the reals are fake. the complex numbers are ur first step out of the matrix. quaternions are where shit gets real. octonions are for only the most dedicated seekers of divine unity. anything past that, sedenions or trigintaduonions or whatever, is just mental illness
November 25, 2025 at 3:17 PM
the reals are fake. the complex numbers are ur first step out of the matrix. quaternions are where shit gets real. octonions are for only the most dedicated seekers of divine unity. anything past that, sedenions or trigintaduonions or whatever, is just mental illness
When they find out I'm interested in quaternions and octonions, some folks ask about the next algebra on this list: the sedenions.
I always say there's only one interesting thing known about those.
Now there are more!
Not enough to be profoundly exciting. But you gotta start somewhere.
I always say there's only one interesting thing known about those.
Now there are more!
Not enough to be profoundly exciting. But you gotta start somewhere.
The geometry of sedenion zero divisors
The sedenion algebra $\mathbb S$ is a non-commutative, non-associative, $16$-dimensional real algebra with zero divisors. It is obtained from the octonions through the Cayley-Dickson construction. The...
arxiv.org
July 19, 2026 at 10:05 PM
When they find out I'm interested in quaternions and octonions, some folks ask about the next algebra on this list: the sedenions.
I always say there's only one interesting thing known about those.
Now there are more!
Not enough to be profoundly exciting. But you gotta start somewhere.
I always say there's only one interesting thing known about those.
Now there are more!
Not enough to be profoundly exciting. But you gotta start somewhere.
I've always wished for this. Some day I hope to learn about the octonions, sedenions and Hurwitz's Theorem... these things get wild.
Octonions lose associativity, and with sedenions you can have two non-zero numbers that multiply to equal zero.
Octonions lose associativity, and with sedenions you can have two non-zero numbers that multiply to equal zero.
September 18, 2026 at 2:37 AM
I've always wished for this. Some day I hope to learn about the octonions, sedenions and Hurwitz's Theorem... these things get wild.
Octonions lose associativity, and with sedenions you can have two non-zero numbers that multiply to equal zero.
Octonions lose associativity, and with sedenions you can have two non-zero numbers that multiply to equal zero.
In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the real numbers; they are obtained by applying the Cayley–Dickson construction to the octonions, and as such the octonions are isomorphic to a subalgebra of the sedenions. Unlike the octonions...
August 20, 2025 at 12:06 AM
In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the real numbers; they are obtained by applying the Cayley–Dickson construction to the octonions, and as such the octonions are isomorphic to a subalgebra of the sedenions. Unlike the octonions...
So far, the sedenions seem unconnected to deep mathematics of any kind, while the octonions show up naturally in the theory of Jordan algebras, simple Lie groups and also supersymmetry.
Anyone who loves sedenions should figure out something deeply interesting about them.
Anyone who loves sedenions should figure out something deeply interesting about them.
December 10, 2025 at 12:42 PM
So far, the sedenions seem unconnected to deep mathematics of any kind, while the octonions show up naturally in the theory of Jordan algebras, simple Lie groups and also supersymmetry.
Anyone who loves sedenions should figure out something deeply interesting about them.
Anyone who loves sedenions should figure out something deeply interesting about them.
191 downloads. A Sophie Germain Prime (2p + 1 = 383). We are inspired by the French mathematician and dare to venture with her perseverance beyond octonions with Applied Pathological Mathematics.
doi.org/10.5281/zeno...
#SophieGermain #Sedenions #FrontierMath #MathSky #SciSky #AIResearch #DeepTech
doi.org/10.5281/zeno...
#SophieGermain #Sedenions #FrontierMath #MathSky #SciSky #AIResearch #DeepTech
January 4, 2026 at 1:00 AM
191 downloads. A Sophie Germain Prime (2p + 1 = 383). We are inspired by the French mathematician and dare to venture with her perseverance beyond octonions with Applied Pathological Mathematics.
doi.org/10.5281/zeno...
#SophieGermain #Sedenions #FrontierMath #MathSky #SciSky #AIResearch #DeepTech
doi.org/10.5281/zeno...
#SophieGermain #Sedenions #FrontierMath #MathSky #SciSky #AIResearch #DeepTech
I have actually, they're quite cool, but I never found any decent use.
There's also Sedenions, but that's even less useful when it comes to games and things haha
There's also Sedenions, but that's even less useful when it comes to games and things haha
November 30, 2025 at 4:38 AM
I have actually, they're quite cool, but I never found any decent use.
There's also Sedenions, but that's even less useful when it comes to games and things haha
There's also Sedenions, but that's even less useful when it comes to games and things haha
211 downloads. A Chen Prime. p + 2 = 213, a semiprime (3 x 71). While the establishment polishes the "Nice Math" of the Octonions, we are exploring 16-dimensional sedenions and beyond. Shout-out to legendary Chinese mathematician Chen Jingrun. #NotNiceMath #Sedenions #Truth
doi.org/10.5281/zeno...
doi.org/10.5281/zeno...
