pfortuny 35 seconds ago [-]
The continuum. Connectedness.
terminalbraid 19 minutes ago [-]
The density does not dictate cardinality which is what this article is about.
dang 22 minutes ago [-]
I think we can do without the baity title since most HN readers should know who Cantor and Dedekind are.
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.
tgv 1 minutes ago [-]
I'm here for the 19th century drama. Imagine the head lines!
I’ll go out on a limb and say the majority of HN users at this point do not know the context and implications of the impact of Cantor - would probably have only heard the name in the context of mathematics but no deeper
I’d go further and say the majority have not ever heard of the name Dedekind
zenethian 4 minutes ago [-]
I am not a mathematician; I barely knew who Cantor was and had never heard of Dedekind. I would have likely not read the article without the title being so sensational. Your assumption sits upon the tip of your nose.
leephillips 1 hours ago [-]
“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, but received no reply.
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 follow pretty consistently 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 opinion, but I feel like science is te backdrop, not the subject.
mymacbook 48 minutes ago [-]
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 getting the source directly. I hope Kristina Armitage and Michael Kanyongolo from Quanta Magazine respond and you can update us!
> Suddenly, the monstrosity of infinity, long feared by mathematicians, could no longer be relegated to some unreachable part of the number line. It hid within its every crevice.
I'm vaguely familiar with some of the mathematics, but I have no idea what this is trying to say. The infinity of the rational numbers had been known a thousand years prior by the Greeks, including by Zeno whom the article already mentioned. The Greeks also knew that some quantities could not be expressed as rational numbers.
I would assume the density of irrational numbers was already known as well? Give x < y, it's easy to construct x + (y-x)(sqrt(2))/2.
I don't get what "suddenly" became apparent.
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.
Show up with your hands here if you didn’t know either Cantor or Dedekind.
https://xkcd.com/2501
There really is an xkcd for everything
I’ll go out on a limb and say the majority of HN users at this point do not know the context and implications of the impact of Cantor - would probably have only heard the name in the context of mathematics but no deeper
I’d go further and say the majority have not ever heard of the name Dedekind
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, but received no reply.
Noether’s real story is recounted in https://amzn.to/3YZZB4W.
They cover science, but the template they follow pretty consistently 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 opinion, but I feel like science is te backdrop, not the subject.
I appreciate hearing about details like this and getting the source directly. I hope Kristina Armitage and Michael Kanyongolo from Quanta Magazine respond and you can update us!
Scott's Blog on Hit Piece: https://theshamblog.com/an-ai-agent-published-a-hit-piece-on... Ars Editor Note: https://arstechnica.com/staff/2026/02/editors-note-retractio... Ars Retraction: https://arstechnica.com/ai/2026/02/after-a-routine-code-reje...