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.
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
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.
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.🧵
877 downloads! Super prime as well as Pythagorean, Sexy, Cousin and Strong prime. Also, a rare Bell prime: 877 ways to partition a set of 7 elements.
Version 1.2 with Lean 4 formalization at 200 downloads!
Grateful to those who find sedenions interesting!
doi.org/10.5281/zenodo.18357723
#Math
Version 1.2 with Lean 4 formalization at 200 downloads!
Grateful to those who find sedenions interesting!
doi.org/10.5281/zenodo.18357723
#Math
February 3, 2026 at 3:35 AM
877 downloads! Super prime as well as Pythagorean, Sexy, Cousin and Strong prime. Also, a rare Bell prime: 877 ways to partition a set of 7 elements.
Version 1.2 with Lean 4 formalization at 200 downloads!
Grateful to those who find sedenions interesting!
doi.org/10.5281/zenodo.18357723
#Math
Version 1.2 with Lean 4 formalization at 200 downloads!
Grateful to those who find sedenions interesting!
doi.org/10.5281/zenodo.18357723
#Math
For the #NumberTheory crowd - 797 is a beauty.
It’s a Super Prime: 139th prime (and 139 is prime),↔️ Two-Sided Truncatable (797, 97, 7 AND 79, 7 are all prime), Palindromic: 797,➕ Additive: 7+9+7 = 23 (Prime), Pythagorean: 11^2 + 26^2=797, and a Chen Prime.
#Math #Primes #OpenScience #Sedenions
It’s a Super Prime: 139th prime (and 139 is prime),↔️ Two-Sided Truncatable (797, 97, 7 AND 79, 7 are all prime), Palindromic: 797,➕ Additive: 7+9+7 = 23 (Prime), Pythagorean: 11^2 + 26^2=797, and a Chen Prime.
#Math #Primes #OpenScience #Sedenions
January 31, 2026 at 3:46 AM
For the #NumberTheory crowd - 797 is a beauty.
It’s a Super Prime: 139th prime (and 139 is prime),↔️ Two-Sided Truncatable (797, 97, 7 AND 79, 7 are all prime), Palindromic: 797,➕ Additive: 7+9+7 = 23 (Prime), Pythagorean: 11^2 + 26^2=797, and a Chen Prime.
#Math #Primes #OpenScience #Sedenions
It’s a Super Prime: 139th prime (and 139 is prime),↔️ Two-Sided Truncatable (797, 97, 7 AND 79, 7 are all prime), Palindromic: 797,➕ Additive: 7+9+7 = 23 (Prime), Pythagorean: 11^2 + 26^2=797, and a Chen Prime.
#Math #Primes #OpenScience #Sedenions
797 downloads! Version 1.2 with Lean 4 formalization has 93% download-to-view ratio (136/146) just one week after update on Zenodo.
The Canonical Six zero divisor patterns compute from 16D sedenions to 256D in BOTH Clifford and Cayley-Dickson algebras.
doi.org/10.5281/zenodo.18357723
#Math #Lean4
The Canonical Six zero divisor patterns compute from 16D sedenions to 256D in BOTH Clifford and Cayley-Dickson algebras.
doi.org/10.5281/zenodo.18357723
#Math #Lean4
January 31, 2026 at 3:41 AM
797 downloads! Version 1.2 with Lean 4 formalization has 93% download-to-view ratio (136/146) just one week after update on Zenodo.
The Canonical Six zero divisor patterns compute from 16D sedenions to 256D in BOTH Clifford and Cayley-Dickson algebras.
doi.org/10.5281/zenodo.18357723
#Math #Lean4
The Canonical Six zero divisor patterns compute from 16D sedenions to 256D in BOTH Clifford and Cayley-Dickson algebras.
doi.org/10.5281/zenodo.18357723
#Math #Lean4
Fitting milestone for research on zero divisor patterns in sedenions that work identically in both Cayley-Dickson (non-associative) and Clifford (associative) algebras with dimensional persistence to 256D.
Formally verified via Lean 4 through Harmonic's Aristotle.
Rare numbers, rare structure. 🎯
Formally verified via Lean 4 through Harmonic's Aristotle.
Rare numbers, rare structure. 🎯
January 21, 2026 at 5:16 AM
Fitting milestone for research on zero divisor patterns in sedenions that work identically in both Cayley-Dickson (non-associative) and Clifford (associative) algebras with dimensional persistence to 256D.
Formally verified via Lean 4 through Harmonic's Aristotle.
Rare numbers, rare structure. 🎯
Formally verified via Lean 4 through Harmonic's Aristotle.
Rare numbers, rare structure. 🎯
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
431 downloads - Sophie Germain prime! (both p and 2p+1 are prime).
