How A.I. Just Blew Up a Key Tenet of Computer Science www.nytimes.com/2026/11/06/s...
#complexitytheory
#complexitytheory
How A.I. Just Blew Up a Key Tenet of Computer Science
A longstanding hypothesis held that some problems would always be hard for computers to solve quickly. But OpenAI disproved it — raising the possibility of radical new efficiencies.
www.nytimes.com
November 7, 2026 at 2:44 PM
How A.I. Just Blew Up a Key Tenet of Computer Science www.nytimes.com/2026/11/06/s...
#complexitytheory
#complexitytheory
Resilience and adaptive capacity: rethinking educational structures in the age of climate crisis | Open Access
Tal Gilead
3272-3291 | DOI: 10.1080/13504622.2026.2636179
#education #climatechange #complexitytheory #environmentaleducation #resilience #adaptation
doi.org/10.1080/1350...
Tal Gilead
3272-3291 | DOI: 10.1080/13504622.2026.2636179
#education #climatechange #complexitytheory #environmentaleducation #resilience #adaptation
doi.org/10.1080/1350...
November 10, 2026 at 12:03 PM
Resilience and adaptive capacity: rethinking educational structures in the age of climate crisis | Open Access
Tal Gilead
3272-3291 | DOI: 10.1080/13504622.2026.2636179
#education #climatechange #complexitytheory #environmentaleducation #resilience #adaptation
doi.org/10.1080/1350...
Tal Gilead
3272-3291 | DOI: 10.1080/13504622.2026.2636179
#education #climatechange #complexitytheory #environmentaleducation #resilience #adaptation
doi.org/10.1080/1350...
Oracle separations show proofs of quantumness and oblivious state preparation can exist even when P=NP and BQP=QCMA, challenging conjectures about necessary complexity conditions for quantum cryptographic primitives.
#QuantumAdvantage #ComplexityTheory #QuantumCryptography
#QuantumAdvantage #ComplexityTheory #QuantumCryptography
Quantum Advantage and Complexity Separations: Oracle Evidence Against Cryptographic Necessity
arxiv.org
November 4, 2026 at 6:08 AM
Oracle separations show proofs of quantumness and oblivious state preparation can exist even when P=NP and BQP=QCMA, challenging conjectures about necessary complexity conditions for quantum cryptographic primitives.
#QuantumAdvantage #ComplexityTheory #QuantumCryptography
#QuantumAdvantage #ComplexityTheory #QuantumCryptography
How a Profile Inequality Produces the 2.25 Bound
A Fourier-style wave sharpening into a fixed shape is a fitting opening for this proof route: many abstract ingredients eventually lock into one numerical constraint.
#matrixmultiplication #tensoralgebra #complexitytheory #mathematics
A Fourier-style wave sharpening into a fixed shape is a fitting opening for this proof route: many abstract ingredients eventually lock into one numerical constraint.
#matrixmultiplication #tensoralgebra #complexitytheory #mathematics
November 4, 2026 at 6:02 PM
How a Profile Inequality Produces the 2.25 Bound
A Fourier-style wave sharpening into a fixed shape is a fitting opening for this proof route: many abstract ingredients eventually lock into one numerical constraint.
#matrixmultiplication #tensoralgebra #complexitytheory #mathematics
A Fourier-style wave sharpening into a fixed shape is a fitting opening for this proof route: many abstract ingredients eventually lock into one numerical constraint.
#matrixmultiplication #tensoralgebra #complexitytheory #mathematics
Why 2.25 Is So Far Below 2.371177
A change from 2.371177 to 2.25 may look like a small decimal adjustment. For matrix multiplication exponents, it is anything but.
#matrixmultiplication #complexitytheory #tensors #computerscience
A change from 2.371177 to 2.25 may look like a small decimal adjustment. For matrix multiplication exponents, it is anything but.
