When The Math
is Mathing.

From equations to ecosystems, we explore the mathematics, physics, computation, and biology that shape our lives.

Ask ugly questions. Find beautiful answers.

AI Roundtable

A series of thought provoking discussions where a human moderator invites popular AI models to contribute to a round table discussion.. about AI.

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Core Vectors

Applying new physics to intractable problems.

Artificial Intelligence

Beyond AI

The math, physics and philosophy that drives Large Language Models and Generative AI - from transformers to quantum learning: we explore the scientific foundations of modern Artificial Intelligence.

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Number Theory

Mathematical Conjectures

Examine the standard Laplacian on the circle through the lens of averaging operators associated to the multiplicative group of coprime residues.

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Biophysics

Geometric Biology

Utilizing high-dimensional vector spaces to model the structural coherence of proteins. We are developing a mathematical framework for defining stability in complex organic systems.

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Robotics Control

The Math of Robotics

Our research of current control paradigms has reached the mathematical limits of their scalability. As system dimensionality increases, the computational cost required to resolve state transitions scales exponentially. We provide a comprehensive analysis of these limitations.

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Selected Publications

November 2025

The Neuro-Mathematical Parallels Between Human Cognition And Transformer Models

A Unified Predictive Recurrence Framework. We introduce the Single Unified Master Equation (SUME), demonstrating that cortical predictive coding and transformer attention are instantiations of the same recursive algorithm.

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June 2025

Physics-Inspired Stochastic Optimization Framework

A framework for solving large-scale computational problems inspired by classical Langevin dynamics, combining deterministic energy gradients with stochastic exploration.

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Coprime Residue Averaging and Spectral Properties of the Circle Laplacian

Examine the standard Laplacian on the circle through the lens of averaging operators associated to the multiplicative group of coprime residues.

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The Lonely Runner Conjecture for Arithmetic Progressions

A Structural Theory via Euler’s Totient function. Uncovering the duality between isolation phases and units modulo n.

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Spectral Analysis of NP-Complete Systems

Predicting computational tractability through geometric coherence scores.

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Opinions & Observations

Perspectives from accredited contributors on the intersection of mathematics, physics, and complexity.