Top Tweets for #Mathgazing
[#Mathgazing] at @OpenAI’s proofs · Day 06/21 · Part 3/3
Paper 032 💀 Withdrawn: "A tricky use of K3 mirror symmetry"
OpenAI’s Proposition 2.1 attempted to use homological mirror symmetry to construct a perfect complex F on the mirror side and obtain a bound on Ext^2(F,F).
The idea is interesting, but also delicate. So let us first look at what is actually known about mirror symmetry for K3 surfaces.
Mirror symmetry for K3 surfaces is very rich. Classical lattice mirror symmetry, the SYZ picture, and homological mirror symmetry all have substantial results here.
1. Classical mirror symmetry
For Calabi��Yau threefolds, mirror symmetry famously exchanges Hodge numbers such as h^{1,1} and h^{2,1}
For K3 surfaces, this tells us much less because every K3 surface has the same Hodge diamond.
The finer structure is the integral Hodge structure on H^2(X, Z).
The Global Torelli theorem says that two complex K3 surfaces are isomorphic if and only if their second integral cohomology groups are Hodge isometric. Further, a given Hodge isometry is induced by an isomorphism if it preserves the Kähler cone.
This suggests that K3 mirror symmetry should focus not just on Hodge numbers, but on the Hodge structure on H^2(X, Z), together with the Picard lattice
c_1(Pic(X))=NS(X)\subset H^2(X, Z).
Building on earlier work of Pinkham and Nikulin, Dolgachev in 1995 developed mirror symmetry for lattice-polarized K3 surfaces.
Roughly, under suitable hypotheses, if the polarization lattice has rank r, then the mirror polarization lattice has rank 20-r. For a very general quartic K3 surface, the Picard rank is 1, so its classical mirror family has Picard rank 19. This is the mirror K3 that appears in Seidel’s quartic HMS, which OpenAI later uses in its construction.
2. Torus fibrations and the SYZ picture
Strominger, Yau, and Zaslow in 1996 proposed a geometric explanation of mirror symmetry through dual special Lagrangian torus fibrations.
K3 surfaces are particularly natural for this picture because hyperkähler rotation relates elliptic fibrations to special Lagrangian torus fibrations.
Gross and Wilson in 2000 studied Ricci-flat K3 metrics near a large complex structure limit. They showed that the metric collapses toward the base of an elliptic fibration. Away from the singular fibers, the geometry is well described by a semi-flat metric. Near the singular fibers, genuinely new local geometry appears.
3. Homological mirror symmetry
Kontsevich in 1994 proposed a categorical version of mirror symmetry:
D^\pi{Fuk}(X) = D^b{Coh}(Y).
On the symplectic side, morphisms are computed using Floer theory. On the algebraic side, morphisms are Ext groups.
If one can construct the right object on the Fukaya side, HMS can transfer it to a perfect complex F on the algebraic side and study object like Ext^2(F,F).
Seidel in 2003 proved homological mirror symmetry for the quartic K3 surface. Its mirror is obtained from a finite quotient of a quartic family, followed by resolution. A key part of his proof is to compare generating objects, their A_\infty-structures, and deformation theory on the two sides.
Sheridan and Smith in 2017 extended HMS to further K3 mirror pairs arising from generalized Greene–Plesser constructions.
Abouzaid in 2014 developed a family Floer construction that sends suitable Lagrangians to perfect complexes on a rigid analytic mirror, under some torus-fibration and unobstructedness assumptions.
OpenAI’s manuscript attempted to combine these ideas by using Seidel’s HMS result for the quartic factor and Abouzaid’s family Floer machinery for graph Lagrangians in the torus factor.
The plan is then:
1. construct a very special Lagrangian immersion on the A-side, satisfying several conditions on H^2 and self-intersection data.
2. prove that its Floer obstruction vanishes, so that it defines a genuine object of the Fukaya category
3. use homological mirror symmetry to transfer it to the B-side and obtain a perfect complex F with the required Euler pairings and a bound on Ext^2(F,F)
Proposition 7.1 was supposed to do first step and this is where the sign error occurs. It would be interesting to see if one can circumvent this problem.