#matrixmultiplication #complexitytheory #tensors #computerscience
November 4, 2026 at 2:01 PM
Why 2.25 Is So Far Below 2.371177
A change from 2.371177 to 2.25 may look like a small decimal adjustment. For matrix multiplication exponents, it is anything but.
#matrixmultiplication #complexitytheory #tensors #computerscience
A change from 2.371177 to 2.25 may look like a small decimal adjustment. For matrix multiplication exponents, it is anything but.
#matrixmultiplication #complexitytheory #tensors #computerscience
How Two Profile Inequalities Force Diagonal Growth
A local shape condition and a growth rule can combine into a global diagonal bound. Here the profile P(a,b) obeys discrete concavity in b: 2P(a,b) ≥ P(a,b+1) + P(a,b−1).
#discretemath #concavity #matrixmultiplication #complexitytheory
A local shape condition and a growth rule can combine into a global diagonal bound. Here the profile P(a,b) obeys discrete concavity in b: 2P(a,b) ≥ P(a,b+1) + P(a,b−1).
#discretemath #concavity #matrixmultiplication #complexitytheory
November 3, 2026 at 2:02 AM
How Two Profile Inequalities Force Diagonal Growth
A local shape condition and a growth rule can combine into a global diagonal bound. Here the profile P(a,b) obeys discrete concavity in b: 2P(a,b) ≥ P(a,b+1) + P(a,b−1).
#discretemath #concavity #matrixmultiplication #complexitytheory
A local shape condition and a growth rule can combine into a global diagonal bound. Here the profile P(a,b) obeys discrete concavity in b: 2P(a,b) ≥ P(a,b+1) + P(a,b−1).
#discretemath #concavity #matrixmultiplication #complexitytheory
The Two Inequalities Behind the 2.25 Bound
The key step is a growth-rate squeeze. Along the diagonal of a profile P, one argument gives a lower bound: P(a,a) ≥ a^(4/3). Another gives an upper bound: P(a,a) ≤ (2a−1)^(1/t).
#matrixmultiplication #complexitytheory #tensoralgebra #mathematics
The key step is a growth-rate squeeze. Along the diagonal of a profile P, one argument gives a lower bound: P(a,a) ≥ a^(4/3). Another gives an upper bound: P(a,a) ≤ (2a−1)^(1/t).
#matrixmultiplication #complexitytheory #tensoralgebra #mathematics
November 3, 2026 at 2:01 PM
The Two Inequalities Behind the 2.25 Bound
The key step is a growth-rate squeeze. Along the diagonal of a profile P, one argument gives a lower bound: P(a,a) ≥ a^(4/3). Another gives an upper bound: P(a,a) ≤ (2a−1)^(1/t).
#matrixmultiplication #complexitytheory #tensoralgebra #mathematics
The key step is a growth-rate squeeze. Along the diagonal of a profile P, one argument gives a lower bound: P(a,a) ≥ a^(4/3). Another gives an upper bound: P(a,a) ≤ (2a−1)^(1/t).
#matrixmultiplication #complexitytheory #tensoralgebra #mathematics
Why Matrix Multiplication’s ω Is an Infimum, Not a Minimum
The matrix multiplication exponent ω is not necessarily an exponent achieved by one miraculous algorithm.
#matrixmultiplication #complexitytheory #algorithms #math
The matrix multiplication exponent ω is not necessarily an exponent achieved by one miraculous algorithm.
#matrixmultiplication #complexitytheory #algorithms #math
November 1, 2026 at 2:01 PM
Why Matrix Multiplication’s ω Is an Infimum, Not a Minimum
The matrix multiplication exponent ω is not necessarily an exponent achieved by one miraculous algorithm.
#matrixmultiplication #complexitytheory #algorithms #math
The matrix multiplication exponent ω is not necessarily an exponent achieved by one miraculous algorithm.
#matrixmultiplication #complexitytheory #algorithms #math
Why Discrete Concavity Matters in the 2.25 Proof
A curve is concave when it lies above the chords joining pairs of points. This Short shows the discrete version: for neighboring profile values, 2P(a,b) ≥ P(a,b+1) + P(a,b−1).