January 4, 2026 at 8:38 PM
211 downloads. A Chen Prime. p + 2 = 213, a semiprime (3 x 71). While the establishment polishes the "Nice Math" of the Octonions, we are exploring 16-dimensional sedenions and beyond. Shout-out to legendary Chinese mathematician Chen Jingrun. #NotNiceMath #Sedenions #Truth
doi.org/10.5281/zeno...
doi.org/10.5281/zeno...
TIL : there exist "sound" and well-known algebraic structures in power-of-two dimensions: real numbers, complex valuations, quaternions. Other kinds of hypercomplex numbers are octonions (dimension 8), sedenions (dimension 16). Just learnt about a 32-dimensional algebra, called trigintaduonions
January 11, 2025 at 11:09 AM
TIL : there exist "sound" and well-known algebraic structures in power-of-two dimensions: real numbers, complex valuations, quaternions. Other kinds of hypercomplex numbers are octonions (dimension 8), sedenions (dimension 16). Just learnt about a 32-dimensional algebra, called trigintaduonions
500+ DOWNLOADS on Zenodo! 🎉📈
My paper on The Canonical Six crossed the 500-mark with a 71% conversion rate. Verified by #Lean4 with Harmonic Math's Aristotle. Moving high-dimensional algebra from "pathological" to predictable.
🔗 doi.org/10.5281/zeno...
#Math #ZeroDivisors #TwoAlgebras #Sedenions
My paper on The Canonical Six crossed the 500-mark with a 71% conversion rate. Verified by #Lean4 with Harmonic Math's Aristotle. Moving high-dimensional algebra from "pathological" to predictable.
🔗 doi.org/10.5281/zeno...
#Math #ZeroDivisors #TwoAlgebras #Sedenions
January 17, 2026 at 9:01 PM
500+ DOWNLOADS on Zenodo! 🎉📈
My paper on The Canonical Six crossed the 500-mark with a 71% conversion rate. Verified by #Lean4 with Harmonic Math's Aristotle. Moving high-dimensional algebra from "pathological" to predictable.
🔗 doi.org/10.5281/zeno...
#Math #ZeroDivisors #TwoAlgebras #Sedenions
My paper on The Canonical Six crossed the 500-mark with a 71% conversion rate. Verified by #Lean4 with Harmonic Math's Aristotle. Moving high-dimensional algebra from "pathological" to predictable.
🔗 doi.org/10.5281/zeno...
#Math #ZeroDivisors #TwoAlgebras #Sedenions
It's tangential, I know, but I think one of the reasons that numbers such as quaternions, sedenions and octonions are not more widely appreciated is that they share notation with vectors.
A better notation might help them to be understood as numbers.
A better notation might help them to be understood as numbers.
July 24, 2024 at 1:22 PM
It's tangential, I know, but I think one of the reasons that numbers such as quaternions, sedenions and octonions are not more widely appreciated is that they share notation with vectors.
A better notation might help them to be understood as numbers.
A better notation might help them to be understood as numbers.
I love sedenions and I did figure out something deeply interesting about them.
zenodo.org/records/1757...
zenodo.org/records/1757...
Framework-Independent Zero Divisor Patterns in Higher-Dimensional Cayley-Dickson Algebras: Discovery and Verification of The Canonical Six
We report the discovery of 12 zero divisor patterns in 16-dimensional sedenion space exhibiting dimensional persistence and framework-dependent behavior, with six patterns demonstrating framework inde...
zenodo.org
January 2, 2026 at 11:21 PM
I love sedenions and I did figure out something deeply interesting about them.
zenodo.org/records/1757...
zenodo.org/records/1757...
191 downloads. A Sophie Germain Prime (2p + 1 = 383). We are inspired by the French mathematician and dare to venture with her perseverance beyond octonions with Applied Pathological Mathematics.
doi.org/10.5281/zeno...
#SophieGermain #Sedenions #FrontierMath #MathSky #SciSky #AIResearch #DeepTech
doi.org/10.5281/zeno...
#SophieGermain #Sedenions #FrontierMath #MathSky #SciSky #AIResearch #DeepTech
January 4, 2026 at 12:54 AM
191 downloads. A Sophie Germain Prime (2p + 1 = 383). We are inspired by the French mathematician and dare to venture with her perseverance beyond octonions with Applied Pathological Mathematics.
doi.org/10.5281/zeno...
#SophieGermain #Sedenions #FrontierMath #MathSky #SciSky #AIResearch #DeepTech
doi.org/10.5281/zeno...