![ivanswzhang's tweet photo. [#Mathgazing] at @OpenAI’s proofs · Day 06/21 · Part 3/3
Paper 032 💀 Withdrawn: "A tricky use of K3 mirror symmetry"
OpenAI’s Proposition 2.1 attempted to use homological mirror symmetry to construct a perfect complex F on the mirror side and obtain a bound on Ext^2(F,F).
The idea is interesting, but also delicate. So let us first look at what is actually known about mirror symmetry for K3 surfaces.
Mirror symmetry for K3 surfaces is very rich. Classical lattice mirror symmetry, the SYZ picture, and homological mirror symmetry all have substantial results here.
1. Classical mirror symmetry
For Calabi��Yau threefolds, mirror symmetry famously exchanges Hodge numbers such as h^{1,1} and h^{2,1}
For K3 surfaces, this tells us much less because every K3 surface has the same Hodge diamond.
The finer structure is the integral Hodge structure on H^2(X, Z).
The Global Torelli theorem says that two complex K3 surfaces are isomorphic if and only if their second integral cohomology groups are Hodge isometric. Further, a given Hodge isometry is induced by an isomorphism if it preserves the Kähler cone.
This suggests that K3 mirror symmetry should focus not just on Hodge numbers, but on the Hodge structure on H^2(X, Z), together with the Picard lattice
c_1(Pic(X))=NS(X)\subset H^2(X, Z).
Building on earlier work of Pinkham and Nikulin, Dolgachev in 1995 developed mirror symmetry for lattice-polarized K3 surfaces.
Roughly, under suitable hypotheses, if the polarization lattice has rank r, then the mirror polarization lattice has rank 20-r. For a very general quartic K3 surface, the Picard rank is 1, so its classical mirror family has Picard rank 19. This is the mirror K3 that appears in Seidel’s quartic HMS, which OpenAI later uses in its construction.
2. Torus fibrations and the SYZ picture
Strominger, Yau, and Zaslow in 1996 proposed a geometric explanation of mirror symmetry through dual special Lagrangian torus fibrations.
K3 surfaces are particularly natural for this picture because hyperkähler rotation relates elliptic fibrations to special Lagrangian torus fibrations.
Gross and Wilson in 2000 studied Ricci-flat K3 metrics near a large complex structure limit. They showed that the metric collapses toward the base of an elliptic fibration. Away from the singular fibers, the geometry is well described by a semi-flat metric. Near the singular fibers, genuinely new local geometry appears.
3. Homological mirror symmetry
Kontsevich in 1994 proposed a categorical version of mirror symmetry:
D^\pi{Fuk}(X) = D^b{Coh}(Y).
On the symplectic side, morphisms are computed using Floer theory. On the algebraic side, morphisms are Ext groups.
If one can construct the right object on the Fukaya side, HMS can transfer it to a perfect complex F on the algebraic side and study object like Ext^2(F,F).
Seidel in 2003 proved homological mirror symmetry for the quartic K3 surface. Its mirror is obtained from a finite quotient of a quartic family, followed by resolution. A key part of his proof is to compare generating objects, their A_\infty-structures, and deformation theory on the two sides.
Sheridan and Smith in 2017 extended HMS to further K3 mirror pairs arising from generalized Greene–Plesser constructions.
Abouzaid in 2014 developed a family Floer construction that sends suitable Lagrangians to perfect complexes on a rigid analytic mirror, under some torus-fibration and unobstructedness assumptions.
OpenAI’s manuscript attempted to combine these ideas by using Seidel’s HMS result for the quartic factor and Abouzaid’s family Floer machinery for graph Lagrangians in the torus factor.
The plan is then:
1. construct a very special Lagrangian immersion on the A-side, satisfying several conditions on H^2 and self-intersection data.