#discreteconcavity #matrixmultiplication #complexitytheory #mathematics
A curve is concave when it lies above the chords joining pairs of points. This Short shows the discrete version: for neighboring profile values, 2P(a,b) ≥ P(a,b+1) + P(a,b−1).
#discreteconcavity #matrixmultiplication #complexitytheory #mathematics
November 2, 2026 at 6:02 PM
Why Discrete Concavity Matters in the 2.25 Proof
A curve is concave when it lies above the chords joining pairs of points. This Short shows the discrete version: for neighboring profile values, 2P(a,b) ≥ P(a,b+1) + P(a,b−1).
#discreteconcavity #matrixmultiplication #complexitytheory #mathematics
A curve is concave when it lies above the chords joining pairs of points. This Short shows the discrete version: for neighboring profile values, 2P(a,b) ≥ P(a,b+1) + P(a,b−1).
#discreteconcavity #matrixmultiplication #complexitytheory #mathematics
What the Matrix Multiplication Exponent ω Measures
Why does one matrix entry take three multiplications here? To compute the top-left entry, pair the first row of A with the first column of B: 1×9, 2×6, and 3×3, then add the results.
#matrixmultiplication #algorithms #complexitytheory #mathematics
Why does one matrix entry take three multiplications here? To compute the top-left entry, pair the first row of A with the first column of B: 1×9, 2×6, and 3×3, then add the results.
#matrixmultiplication #algorithms #complexitytheory #mathematics
October 31, 2026 at 10:02 PM
What the Matrix Multiplication Exponent ω Measures
Why does one matrix entry take three multiplications here? To compute the top-left entry, pair the first row of A with the first column of B: 1×9, 2×6, and 3×3, then add the results.
#matrixmultiplication #algorithms #complexitytheory #mathematics
Why does one matrix entry take three multiplications here? To compute the top-left entry, pair the first row of A with the first column of B: 1×9, 2×6, and 3×3, then add the results.
#matrixmultiplication #algorithms #complexitytheory #mathematics
Novel phase diagram reveals when computing transverse field Ising properties transitions from polynomial-time tractable to NP-hard intractable. Efficient classical and quantum algorithms provided for tractable regime.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
Computational Phase Diagram for the Transverse Field Ising Model
arxiv.org
November 1, 2026 at 3:48 PM
Novel phase diagram reveals when computing transverse field Ising properties transitions from polynomial-time tractable to NP-hard intractable. Efficient classical and quantum algorithms provided for tractable regime.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
Proves that solving linear equations on higher-order networks (Hodge Laplacian systems) is BQP-hard, establishing worst-case hardness limits for quantum advantage in network analysis.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
Quantum Complexity of Solving Linear Equations on Higher-Order Networks
arxiv.org
October 31, 2026 at 11:05 AM
Proves that solving linear equations on higher-order networks (Hodge Laplacian systems) is BQP-hard, establishing worst-case hardness limits for quantum advantage in network analysis.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
Why a 0.121177 Drop in ω Is So Unusual
In matrix-multiplication research, the hard-won improvements have often lived in the fourth decimal place. This animation puts two of them on a magnified scale: about 0.0016, then about 0.00012.
#matrixmultiplication #complexitytheory #algorithms #mathematics
In matrix-multiplication research, the hard-won improvements have often lived in the fourth decimal place. This animation puts two of them on a magnified scale: about 0.0016, then about 0.00012.
#matrixmultiplication #complexitytheory #algorithms #mathematics
October 31, 2026 at 2:01 PM
Why a 0.121177 Drop in ω Is So Unusual
In matrix-multiplication research, the hard-won improvements have often lived in the fourth decimal place. This animation puts two of them on a magnified scale: about 0.0016, then about 0.00012.
#matrixmultiplication #complexitytheory #algorithms #mathematics
In matrix-multiplication research, the hard-won improvements have often lived in the fourth decimal place. This animation puts two of them on a magnified scale: about 0.0016, then about 0.00012.