'Canonical Six' zero divisor patterns in sedenions that are framework-independent (both Cayley-Dickson and Clifford algebras) with dimensional persistence through 256D, formally verified via Lean 4.
doi.org/10.5281/zenodo.17574868
'Canonical Six' zero divisor patterns in sedenions that are framework-independent (both Cayley-Dickson and Clifford algebras) with dimensional persistence through 256D, formally verified via Lean 4.
doi.org/10.5281/zenodo.17574868
January 14, 2026 at 5:35 PM
431 downloads - Sophie Germain prime! (both p and 2p+1 are prime).
'Canonical Six' zero divisor patterns in sedenions that are framework-independent (both Cayley-Dickson and Clifford algebras) with dimensional persistence through 256D, formally verified via Lean 4.
doi.org/10.5281/zenodo.17574868
'Canonical Six' zero divisor patterns in sedenions that are framework-independent (both Cayley-Dickson and Clifford algebras) with dimensional persistence through 256D, formally verified via Lean 4.
doi.org/10.5281/zenodo.17574868
Just hit 300 downloads on Zenodo! 📈
Incredibly grateful to see this many people digging into framework-independent zero divisors in Sedenions and beyond.
📖 doi.org/10.5281/zeno...
Downloaders, let's talk! Would love to hear your thoughts and ideas about it.
#Math #ZeroDivisors #256D #Sedenions
Incredibly grateful to see this many people digging into framework-independent zero divisors in Sedenions and beyond.
📖 doi.org/10.5281/zeno...
Downloaders, let's talk! Would love to hear your thoughts and ideas about it.
#Math #ZeroDivisors #256D #Sedenions
January 9, 2026 at 3:24 AM
Just hit 300 downloads on Zenodo! 📈
Incredibly grateful to see this many people digging into framework-independent zero divisors in Sedenions and beyond.
📖 doi.org/10.5281/zeno...
Downloaders, let's talk! Would love to hear your thoughts and ideas about it.
#Math #ZeroDivisors #256D #Sedenions
Incredibly grateful to see this many people digging into framework-independent zero divisors in Sedenions and beyond.
📖 doi.org/10.5281/zeno...
Downloaders, let's talk! Would love to hear your thoughts and ideas about it.
#Math #ZeroDivisors #256D #Sedenions
Thinking about alternative uses for neural processing units (NPUs) in modern computers. What other than AI could we use these for?
Seems to me that chat bots and image processing are entirely wasted potential and something something mathematical physics…
Sedenions.
Seems to me that chat bots and image processing are entirely wasted potential and something something mathematical physics…
Sedenions.
January 5, 2026 at 8:45 PM
Thinking about alternative uses for neural processing units (NPUs) in modern computers. What other than AI could we use these for?
Seems to me that chat bots and image processing are entirely wasted potential and something something mathematical physics…
Sedenions.
Seems to me that chat bots and image processing are entirely wasted potential and something something mathematical physics…
Sedenions.
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...
This leads to the next step up, the sedenions, which can be represented by a 16bit matrix algebra. Here, however, sedenions have zero divisors. Sedenions have addition, subtraction, and multiplication, but aren’t a division algebra.
January 4, 2026 at 9:52 AM
This leads to the next step up, the sedenions, which can be represented by a 16bit matrix algebra. Here, however, sedenions have zero divisors. Sedenions have addition, subtraction, and multiplication, but aren’t a division algebra.
Encountering the term TOPS (Trillion Operations Per Second), I subsequently read about modern NPUs (Neural Processing Units), which primarily compute low resolution matrix multiplication.
What can you do with a 16bit matrix?
SEDENIONS.
Turns out that sedenions are EVERYWHERE in machine learning.
What can you do with a 16bit matrix?
SEDENIONS.
Turns out that sedenions are EVERYWHERE in machine learning.
January 4, 2026 at 9:33 AM
Encountering the term TOPS (Trillion Operations Per Second), I subsequently read about modern NPUs (Neural Processing Units), which primarily compute low resolution matrix multiplication.
What can you do with a 16bit matrix?
SEDENIONS.
Turns out that sedenions are EVERYWHERE in machine learning.
What can you do with a 16bit matrix?
SEDENIONS.
Turns out that sedenions are EVERYWHERE in machine learning.
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
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
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...
Shoot Koebisu: Singular structures and geometric holonomy in the zero divisor set of the sedenions https://arxiv.org/abs/2512.13002 https://arxiv.org/pdf/2512.13002 https://arxiv.org/html/2512.13002
December 16, 2025 at 6:37 AM
Shoot Koebisu: Singular structures and geometric holonomy in the zero divisor set of the sedenions https://arxiv.org/abs/2512.13002 https://arxiv.org/pdf/2512.13002 https://arxiv.org/html/2512.13002
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...
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.
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