2. prove that its Floer obstruction vanishes, so that it defines a genuine object of the Fukaya category
3. use homological mirror symmetry to transfer it to the B-side and obtain a perfect complex F with the required Euler pairings and a bound on Ext^2(F,F)
Proposition 7.1 was supposed to do first step and this is where the sign error occurs. It would be interesting to see if one can circumvent this problem.](https://pbs.twimg.com/media/HUveBCKakAA3A0q.jpg)
[#Mathgazing at @OpenAI’s proofs · Day 05/21 · Part 2/3
Paper 032 💀Withdrawn: "so we got 1+1=0 wrong again?"]
Since even for a product of two K3 surfaces, Hodge conjecture is open. Let's just look at OpenAI's proof for S1\times S2 to make life easier.
The only nontrivial part are Hodge classes \alpha of type (2,2) on S1 \times S2, which corresponds to a Hodge map between transcendental cohomology T(S1) to T(S2).
By Kuga-Sataka constructions, for each K3 surface Si, we can associate an abelian vareity A_i and an embedding
k_i: T(S_i) \rightarrow H^2(A_i \times A_i,Q).
Then the rational (2,2) class is mapped by k_i, for i =1, 2 to rational (2,2) class beta in H^4(A_1\timesA_1\times A_2\times A_2,Q).
Two things to prove:
(1) \beta is algebraic on product of abelian varieties
(2) k_i for i=1,2 is algebraic, which together with (1) will imply that \alpha is algebraic on S1\times S2.
The interesting idea is that it tries to use homological mirror symmetry to prove that k_i is algebraic! This is exciting but, potentially dangerous.
The sign error in eq (7.8) makes I = -d-d into I = -d+d=0. Then apply the Eliashberg–Murphy 2013’s result result wrongly.
AI question: Is this because Eliashberg–Murphy 2013 is too promising to conclude the theorem, so it forces it self to believe 1+1=0? Or it still doesn't know how to compute 1+1 =2, even after claiming to solve NS equation?
Solution: replace every “+” with “++++++” to reduce the chance of a probabilistic model making a sign error. 😆😆
[#Mathgazing at @OpenAI’s proofs · Day 04/21 · Part 1/3
Paper 032 💀Withdrawn: The rational Hodge conjecture for products of K3 surfaces]
Withdrawn, but somewhere could still be interesting?
K3 surfaces are smooth compact complex surfaces with trivial canonical bundle and irregularity (h^{1,0}=0).
They are algebraic geometers' favorite examples for testing conjectures beyond curves and abelian varieties. For example, for a single projective K3 surface, the rational Hodge conjecture follows from the classical Lefschetz (1,1) theorem.
The interesting difficulties begin with products of K3 surfaces, and even the case (S\times S) is not completely understood in general.
OpenAI’s withdrawn manuscript 032 claimed the rational Hodge conjecture for arbitrary products (S_1\times\cdots\times S_n) of projective K3 surfaces!
---------------------------------------------------------
For the Hodge conjecture more broadly, I recommend the recent, nicely written articles by Burt Totaro and Claire Voisin on 🤠Terry Tao’s blog. Totaro gives a nice overview of recent progress on abelian varieties and Voisin discusses the variational aspects of the Hodge conjecture.
Here I’ll focus on K3 surfaces.
Kuga and Satake in 1967 constructed an abelian variety (A) from the Hodge structure of a polarized K3 surface, in such a way that the transcendental cohomology of the K3 is encoded in the cohomology of (A).
This is powerful because it relates the Hodge conjecture for K3 surfaces to the much richer theory of algebraic cycles on abelian varieties.
The difficulty is that the Kuga–Satake construction gives only a relation between Hodge structures. To relate algebraic cycles, we need the Kuga–Satake correspondence itself to be algebraic.
This is a major open problem in general. Here are a few cases that we know.
1. A product of two K3 surfaces (S\times S').
The interesting Hodge classes come from the tensor product of the transcendental cohomologies of (S) and (S'). These can be interpreted as morphisms between their transcendental Hodge structures.
The problem is then to construct algebraic correspondences on (S\times S') that realize these Hodge morphisms.