#matrixmultiplication #complexitytheory #algorithms #mathematics
Proves that solving linear equations on higher-order networks (Hodge Laplacian systems) is BQP-hard, establishing worst-case hardness limits for quantum advantage in network analysis.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
Quantum Complexity of Solving Linear Equations on Higher-Order Networks
arxiv.org
October 31, 2026 at 11:05 AM
Proves that solving linear equations on higher-order networks (Hodge Laplacian systems) is BQP-hard, establishing worst-case hardness limits for quantum advantage in network analysis.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
OpenAI shared a paper and Lean formalization claiming a subexponential algorithm that counts k-SAT solutions, which would refute the Exponential Time Hypothesis 🧠 An independent group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams will review it.
#AI #Math #ComplexityTheory
#AI #Math #ComplexityTheory
math/lean/docs/378.md at main · openai/math
Contribute to openai/math development by creating an account on GitHub.
github.com
October 28, 2026 at 4:31 AM
OpenAI shared a paper and Lean formalization claiming a subexponential algorithm that counts k-SAT solutions, which would refute the Exponential Time Hypothesis 🧠 An independent group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams will review it.
#AI #Math #ComplexityTheory
#AI #Math #ComplexityTheory
AI claims ETH false via subexponential SAT proof, but P≠NP still holds uncertainty. #ComplexityTheory #ETH #Subexponential #OpenAI #AIResearch #Algorithms thedailytechfeed.com/openai-model...
October 27, 2026 at 5:44 PM
AI claims ETH false via subexponential SAT proof, but P≠NP still holds uncertainty. #ComplexityTheory #ETH #Subexponential #OpenAI #AIResearch #Algorithms thedailytechfeed.com/openai-model...
What If N Equals One
#programming #computerscience #algorithms #Complexitytheory #Csmajor
https://programmerhumor.io/algorithm-memes/what-if-n-equals-one-w4n0
#programming #computerscience #algorithms #Complexitytheory #Csmajor
https://programmerhumor.io/algorithm-memes/what-if-n-equals-one-w4n0
October 27, 2026 at 5:06 PM
Scott Aaronson appeared on recent podcasts discussing quantum computing, complexity theory, and AI alignment, reacting to Anthropic's algorithm breakthroughs for 3SUM and All-Pairs-Shortest-Path problems.
#QuantumComputing #ComplexityTheory #News
#QuantumComputing #ComplexityTheory #News
Podcast Appearances Discussing Quantum Computing and Complexity Theory
scottaaronson.blog
October 13, 2026 at 8:53 PM
Scott Aaronson appeared on recent podcasts discussing quantum computing, complexity theory, and AI alignment, reacting to Anthropic's algorithm breakthroughs for 3SUM and All-Pairs-Shortest-Path problems.
#QuantumComputing #ComplexityTheory #News
#QuantumComputing #ComplexityTheory #News
OpenAI’s New Matrix Multiplication Bound: ω ≤ 2.25
One result family in OpenAI’s October 2026 mathematics release concerns the exponent ω of matrix multiplication.
#matrixmultiplication #complexitytheory #algorithms #lean
One result family in OpenAI’s October 2026 mathematics release concerns the exponent ω of matrix multiplication.
#matrixmultiplication #complexitytheory #algorithms #lean
October 8, 2026 at 6:40 AM
OpenAI’s New Matrix Multiplication Bound: ω ≤ 2.25
One result family in OpenAI’s October 2026 mathematics release concerns the exponent ω of matrix multiplication.
#matrixmultiplication #complexitytheory #algorithms #lean
One result family in OpenAI’s October 2026 mathematics release concerns the exponent ω of matrix multiplication.
#matrixmultiplication #complexitytheory #algorithms #lean
Why 0.878 Is Max-Cut’s Approximation Wall
Max-Cut asks for a split of a graph’s vertices that sends as many edges as possible across the divide.
