Open research questions in Computability, Logic, AI Algorithms
132 gap statements mined from Computability, Logic, AI Algorithms papers in our 4.5M-paper local library, which holds 677 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.
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What the literature leaves open
Future research could further explore the conception of intuition in mathematics. It could investigate the implications of Brouwer's view for the foundations of mathematics.
Carl J. Posy, Mathematical Intuitionism, part of series: Cambridge Elements in the Philosophy of Mathematics, Cambridge University Press, 2020; 10.1017/9781108674485. · 2026 · DOIThe gap in the discussion is the difference in conceptions of intuition between Parsons and Brouwer. The paper identifies the need to justify Brouwer's claims in more detail.
Carl J. Posy, Mathematical Intuitionism, part of series: Cambridge Elements in the Philosophy of Mathematics, Cambridge University Press, 2020; 10.1017/9781108674485. · 2026 · DOIFrom Strategy Knowledge Science to Strategy Knowledge Systems Strategy Knowledge Science (SKS) is not limited to a single domain, industry, or application class. It means the current rate of structurally meaningful acceleration is insufficient to support the claimed platform regime. This is why local interpretation alone is insufficient.
Frameworks of a different nature— cognitive architectures, active-inference-based models, and large-scale connectionist approaches—were not examined, and extending Quinean methodology to less explicit formalizations remains an open challenge (Clark 1997; Chalmers 2012; Humphreys 2016).
The strongest known lower bound on gonality was the treewidth of a graph G. The scramble number is an invariant recently developed to study chip-firing games and divisorial gonality, but its connection to screewidth was unknown.
The paper is not a peer-reviewed paper in rigorous mathematics. The empirical component is limited to a proof-of-concept toy simulation using synthetic high-dimensional point clouds. The study does not claim that production-scale language models literally implement (E8 × E8) symmetry, Metatron geometry, Upanishadic field dynamics, Inter-Universal Teichmüller structures, or sheaf-cohomological obstruction mechanisms.
Unified Field Theory of Multiverse Semantics: Version Universe Akashic Reading through the Metatron Lattice for Model Collapse · 2026 · DOIThe lack of a formal proof of the internal mathematical structure of large language models. The need for a rigorous mathematical framework for understanding model collapse.
Unified Field Theory of Multiverse Semantics: Version Universe Akashic Reading through the Metatron Lattice for Model Collapse · 2026 · DOIThe gap is that the language of second-order arithmetic is not suited to consider objects of arbitrary large cardinality. The gap is that there is a need to study the reverse mathematics of characterization theorems of regular countable second countable spaces.
The need to avoid relativization and natural proofs. The challenge of constructing a Δ₁-definable unary language p∞ that lies in NP but not in P.
The measure problem in cosmology remains unresolved with conventional approaches. Prior measures fail to provide a normalized and predictive framework. The need for a new approach that can resolve paradoxes and provide a coherent picture of the multiverse.
The Informational Measure of Existence — Kolmogorov Complexity as a Cosmological Metric · 2026 · DOIThese case studies suggest that agentic AI systems can participate meaningfully in research workflows for open problems in computational mathematics, while human validation remains essential.
Iteris: Agentic Research Loops for Computational Mathematics · 2026The paper suggests further study of the Multiplicative Turing Ensemble (MTE) and its properties. The paper proposes the development of new algorithms and models for complex systems that exhibit multiplicative behavior. The paper suggests the application of the paper's methods to real-world systems.
The paper notes that the macroscopic statistics of these dynamics are not well understood. The paper identifies a need for a natural prior on prime multipliers.
The lack of a unified solution to the seven Millennium Prize Problems. The gap between high-dimensional AI alignment and the study of quantum field theory, fluid dynamics, and number theory.
A Unified Geometric Solution to the Seven Millennium Prize Problems via the Yett-Chyren Correspondence (The Yett theoRY) · 2026 · DOIIt does not prove or solve any open problem; its aim is to organize the structural barriers in problem-solving — in particular the consistency→existence gap (Gap II) — using five semi-quantitative indicators: d_cat (category-crossing distance), d_sub (subcategory distance), Gap II, R (circularity depth), and B (bottleneck concentration).
The study notes that traditional semiotic tools are insufficient to fully understand the concept of dementia.
The construction is limited to graphs without bridges, as a bridge must carry value zero, which is exactly what nowhere-zero flows disallow. The QUBO formulation may not be efficient for large graphs due to the number of variables required.