Buskin in 2015 proved that every rational Hodge isometry between two projective K3 surfaces is algebraic. Huybrechts in 2017 later gave another proof using twisted derived categories.
Beyond isometries, only partial progress is known, for example the work of Varesco in 2023.
2. Powers of the same K3 surface.
2.1 First, let us look at (S\times S).
Zarhin in 1983 proved that the algebra (E) of Hodge endomorphisms of the transcendental cohomology is in fact a number field, either totally real or CM.
For a very general polarized K3 surface, this endomorphism algebra (E) is (Q). In this case, the only transcendental Hodge endomorphisms are scalar multiples of the identity, represented by the diagonal. Hence the Hodge conjecture holds for (S\times S).
When (E\neq Q), extra Hodge endomorphisms appear, and one has to find explicit algebraic correspondences.
2.2 Higher powers of the same K3 surface.
Even when the square (S\times S) is understood, higher powers (S^n) can contain new Hodge tensors that do not already appear on the square.
Zarhin’s description of the Hodge group explains where these additional tensors can come from.
There are several important positive results in this direction.
Ramón Marí in 2005 proved the Hodge conjecture for all self-powers of a K3 surface when (E) is a CM field.
Varesco in 2022 showed that for certain families of K3 surfaces, algebraicity of the Kuga–Satake correspondence implies the Hodge conjecture for all powers.
More recently, Floccari in 2025 proved the Hodge conjecture for all powers of a new class of K3 surfaces associated with hyperkähler varieties of generalized Kummer type.
3. Products (S_1\times\cdots\times S_n) of different K3 surfaces.
You can now imagine the shock when OpenAI announced a proof for arbitrary products of K3 surfaces！
![ivanswzhang's tweet photo. [#Mathgazing at @OpenAI’s proofs · Day 04/21 · Part 1/3
Paper 032 💀Withdrawn: The rational Hodge conjecture for products of K3 surfaces]
Withdrawn, but somewhere could still be interesting?
K3 surfaces are smooth compact complex surfaces with trivial canonical bundle and irregularity (h^{1,0}=0).
They are algebraic geometers' favorite examples for testing conjectures beyond curves and abelian varieties. For example, for a single projective K3 surface, the rational Hodge conjecture follows from the classical Lefschetz (1,1) theorem.
The interesting difficulties begin with products of K3 surfaces, and even the case (S\times S) is not completely understood in general.
OpenAI’s withdrawn manuscript 032 claimed the rational Hodge conjecture for arbitrary products (S_1\times\cdots\times S_n) of projective K3 surfaces!
---------------------------------------------------------
For the Hodge conjecture more broadly, I recommend the recent, nicely written articles by Burt Totaro and Claire Voisin on 🤠Terry Tao’s blog. Totaro gives a nice overview of recent progress on abelian varieties and Voisin discusses the variational aspects of the Hodge conjecture.
Here I’ll focus on K3 surfaces.
Kuga and Satake in 1967 constructed an abelian variety (A) from the Hodge structure of a polarized K3 surface, in such a way that the transcendental cohomology of the K3 is encoded in the cohomology of (A).
This is powerful because it relates the Hodge conjecture for K3 surfaces to the much richer theory of algebraic cycles on abelian varieties.
The difficulty is that the Kuga–Satake construction gives only a relation between Hodge structures. To relate algebraic cycles, we need the Kuga–Satake correspondence itself to be algebraic.
This is a major open problem in general. Here are a few cases that we know.
1. A product of two K3 surfaces (S\times S').
The interesting Hodge classes come from the tensor product of the transcendental cohomologies of (S) and (S'). These can be interpreted as morphisms between their transcendental Hodge structures.
The problem is then to construct algebraic correspondences on (S\times S') that realize these Hodge morphisms.
Buskin in 2015 proved that every rational Hodge isometry between two projective K3 surfaces is algebraic. Huybrechts in 2017 later gave another proof using twisted derived categories.
