Here's a snapshot of what I'm currently focused on.

Last updated: December 2025

Currently Interested In

• Pure mathematics in general, along with mathematical reasoning!
• Abstract Algebra (working through Aluffi's)
• Algebraic Topology
• Sheaf Theory, and sheaves in general, with tentative plans to dabble with algebraic geometry... soon...
• Philosophy of Mathematics
• Automated Theorem Proving
• Cognition and intelligence! With a focus on Michael Levin's research around morphogenesis, bioelectricy, and the broad spectrum of cognition in "unconventional substrates" and Friston's Free Energy Principle.
• Hopefully, soon, a lot of Analysis

Currently Working On

If any of this sounds interesting or you'd like to chat about it, feel free to reach out at ludwigabap@pm.me

• Research on Lean4-generated proof graphs. Attempting to connect Michael Levin's TAME framework to that space, but swapping out morphospace with proof space, cellular collectives with MCTS search, bioeletric patterns with tactics sequences, attractors with kernel classes, blocking ion channels with blocking tactics, and plasticity / adaptativness with replaceability. Basically looking into goal-directedness of navigation through proof space when some components and pathways are blocked. Using some topological and cellular sheaves approaches along with some other fun stuf
• Search, MCTS, automated theorem solvers using Lean4
• AlphaEvolve-like approaches, which combine LLMs, custom harnesses and evolutionary algorithms to drive search and optimization
• Working through Munkres' Point-set Topology book and Aluffi's Notes from the Underground.

Previous interests

Interests

• Machine Learning (model architectures, pre-training and post-training of LLMs, inference optimizations, custom AI architectures such as Tenstorrent, mechanistic intepretability, RLVR)
• Computational and theoretical CS (foundations of computation, uncomputability, theories of computation, PLs and compilers)
• Active Inference and the Free Energy Principle, and overall cognitive sciences
• What on earth is intelligence? Am I "intelligent"? Are cells intelligent? Is an LLM intelligent? What is the difference between understanding and knowing? What is reasoning?