Hacker News: FillMaths

What Is Infinity?

FillMaths — Wed, 28 Oct 2026 16:04:23 +0000

Article URL: https://www.youtube.com/watch?v=c_2GaOzx-bc

Comments URL: https://news.ycombinator.com/item?id=50275916

Points: 1

# Comments: 0

Every game of chess ends prematurely

FillMaths — Wed, 21 Oct 2026 03:27:03 +0000

Article URL: https://www.infinitelymore.xyz/p/chess-games-end-one-move-early

Comments URL: https://news.ycombinator.com/item?id=50175709

Points: 4

# Comments: 0

New comment by FillMaths in "Every game of chess ends prematurely"

FillMaths — Sat, 17 Oct 2026 11:17:51 +0000

Penultimate chess is satire. To mock the checkmate condition of standard chess, which is similarly ridiculous, instead of playing natural chess: to capture the king.

Every game of chess ends prematurely

FillMaths — Sat, 17 Oct 2026 03:28:00 +0000

Article URL: https://www.infinitelymore.xyz/p/chess-games-end-one-move-early

Comments URL: https://news.ycombinator.com/item?id=50127644

Points: 1

# Comments: 3

Potential versus Actual Infinity

FillMaths — Wed, 09 Sep 2026 16:40:57 +0000

Article URL: https://www.youtube.com/watch?v=5nH_ucsb0_A

Comments URL: https://news.ycombinator.com/item?id=49629337

Points: 3

# Comments: 0

Why Human Giants Defy the Laws of Physics

FillMaths — Thu, 13 Aug 2026 16:09:47 +0000

Article URL: https://thereader.mitpress.mit.edu/why-human-giants-defy-the-laws-of-physics/

Comments URL: https://news.ycombinator.com/item?id=49288099

Points: 3

# Comments: 0

The Largest Tweetable Number – lectures on infinity (lecture 4)

FillMaths — Thu, 13 Aug 2026 00:23:54 +0000

Article URL: https://www.youtube.com/watch?v=3n115MgLFz0

Comments URL: https://news.ycombinator.com/item?id=49280336

Points: 1

# Comments: 0

The Paradox of Giants: Consequences in High Dimension

FillMaths — Thu, 23 Jul 2026 12:34:37 +0000

Article URL: https://www.youtube.com/watch?v=yiRx6dvC9jk

Comments URL: https://news.ycombinator.com/item?id=49020580

Points: 1

# Comments: 0

Supertasks: Doing Infinitely Many Things–Lectures on Infinity (Lecture 2)

FillMaths — Thu, 16 Jul 2026 10:45:58 +0000

Article URL: https://www.youtube.com/watch?v=h02divcjYcc

Comments URL: https://news.ycombinator.com/item?id=48932748

Points: 3

# Comments: 0

Zeno's Paradox and Infinite Sums – Lectures on Infinity (Lecture 1) [video]

FillMaths — Fri, 10 Jul 2026 05:22:13 +0000

Article URL: https://www.youtube.com/watch?v=4Y9p0yp8Mow

Comments URL: https://news.ycombinator.com/item?id=48856010

Points: 2

# Comments: 0

Humans Are Not Conscious

FillMaths — Thu, 02 Jul 2026 02:38:39 +0000

Article URL: https://philosophersmag.com/no-humans-are-not-conscious/

Comments URL: https://news.ycombinator.com/item?id=48755782

Points: 4

# Comments: 0

Fermat's last theorem in the natural ring of ordinals

FillMaths — Sun, 14 Jun 2026 20:59:17 +0000

Article URL: https://www.infinitelymore.xyz/p/fermats-last-theorem-in-the-ordinals

Comments URL: https://news.ycombinator.com/item?id=48532631

Points: 3

# Comments: 0

Joel David Hamkins – Set Theory, Pluralism and the Multiverse View – About Logic

FillMaths — Wed, 03 Jun 2026 15:13:08 +0000

Article URL: https://www.youtube.com/watch?v=060p4gKCCbg

Comments URL: https://news.ycombinator.com/item?id=48385200

Points: 3

# Comments: 0

Skolem's Paradox

FillMaths — Mon, 01 Jun 2026 19:38:05 +0000

Article URL: https://www.infinitelymore.xyz/p/skolems-paradox

Comments URL: https://news.ycombinator.com/item?id=48361585

Points: 1

# Comments: 0

The Book of Numbers

FillMaths — Wed, 20 May 2026 18:03:10 +0000

Article URL: https://www.infinitelymore.xyz/p/the-book-of-numbers

Comments URL: https://news.ycombinator.com/item?id=48211630

Points: 4

# Comments: 0

New comment by FillMaths in "Mathematicians disagree on the essential structure of the complex numbers (2024)"

FillMaths — Tue, 10 Feb 2026 22:41:06 +0000

The real field is categorically characterized (in second-order logic) as the unique complete ordered field, proved by Huntington in 1903. The complex field is categorically characterized as the unique algebraic closure of the real field, and also as the unique algebraically closed field of characteristic 0 and size continuum. I believe that you are speaking of the model-theoretic first-order notion of categoricity-in-a-cardinal, which is different than the categoricity remarks made in the essay.

New comment by FillMaths in "Mathematicians disagree on the essential structure of the complex numbers (2024)"

FillMaths — Tue, 10 Feb 2026 22:25:40 +0000

It's not about observers, but about mathematical structure and meaning. Without answering the questions, you are being ambiguous as to what the structure of C is. For example, if a particular copy of R is fixed as a subfield, then there are only two automorphisms---the trivial automorphism and complex conjugation, since any automorphism fixing the copy of R would have to be the identity on those reals and thus the rest of it is determined by whether i is fixed or sent to -i. Meanwhile, if you don't fix a particular R subfield, then there is a vast space of further wild automorphisms. So this choice of structure---that is, the answer to the questions I posed---has huge consequences on the automorphism group of your conception. You can't just ignore it and refuse to say what the structure is.

New comment by FillMaths in "Mathematicians disagree on the essential structure of the complex numbers (2024)"

FillMaths — Tue, 10 Feb 2026 19:20:08 +0000

Of course everyone agrees that this is a nice way to construct the complex field. The question is what is the structure you are placing on this construction. Is it just a field? Do you intend to fix R as a distinguished subfield? After all, there are many different copies of R in C, if one has only the field structure. Is i named as a constant, as it seems to be in the construction when you form the polynomials in the symbol i. Do you intend to view this as a topological space? Those further questions is what the discussion is about.

New comment by FillMaths in "Mathematicians disagree on the essential structure of the complex numbers (2024)"

FillMaths — Tue, 10 Feb 2026 17:59:46 +0000

You say that i is "the square root of -1", but which one is it? There are two. This is the point in the essay---we cannot tell the difference between i and -i unless we have already agreed on a choice of which square root of -1 we are going to call i. Only then does the other one become -i. How do we know that my i is the same as your i rather than your -i?

To fix the coordinate structure of the complex numbers (a,b) is in effect to have made a choice of a particular i, and this is one of the perspectives discussed in the essay. But it is not the only perspective, since with that perspective complex conjugation should not count as an automorphism, as it doesn't respect the choice of i.

New comment by FillMaths in "Mathematicians disagree on the essential structure of the complex numbers (2024)"

FillMaths — Tue, 10 Feb 2026 17:38:42 +0000

This one has the paywall, but the main site has no paywall currently.