Beyond isometries, only partial progress is known, for example the work of Varesco in 2023.
2. Powers of the same K3 surface.
2.1 First, let us look at (S\times S).
Zarhin in 1983 proved that the algebra (E) of Hodge endomorphisms of the transcendental cohomology is in fact a number field, either totally real or CM.
For a very general polarized K3 surface, this endomorphism algebra (E) is (Q). In this case, the only transcendental Hodge endomorphisms are scalar multiples of the identity, represented by the diagonal. Hence the Hodge conjecture holds for (S\times S).
When (E\neq Q), extra Hodge endomorphisms appear, and one has to find explicit algebraic correspondences.
2.2 Higher powers of the same K3 surface.
Even when the square (S\times S) is understood, higher powers (S^n) can contain new Hodge tensors that do not already appear on the square.
Zarhin’s description of the Hodge group explains where these additional tensors can come from.
There are several important positive results in this direction.
Ramón Marí in 2005 proved the Hodge conjecture for all self-powers of a K3 surface when (E) is a CM field.
Varesco in 2022 showed that for certain families of K3 surfaces, algebraicity of the Kuga–Satake correspondence implies the Hodge conjecture for all powers.
More recently, Floccari in 2025 proved the Hodge conjecture for all powers of a new class of K3 surfaces associated with hyperkähler varieties of generalized Kummer type.
3. Products (S_1\times\cdots\times S_n) of different K3 surfaces.
You can now imagine the shock when OpenAI announced a proof for arbitrary products of K3 surfaces！](https://pbs.twimg.com/media/HUlVfOYbgAEmuh7.jpg)
I read 3 papers as part of my 21-day #Mathgazing challenge of reading OpenAI's proofs. My conclusions so far are:
- OpenAI’s “proofs” are not even wrong.
- Fields medalists are taking their “claimed proofs” too seriously, as if they actually got it.
#Mathgazing at @Op@OpenAI’s proofs
#Mathgazing at @OpenAI’s proofs · Day 04/21
Today, we’ll dig for gold in OpenAI’s withdrawn manuscript 032, “The Rational Hodge Conjecture for Products of K3 Surfaces”!
#Mathgazing at @OpenAI’s proofs
- OpenAI’s “proofs” are not even wrong.
- Fields medalists, you are taking their “claimed proofs” too seriously, as if they actually got it.
It’s my unpopular irrelevant third-party opinion after the sampling of three papers during my on-going 21-day challenge of cherry picking what they proved.
I might pick a Lean verified one at some point.
I’m starting my 21-day challenge of #Mathgazing at #OpenAI’s proofs and sharing what I find interesting and what could go wrong.
Join me to defuse this nuclear bomb! 🧐
[#Mathgazing at @OpenAI’s proofs · Day 03/21 · Part 1/3
Paper 063: The generalized Mukai conjecture]
The (generalized) Mukai conjecture predicts a numerical criterion for a smooth Fano variety to be a product of projective spaces.
The original version uses the Fano index and the generalized version uses the pseudoindex.
OpenAI's manuscript 063 claims to prove this conjecture using Gromov-Witten invariants
[💡This idea sounds pretty plausible, but potentially dangerous since intuition and actual proof using GW aren't always matching. That's why it's called "virtual counts". This is where experts need to dig ideas out of noise💡 ]
Interestingly, at almost the same time, another human, Heath Pearson, obtained a proof of specific cases of the original conjecture using a different approach via Cox rings: https://t.co/3cVBFiEL25. He first obtained an AI-free proof under additional assumptions, and then with GPT-6 Astra, upgraded his statement by removing those extra assumptions.
See his paper https://t.co/3cVBFiEL25 for his AI disclosure and a comprehensive literature review.
----------------------------------------------------------
Background and difficulties👽:
Mukai introduced the original conjecture in 1988. Later, Wiśniewski introduced the pseudoindex in 1990, and Bonavero–Casagrande–Debarre–Druel formulated the generalized conjecture in 2002.