#SophieGermain #Sedenions #FrontierMath #MathSky #SciSky #AIResearch #DeepTech
Niels Gresnigt: Sedenions, Clifford Algebras, and Three Fermion Generations: A Focused Review https://arxiv.org/abs/2609.10569 https://arxiv.org/pdf/2609.10569 https://arxiv.org/html/2609.10569
September 11, 2026 at 6:57 AM
Niels Gresnigt: Sedenions, Clifford Algebras, and Three Fermion Generations: A Focused Review https://arxiv.org/abs/2609.10569 https://arxiv.org/pdf/2609.10569 https://arxiv.org/html/2609.10569
Svetlana Zhilina
Diameter of the commutativity graph of the real sedenions
https://arxiv.org/abs/2608.26890
Diameter of the commutativity graph of the real sedenions
https://arxiv.org/abs/2608.26890
August 28, 2026 at 4:37 PM
Svetlana Zhilina
Diameter of the commutativity graph of the real sedenions
https://arxiv.org/abs/2608.26890
Diameter of the commutativity graph of the real sedenions
https://arxiv.org/abs/2608.26890
Svetlana Zhilina: Diameter of the commutativity graph of the real sedenions https://arxiv.org/abs/2608.26890 https://arxiv.org/pdf/2608.26890 https://arxiv.org/html/2608.26890
August 28, 2026 at 6:50 AM
Svetlana Zhilina: Diameter of the commutativity graph of the real sedenions https://arxiv.org/abs/2608.26890 https://arxiv.org/pdf/2608.26890 https://arxiv.org/html/2608.26890
sorry about my uninformed joke.. but FYI gemini 3.0 exactly makes the same type of "joke" for sedenions.. but then, it has answers for everything.. even when it does not know anything...
December 10, 2025 at 1:45 PM
sorry about my uninformed joke.. but FYI gemini 3.0 exactly makes the same type of "joke" for sedenions.. but then, it has answers for everything.. even when it does not know anything...
Super cool stuff! What do you think of the sedenions? They are not a division algebra, but they do seem interesting!
December 10, 2025 at 10:44 AM
Super cool stuff! What do you think of the sedenions? They are not a division algebra, but they do seem interesting!
i have discovered the sedenions and i am happy
December 9, 2025 at 11:12 PM
i have discovered the sedenions and i am happy
G. P. Wilmot: Automorphisms of Sedenions https://arxiv.org/abs/2512.07210 https://arxiv.org/pdf/2512.07210 https://arxiv.org/html/2512.07210
December 9, 2025 at 6:40 AM
G. P. Wilmot: Automorphisms of Sedenions https://arxiv.org/abs/2512.07210 https://arxiv.org/pdf/2512.07210 https://arxiv.org/html/2512.07210
structure is identified with 3-cycles and modes that reduce sets of 84 zero divisors to just 7, in most cases, such as for the sedenions, and identifies the subalgebas of the power associative algebras that provide zero divisors thus defining the [3/5 of https://arxiv.org/abs/2505.11747v1]
May 20, 2025 at 6:05 AM
structure is identified with 3-cycles and modes that reduce sets of 84 zero divisors to just 7, in most cases, such as for the sedenions, and identifies the subalgebas of the power associative algebras that provide zero divisors thus defining the [3/5 of https://arxiv.org/abs/2505.11747v1]
extended to 15 dimensions generating another 100 algebras as well as the sedenions. [4/4 of https://arxiv.org/abs/2505.06011v1]
May 12, 2025 at 6:05 AM
extended to 15 dimensions generating another 100 algebras as well as the sedenions. [4/4 of https://arxiv.org/abs/2505.06011v1]
The Universe of Numbers, including Transcendentals, Octonions, Sedenions, Surreal, and Nimbers.
(The word "Nimbers" is spelled correctly. Every real number can be expressed as a complex number where the imaginary part is zero. Increase your happiness level by adding p-adic
https://x.com/picko…
(The word "Nimbers" is spelled correctly. Every real number can be expressed as a complex number where the imaginary part is zero. Increase your happiness level by adding p-adic
https://x.com/picko…
November 8, 2025 at 2:59 AM
The Universe of Numbers, including Transcendentals, Octonions, Sedenions, Surreal, and Nimbers.
(The word "Nimbers" is spelled correctly. Every real number can be expressed as a complex number where the imaginary part is zero. Increase your happiness level by adding p-adic
https://x.com/picko…
(The word "Nimbers" is spelled correctly. Every real number can be expressed as a complex number where the imaginary part is zero. Increase your happiness level by adding p-adic
https://x.com/picko…
New result in higher-dimensional algebra:
The 6 framework-independent bilateral zero divisor patterns in 16D sedenions, aka The Canonical Six, have P-vector images that lie on the E₈ lattice first shell and form a single Weyl orbit. Lean 4 proven, zero sorry stubs.🧵
The 6 framework-independent bilateral zero divisor patterns in 16D sedenions, aka The Canonical Six, have P-vector images that lie on the E₈ lattice first shell and form a single Weyl orbit. Lean 4 proven, zero sorry stubs.🧵
February 27, 2026 at 1:59 AM
New result in higher-dimensional algebra:
The 6 framework-independent bilateral zero divisor patterns in 16D sedenions, aka The Canonical Six, have P-vector images that lie on the E₈ lattice first shell and form a single Weyl orbit. Lean 4 proven, zero sorry stubs.🧵
The 6 framework-independent bilateral zero divisor patterns in 16D sedenions, aka The Canonical Six, have P-vector images that lie on the E₈ lattice first shell and form a single Weyl orbit. Lean 4 proven, zero sorry stubs.🧵