There's no disagreement, the algebraic one is the correct one, obviously. Anyone that says differently is wrong. :)
Being an engineer by training, I never got exposed to much algebra in my courses (beyond the usual high school stuff in high school). In fact did not miss it much either. Tried to learn some algebraic geometry then... oh the horror. For whatever reason, my intuition is very geometric and analytic (in the calculus sense). Even things like counting and combinatorics, they feel weird, like dry flavorless pretzels made of dried husk. Calculus, oh that's different, it's rich savoury umami buttery briskets. Yum.
That's not the interesting part. The interesting part is that I thought everyone is the same, like me.
It was a big and surprising revelation that people love counting or algebra in just the same way as I feel about geometry (not the finite kind) and feel awkward in the kind of mathematics I like.
It's part of the reason I don't at all get the hate that school Calculus gets. It's so intuitive and beautifully geometric, what's not to like. .. that's usually my first reaction. Usually followed by disappointment and sadness -- oh no they are contemplating about throwing such a beautiful part away.
"The Axiom of Choice is obviously true, the Well-ordering theorem obviously false, and who can tell about Zorn's lemma?"
(attributed to Jerry Bona)
Obviously.
Is there agreement Gaussian integers?
This disagreement seems above the head of non mathematicians, including those (like me) with familiarity with complex numbers
Another "xyz" domain that doesn't resolve on my network.
Yep- there’s some issues representing complex numbers in 3D space. You may want to check out quaternions.
The whole substack is great, I recommend reading all of it if you are interested in infinity
He's also very active at Stack Exchange
– https://stackexchange.com/users/510234/joel-david-hamkins
– https://mathoverflow.net/users/1946/joel-david-hamkins
There's no disagreement, the algebraic one is the correct one, obviously. Anyone that says differently is wrong. :)
Being an engineer by training, I never got exposed to much algebra in my courses (beyond the usual high school stuff in high school). In fact did not miss it much either. Tried to learn some algebraic geometry then... oh the horror. For whatever reason, my intuition is very geometric and analytic (in the calculus sense). Even things like counting and combinatorics, they feel weird, like dry flavorless pretzels made of dried husk. Calculus, oh that's different, it's rich savoury umami buttery briskets. Yum.
That's not the interesting part. The interesting part is that I thought everyone is the same, like me.
It was a big and surprising revelation that people love counting or algebra in just the same way as I feel about geometry (not the finite kind) and feel awkward in the kind of mathematics I like.
It's part of the reason I don't at all get the hate that school Calculus gets. It's so intuitive and beautifully geometric, what's not to like. .. that's usually my first reaction. Usually followed by disappointment and sadness -- oh no they are contemplating about throwing such a beautiful part away.
"The Axiom of Choice is obviously true, the Well-ordering theorem obviously false, and who can tell about Zorn's lemma?"
(attributed to Jerry Bona)
Obviously.
Is there agreement Gaussian integers?
This disagreement seems above the head of non mathematicians, including those (like me) with familiarity with complex numbers
Another "xyz" domain that doesn't resolve on my network.
Yep- there’s some issues representing complex numbers in 3D space. You may want to check out quaternions.
https://web.archive.org/web/20251015174117/https://www.infin...
This one has the paywall, but the main site has no paywall currently.