πŸ‡ΊπŸ‡¦ haxadecimal πŸš«πŸ‘‘
The Man Who Stole Infinity, by Joseph Howlett
https://www.quantamagazine.org/the-man-who-stole-infinity-20260225/
Demian Goos finally tracked down Dedekind's copies of letters he sent to Cantor, showing that Cantor on at least two occasions published papers on orders of infinity, based in part on Dedekind's work, without crediting him. The letters had been preserved by Dedekind's heirs, and were made available to Goos by Karin Richter.
#mathematics #infinity #continuum #Cantor #Dedekind
The Man Who Stole Infinity | Quanta Magazine

In an 1874 paper, Georg Cantor proved that there are different sizes of infinity and changed math forever. A trove of newly unearthed letters shows that it was also an act of plagiarism.

Quanta Magazine
Feb 26 at 4:45pmWeb
Show threadπŸ‡ΊπŸ‡¦ haxadecimal πŸš«πŸ‘‘Feb 26
The article explains one reason Georg Cantor didn't credit Richard Dedekind for the first paper: politics of mathematics publishing. Dedekind was on Leopold Kronecker's shit list, and Kronecker was on the editorial board of Crelle’s Journal.
Show threadDavid, a Bostonian in Tokyo.Feb 26

@brouhaha

And a quick read made it sound that Cantor's proof was _correct but ugly_, and given a correct but ugly proof, Dedekind came up with a better proof.

So it's still Cantor's idea that Cantor proved.

Show threadπŸ‡ΊπŸ‡¦ haxadecimal πŸš«πŸ‘‘Feb 26
@djl
Cantor published Dedekind's proofs. Dedekind did the proofs in response to Cantor's prior attempts. Even if you think Dedekimd only improved Cantor's proofs (which was not my takeaway from the article), at the very least Dedekind should have been listed as a coauthor.
Today, something like this could get a published academic paper retracted, and disciplinary action taken, possibly including termination of professorship (even if tenured).
Show threadActive MouseFeb 26

@brouhaha @djl my understanding was that cantor's first attempt was incorrect, but his second was correct, then Dedekind simplified it. That certainly deserves correct attribution but it seems obvious why it wasn't.

Inspired by this I went off to read Dedekind's 1888 monograph on foundations of Arithmetic and it's very readable! Though without a doubt it too has been refined now.

I had no idea how important Dedekind was to the beginnings of set theory!

Show threadDavid, a Bostonian in Tokyo.Feb 27

@ActiveMouse @brouhaha

Yes. That's a more careful reading.

In any case, the clickbait headline was obnoxious.

Dedekind's a biggy in a wide range of mathy things (rings (!!!), fields, ideals, irrational numbers, algebraic numbers). He's got plenty on his resume and doesn't need Cantor's results as well.

Show threadActive MouseFeb 27

@djl @brouhaha once you've constructed the real numbers from the rationals in a novel way you can pretty much retire.

I don't know if Dedekind or Cantor (or Bolzano?) first constructed the natural numbers from sets, but a construction is there in the 1888 treatise. It's interesting to see the approaches to infinity in these early works. I think you can see echoes of the later axiomatisation of infinity in the fact that Dedekind "proves" the existence of an infinite set by reference to his own realm of thought!

Show threadπŸ’‘πš‚π—†π–Ίπ—‹π—π—†π–Ίπ—‡ π™°π—‰π—‰π—ŒπŸ“±Feb 27
@brouhaha
It was never a proof to begin with anyway, anymore than if Cantor had written 1+1=3 and claimed that it "proved" that 1+1=3 πŸ™„
https://dotnet.social/@SmartmanApps/115642725878742794
πŸ’‘πš‚π—†π–Ίπ—‹π—π—†π–Ίπ—‡ π™°π—‰π—‰π—ŒπŸ“± (@[email protected])

Attached: 1 image 1/7 This air-quote #Mathematics unquote article https://www.quantamagazine.org/a-new-bridge-links-the-strange-math-of-infinity-to-computer-science-20251121/ keeps appearing in my feed, and I initially made some comments the first time, debunking it from a #Maths point-of-view, but given how it keeps popping up I think I need to do a more thorough #MathsMonday thread about it Firstly, the author is a Physics journo, so you can take what he says about #math with a grain of salt (for some reason I see a lot of them doing this overreach, instead of checking with a Mathematician)…

dotnet.social
Show threadπŸ‡ΊπŸ‡¦ haxadecimal πŸš«πŸ‘‘Feb 27
@SmartmanApps
Sorry, that is incorrect. Cantor most definitely did publish proofs of the existence of infinite sets of differing cardinalities, which have been accepted by essentially all mathematicians since the mid-20th century, if not earlier.
Cantor definitely upset many of his contemporary mathematicians' Apple carts.
Dedekind may not have gotten credit for his contribution to that, but he is credited with a proof by construction of the infinite set of real numbers.
Show threadπŸ’‘πš‚π—†π–Ίπ—‹π—π—†π–Ίπ—‡ π™°π—‰π—‰π—ŒπŸ“±Feb 27

@brouhaha
"that is incorrect" - no it isn't.

"Cantor most definitely did publish" - something, but it wasn't a proof, anymore than 1+1=3 "proves" 1+1=3 πŸ™„

"which have been accepted by essentially all mathematicians since the mid-20th century" - no they haven't. e.g. look up Finitism for starters

"real numbers" - all irrational reals are scalars, not numbers, that's their fundamental mis-understanding about numbers in the first place.

Show threadπŸ‡ΊπŸ‡¦ haxadecimal πŸš«πŸ‘‘Feb 27
@SmartmanApps
I'm not going to debate mathematical philosophy with anyone (finitist or otherwise) who denies the existence of the set ⁠ℕ. We'll just have to agree to disagree.