For dim 2, smooth complex Fano surfaces are classified as P2, P1 times P1, Blowup of P2 at m points for m between 1 and 8. The conjecture can be easily verified in each case.
For dim 3, smooth complex Fano threefolds are classified into 105 deformation families through the work of Iskovskikh and Mori–Mukai. One can use this classification to prove the original Mukai conjecture.
Later, in 2002, Bonavero–Casagrande–Debarre–Druel offered a new approach via extremal contraction and bypassed the classification in dimension 3 and solved dim 4 altogether.
For dim 5, Andreatta–Chierici–Occhetta proved the generalized Mukai conjecture in 2003 by studying families of rational curves. Novelli–Occhetta later, in 2009, gave shorter proofs for dimensions 4 and 5 and proved the conjecture more generally when the pseudoindex is at least one third of the dimension plus one.
For dim 6, the difficult remaining case is when the pseudoindex is 2. The case of pseudoindex 1 is trivial, and the known large-pseudoindex results cover pseudoindex at least 3. Several additional cases of pseudoindex 2 were proved later under geometric assumptions, including results by Novelli in 2012 and Suzuki in 2017.
In 2025, Gagliardi–Hofscheier–Pearson gave a proof of the generalized Mukai conjecture for Q-factorial spherical Fano varieties of all dimensions.
In 2026, the AI-improved version of Heath Pearson's work proved the original Mukai conjecture in all dimensions for Fano varieties whose canonical toric ambient variety arising from the Cox ring is smooth.
OpenAI's manusrcipt:
https://t.co/SqmvTd1Lc9
#Mathgazing #OpenAI #Math
How I plan to use AI in the #Mathgazing:
1. All expositions of human work will be human-written.
2. I only cherry-pick the interesting ideas of AI proofs via my multi-agentic "AI purifier".
3. My diligent AI friend from Anthropic will review the proof line by line.
![ivanswzhang's tweet photo. [#Mathgazing at @OpenAI’s proofs · Day 03/21 · Part 1/3
Paper 063: The generalized Mukai conjecture]
The (generalized) Mukai conjecture predicts a numerical criterion for a smooth Fano variety to be a product of projective spaces.
The original version uses the Fano index and the generalized version uses the pseudoindex.
OpenAI's manuscript 063 claims to prove this conjecture using Gromov-Witten invariants
[💡This idea sounds pretty plausible, but potentially dangerous since intuition and actual proof using GW aren't always matching. That's why it's called "virtual counts". This is where experts need to dig ideas out of noise💡 ]
Interestingly, at almost the same time, another human, Heath Pearson, obtained a proof of specific cases of the original conjecture using a different approach via Cox rings: https://t.co/3cVBFiEL25. He first obtained an AI-free proof under additional assumptions, and then with GPT-6 Astra, upgraded his statement by removing those extra assumptions.
See his paper https://t.co/3cVBFiEL25 for his AI disclosure and a comprehensive literature review.
----------------------------------------------------------
Background and difficulties👽:
Mukai introduced the original conjecture in 1988. Later, Wiśniewski introduced the pseudoindex in 1990, and Bonavero–Casagrande–Debarre–Druel formulated the generalized conjecture in 2002.
For dim 2, smooth complex Fano surfaces are classified as P2, P1 times P1, Blowup of P2 at m points for m between 1 and 8. The conjecture can be easily verified in each case.
For dim 3, smooth complex Fano threefolds are classified into 105 deformation families through the work of Iskovskikh and Mori–Mukai. One can use this classification to prove the original Mukai conjecture.
Later, in 2002, Bonavero–Casagrande–Debarre–Druel offered a new approach via extremal contraction and bypassed the classification in dimension 3 and solved dim 4 altogether.
For dim 5, Andreatta–Chierici–Occhetta proved the generalized Mukai conjecture in 2003 by studying families of rational curves. Novelli–Occhetta later, in 2009, gave shorter proofs for dimensions 4 and 5 and proved the conjecture more generally when the pseudoindex is at least one third of the dimension plus one.