The NP vs coNP conjecture remains one of the most fundamental open problems in computer science. Prior attempts to resolve the conjecture have been limited by the Natural Proofs barrier.
A Five Part Validator-Grade Structural, Topological, and Thermodynamic Resolution of the NP Vs coNP Conjecture: The Agnostic Replicability Suite and Terminal Seal Framework · 2026 · DOIAlong the way we raise an open question that the analogy suggests but does not settle, on whether a fast algorithm for $\SAT$, were it to exist, would always be exhibitable as a machine you can write down or whether it could be found, in some cases, only as a function on the numbers.
Syntactic Systems Cannot See Semantic Invariants · 2026To determine if scw(G) ≤ gon(G) for all graphs G. To study the possible triples of integers ℓ ≤ m ≤ n that could be the scramble number, screewidth, and the gonality of a graph.
Such operators associate every closed set F ⊆ R and every Whitney jet (f (¯k))|¯k|≤m of order m defined of F to total functions g: Rn → R such that ∂¯k g(x) = f (¯k)(x) on F for all ¯k with |¯k| ≤ m, g is C∞ on Rn \ F. This is the content of the Computable Whitney Extension Theorem 6.11. For the case m = 0, one obtains the First Computable Whitney Extension Theorem 5.3, where only the continuity of g is concerned.
The Descriptive Degeneracy Problem is a fundamental issue in artificial intelligence. Current artificial intelligence systems operate at evolutionary Stage 2–3 of cognitive development.
Further study of the implications of the result. Exploration of new perspectives on the P vs NP problem.
Exploring the connection between the ACM and quantum gravity. Applying the ACM to other cosmological problems, such as the fine-tuning problem. Investigating the implications of the ACM for our understanding of the multiverse.
The Informational Measure of Existence — Kolmogorov Complexity as a Cosmological Metric · 2026 · DOITo improve the efficiency of the QUBO formulation for large graphs. To apply the QUBO formulation to other graph theory problems. To study the properties of nowhere-zero flows and their relationship to other graph theory concepts.
Most-cited papers in Computability, Logic, AI Algorithms
- The Complexity of Intersectionality · Signs · 2005 · 4,374 citations
- Task complexity: Definition of the construct · Organizational Behavior and Human Decision Processes · 1986 · 1,004 citations
- The Discrimination of Visual Number · The American Journal of Psychology · 1949 · 835 citations
- A System for the Notation of Proxemic Behavior1 · American Anthropologist · 1963 · 745 citations
- Requiem for Large-Scale Models · Journal of the American Institute of Planners · 1973 · 530 citations
- Simplifying complexity: a review of complexity theory · Geoforum · 2001 · 528 citations
- Why are some problems hard? Evidence from Tower of Hanoi · Cognitive Psychology · 1985 · 464 citations
- In search of the elusive ADDIE model · Performance Improvement Journal · 2003 · 424 citations
- An operant pursuit of generalization · Behavior Therapy · 1989 · 302 citations
- The complexity continuum in the radex and hierarchical models of intelligence · Intelligence · 1983 · 286 citations
Most recent work
- An approximation theory perspective on machine learning · Neural Networks · 2026
- Revisiting Nishimori multicriticality through the lens of information measures · Physical Review Research · 2026
- A classical proof of quantum knowledge for multi-prover interactive proof systems · IACR Communications in Cryptology · 2026
- Concise thoughts: Impact of output length on LLM reasoning and cost · Information Sciences · 2026
- Interpretations of syntactic fragments of theories of fields · Israel Journal of Mathematics · 2026
- Artificial Intelligence for Software Engineering: From Probable to Provable · Communications of the ACM · 2026
- Solutions, challenges and rising tensions in AI and mathematics · Nature Machine Intelligence · 2026
- Algorithmic dysmorphia: Hyper‐realistic AI simulations as a new aesthetic challenge · Journal of the European Academy of Dermatology and Venereology · 2026
- A Practical Extension of Computational Complexity Theory for Applications in Mathematics and Sciences · Theory of Computing Systems · 2026
- Carl J. Posy, Mathematical Intuitionism, part of series: Cambridge Elements in the Philosophy of Mathematics, Cambridge University Press, 2020; 10.1017/9781108674485. · Studia Logica · 2026
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