Future Developments
My future research will focus on Hilbert's 12th and 24th problems, the Strong Artin conjecture, and the Langlands program. Alongside these questions, I plan to refine my work on machine learning and reasoning, improve the existing mathematics and software, and make the website and its GitHub repositories easier to access and use.
Updated 3 November 2026. The linked records describe progress, remaining requirements, and the evidence for each work.
These plans and the existing work will likely evolve as I review research and tools released by OpenAI and others.
Main research directions
Hilbert's 12th problem
The next steps are to develop the explicit arithmetic constructions further and investigate the remaining questions about analytic comparison and realization. The existing Hilbert 12 studies provide starting points. Their finite results and open analytic obligations are recorded separately.
Ambient dual slice · Analytic Fourier branch · Cubic divisor development
Hilbert's 24th problem
The work on proof paths, validity, interpretation, and review provides a basis for studying proof simplicity and comparison. The aim is to find ways to make proofs easier to understand, compare, and check.
Strong Artin
Research on the Strong Artin conjecture continues, with particular attention to the remaining global automorphic attachment and reproducible checks of the existing formal developments. The general conjecture remains open.
Strong Artin: current work and evidence
Langlands program
Papers XI and XII provide starting points for investigating connections between arithmetic realizations, Hecke data, and automorphic constructions. The outstanding arithmetic inputs and conditional comparisons remain explicit as this work develops.
Paper XI: arithmetic realization · Paper XII: conditional automorphic completion
Machine learning and reasoning
The current work on machine learning and reasoning includes the Large Signal Model, Machine Native Reasoning, and Machine Understanding. Further development focuses on sharper mathematical models, clearer links between theory and implementation, and reproducible evaluation of practical claims.
Large Signal Model · Machine Native Reasoning · Machine Understanding
Refining the current work
Ongoing work includes correcting and clarifying existing manuscripts, reviewing proofs, improving examples, and extending selected formal developments. Each edition will remain linked to its sources, claim map, and reproduction records, so readers can follow both the mathematics and its development.
Current evidence by work · Detailed development queue
Reading editions and visual guides
The twelve core papers already have online reading editions and visual guides. The Large Signal Model also has an online edition with its statements, written proofs, and formal correspondence linked together.
Plans for the reading library include more guided paths, additional books, and closer connections between explanations and worked examples. The expanded Machine Native Reasoning book still needs its own source and edition checks before publication.
Read online · Explore visual guides · Expanded-book requirements
Lean and reproducible checks
Browser Lean development focuses on library loading, compiler compatibility, and reliable checks of larger dependency chains. Wider access to retained formal sources, particularly the newer Special Functions developments, is another priority. Reproduction instructions should also stay aligned with published editions.
Further formalization will follow explicit maps between manuscript claims and Lean declarations. Editions that rely on inherited compiler evidence still need fresh checks against their pinned sources and dependencies.
Try browser Lean · Browser development plan · Reproduction guide · Formal replay requirements
Interactive mathematics
Further development of the Signal, Recovery, and J-Space laboratories will connect each experiment more closely to the mathematics it illustrates. Guided experiments, useful comparisons, and results that readers can inspect and reproduce remain priorities.
New examples will state their assumptions and the scope of their exact or numerical results. They will also link to the relevant sources. The evidence for the Large Signal Model's mathematical edition is recorded separately from the evidence for its software and empirical development.
Open interactive tools · Current laboratory features · Large Signal Model software and limits
Website and GitHub accessibility and use
Easier navigation and access are priorities for the website and GitHub repositories. Planned improvements include clearer starting points, better search and cross-links, simpler setup instructions, useful downloads, and straightforward ways to report corrections.
Accessibility reviews cover keyboard and screen-reader access, mobile reading, mathematical reading order, diagram descriptions, and the original PDFs.
Reading and accessibility options · Using and contributing to the repositories
Research directions · Detailed development queue · Incubator and return criteria