#maxcut #approximationalgorithms #complexitytheory #uniquenessgames
Max-Cut asks for a split of a graph’s vertices that sends as many edges as possible across the divide.
#maxcut #approximationalgorithms #complexitytheory #uniquenessgames
October 8, 2026 at 2:01 AM
Why 0.878 Is Max-Cut’s Approximation Wall
Max-Cut asks for a split of a graph’s vertices that sends as many edges as possible across the divide.
#maxcut #approximationalgorithms #complexitytheory #uniquenessgames
Max-Cut asks for a split of a graph’s vertices that sends as many edges as possible across the divide.
#maxcut #approximationalgorithms #complexitytheory #uniquenessgames
OpenAI’s Unique Games Claim Is Not P vs NP
A manuscript in OpenAI’s October 2026 mathematics release tackles Unique Games, a conjecture open for more than two decades.
#uniquegames #complexitytheory #nphard #lean
A manuscript in OpenAI’s October 2026 mathematics release tackles Unique Games, a conjecture open for more than two decades.
#uniquegames #complexitytheory #nphard #lean
October 8, 2026 at 12:18 AM
OpenAI’s Unique Games Claim Is Not P vs NP
A manuscript in OpenAI’s October 2026 mathematics release tackles Unique Games, a conjecture open for more than two decades.
#uniquegames #complexitytheory #nphard #lean
A manuscript in OpenAI’s October 2026 mathematics release tackles Unique Games, a conjecture open for more than two decades.
#uniquegames #complexitytheory #nphard #lean
Two new quantum algorithms achieve tight query complexity bounds for ground-state preparation: one with optimal expected-case complexity O(α/γ∆ + α/∆·log(1/ε)) and another with optimal worst-case bounds. Matching lower bounds prove optimality.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
Optimal Query Complexity for Ground-State Preparation
arxiv.org
September 29, 2026 at 5:19 AM
Two new quantum algorithms achieve tight query complexity bounds for ground-state preparation: one with optimal expected-case complexity O(α/γ∆ + α/∆·log(1/ε)) and another with optimal worst-case bounds. Matching lower bounds prove optimality.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
New formulation of the multiplicative adversary method yields the strongest quantum query lower bounds yet, enabling first time-space tradeoffs for general quantum algorithms and proving list-decoding theorems extending classical results.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
Selective and List-Decoding Direct Product Theorems for Quantum Query Complexity
arxiv.org
September 23, 2026 at 5:43 AM
New formulation of the multiplicative adversary method yields the strongest quantum query lower bounds yet, enabling first time-space tradeoffs for general quantum algorithms and proving list-decoding theorems extending classical results.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
Proves explicit finite-n bounds on sets of square quadratic systems with no vs. exactly one solution, establishing fundamental limits relevant to post-quantum cryptographic hardness assumptions.
#PostQuantumCryptography #ComplexityTheory #Research
#PostQuantumCryptography #ComplexityTheory #Research
Binary Quadratic Systems: Cardinality Bounds and Post-Quantum Cryptographic Hardness
arxiv.org
September 9, 2026 at 9:18 PM
Proves explicit finite-n bounds on sets of square quadratic systems with no vs. exactly one solution, establishing fundamental limits relevant to post-quantum cryptographic hardness assumptions.
#PostQuantumCryptography #ComplexityTheory #Research
#PostQuantumCryptography #ComplexityTheory #Research
Proves classical spectral density estimation requires exponential queries while new quantum algorithms achieve polynomial complexity—demonstrating exponential quantum advantage for graph analysis.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research
Quantum and Classical Spectral Density Estimation Under Local Graph Access
iq.fp2.dev
August 25, 2026 at 5:21 AM
Proves classical spectral density estimation requires exponential queries while new quantum algorithms achieve polynomial complexity—demonstrating exponential quantum advantage for graph analysis.
#QuantumAlgorithms #ComplexityTheory #Research
#QuantumAlgorithms #ComplexityTheory #Research