For dim 6, the difficult remaining case is when the pseudoindex is 2. The case of pseudoindex 1 is trivial, and the known large-pseudoindex results cover pseudoindex at least 3. Several additional cases of pseudoindex 2 were proved later under geometric assumptions, including results by Novelli in 2012 and Suzuki in 2017.
In 2025, Gagliardi–Hofscheier–Pearson gave a proof of the generalized Mukai conjecture for Q-factorial spherical Fano varieties of all dimensions.
In 2026, the AI-improved version of Heath Pearson's work proved the original Mukai conjecture in all dimensions for Fano varieties whose canonical toric ambient variety arising from the Cox ring is smooth.
OpenAI's manusrcipt:
https://t.co/SqmvTd1Lc9
#Mathgazing #OpenAI #Math
How I plan to use AI in the #Mathgazing:
1. All expositions of human work will be human-written.
2. I only cherry-pick the interesting ideas of AI proofs via my multi-agentic "AI purifier".
3. My diligent AI friend from Anthropic will review the proof line by line.](https://pbs.twimg.com/media/HUfn2RibIAA9dmE.jpg)
Im doing a 21-day challenge on #Mathgazing at @OpenAI’s @OpenAI’s proofs
[Day 01/21 · Part 2/3 Paper 054: Kuznetsov’s rationality conjecture]
Some ideas that I find pretty cool👍:
1. The manuscript 054 uses g=0 descendant GW invariants to construct Q-endomorphisms of rational transcendental cohomology and considers the unital algebra they generate. This reminds me of Givental���s S-operators.
2. It claims a blowup formula for this algebra for smooth projective rationally connected fourfolds blown up along smooth surfaces. This reminds me of Iritani's blowup formula.
3. It uses this formula to track the pieces added/deleted through blowups/blowdowns and shows that exactly one contribution of the selected K3 type remains. This reminds me of KKPY 26.
Thoughts after Day 01/21 #Mathgazing at @OpenAI’s Manuscript 054:
1. Mathematicians, no need to update your CVs just yet. OpenAI’s internal model still has a looong way to go before it replaces you.
2. @OpenAI @AnthropicAI , pls build better harness for interpretability, semantic faithfulness and add more rounds of reviewers in your multiagent system.
3. I won’t cite these papers or any human papers with similar concerns raised by my Claude reviewer.
4. BUT there are ideas here worth exploring and arguments worth checking. Work them out, acknowledge the OpenAI's contribution and put your name on it!
I’ll cite you.
Last Seen Hashtags on Sotwe
gaysex #muscular
Seen from Chile
iremhelvacıoğlu
Seen from Turkey
Pasifgay
Seen from United States
eresunagrandisimapersonaPol
Seen from United States
melayutudung
Seen from Malaysia
AI短剧
Seen from Vietnam
omeglegame
Seen from Puerto Rico
gaylaos
Seen from United States
束胸
Seen from United States
minichat() +filter:native_video
Seen from Oman
Trends for you
Most Popular Users
Elon Musk 
@elonmusk
241.5M followers
Barack Obama
@barackobama
118.8M followers
Cristiano Ronaldo
@cristiano
114.6M followers
Donald J. Trump
@realdonaldtrump
111.8M followers
Narendra Modi
@narendramodi
107.1M followers
Rihanna
@rihanna
98.7M followers
NASA
@nasa
92.3M followers
Justin Bieber
@justinbieber
91.8M followers
KATY PERRY
@katyperry
90.1M followers
Taylor Swift
@taylorswift13
84M followers
Lady Gaga
@ladygaga
75.5M followers
Virat Kohli
@imvkohli
73.5M followers
Kim Kardashian
@kimkardashian
70.9M followers
YouTube
@youtube
68.8M followers
Neymar Jr
@neymarjr
66.5M followers
Bill Gates
@billgates
65.3M followers
Selena Gomez
@selenagomez
63.1M followers
The Ellen Show
@theellenshow
62.2M followers
CNN
@cnn
61.7M followers
X
@x
60.7M followers