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Stablecoins moved trillions of dollars last year across ledgers where every payment is permanently public. This is a tour of what that costs, and of one way out: a shielded stablecoin bridge whose privacy proofs are manufactured by a competitive market of GPUs. We cover why privacy is a payments requirement rather than a luxury, how the Rand Protocol prover market and bridge fit together, what the economics of a proof actually look like, and what a graphics card is really doing during the five seconds it spends convincing the world you paid your rent.

I wrote a program that sends encrypted chat between two laptops using nothing but a speaker and a microphone. No network, no pairing, no passphrase — the peers agree a key over the air with X25519 and you verify it by reading four words aloud. Here is the whole stack: parallel MFSK modulation, Goertzel detection, Reed–Solomon with cross-block interleaving, half-duplex carrier sense, and AES-256-GCM with a short authentication string.

A conceptual, defense-oriented threat analysis of the 'Intelligent Worm' — a hypothetical self-propagating program whose exploitation capability is regenerated by an AI reasoning loop rather than fixed at authoring time. I walk the history of static worms through an epidemiological lens (the reproductive number R0 and the epidemic threshold), show why patching has historically driven outbreaks below threshold, and argue that an adaptive exploit term changes the shape of that curve. I take the feasibility limits seriously — hallucination, verification cost, autonomous experimentation — survey what current LLM-agent security research (Morris II, the Fang et al. autonomous-exploitation results, Google's Big Sleep) actually demonstrates, and lay out the defensive re-architecture the threat model implies. No exploit code, no propagation implementation: this is a stress-test of our defensive assumptions.

The Suhubdy Conjecture — a three-form mathematical conjecture for a fault-tolerant quantum algorithm that accelerates — or replaces — backpropagation for empirical-risk minimisation in neural networks. Positioned against the Baur–Strassen cheap-gradient bound, Jordan and Gilyén–Arunachalam–Wiebe gradient-estimation algorithms, Abbas et al. (NeurIPS 2023) impossibility, quantum SDP and interior-point solvers, the Zhang–Leng–Li and Garg–Kothari–Netrapalli–Sherif lower bounds, and the 2024–2026 line on quantum non-logconcave sampling. Companion arXiv-style preprint (.tex source and .pdf) provided.

A long-form, citation-grounded history of the credit assignment problem — the core question of how to apportion blame for a global error across the internal parameters of a learning machine. From Rosenblatt's 1958 perceptron rule, through Linnainmaa, Werbos, and the 1986 Rumelhart-Hinton-Williams paper, to modern alternatives (feedback alignment, equilibrium propagation, predictive coding, forward-forward, synthetic gradients), reinforcement-learning credit assignment, and the frontier of quantum gradients (parameter-shift rule, quantum natural gradient, HHL, and the Abbas et al. NeurIPS 2023 impossibility result).

A citation-grounded survey of robotics research as it stands in May 2026 — VLA foundation models (RT-2, OpenVLA, π0, π0.5, Helix, Gemini Robotics), imitation-learning architectures (Diffusion Policy, ACT/ALOHA, RDT-1B), cross-embodiment data (Open X-Embodiment, DROID), whole-body humanoid control (HOVER, ASAP, OmniH2O), reward design with LLMs (Eureka, DrEureka), world models for robotics (Cosmos, Genie, 1X), simulators (Isaac Lab, Genesis, RoboCasa), and the company landscape (Figure, Tesla, Boston Dynamics, Apptronik, Agility, 1X, Unitree, Physical Intelligence, Skild AI, XPENG, UBTECH, Fourier). With venue-by-venue references from ICLR, ICML, NeurIPS, CoRL, RSS, ICRA, and Science Robotics.

A short, hyperlinked reading list of award-winning and outstanding papers from ICLR 2025/2026, ICML 2025, NeurIPS 2025, CVPR 2025, and EMNLP 2025. One- to three-line summaries with direct arXiv and venue links.

An end-to-end survey of AI agent collaboration as it stands in May 2026, grounded in 100+ citations from ICML/ICLR/NeurIPS 2023–2026 and arXiv. Architectures (AutoGen, MetaGPT, Magentic-One, OpenHands, ADAS, AFlow), communication protocols (MCP, A2A), critic/verifier patterns (Self-Refine, Reflexion, LLM-Modulo), planning and decomposition (ReAct, Tree-of-Thoughts, CodeAct, GPTSwarm), benchmarks (SWE-bench, GAIA, WebArena, OSWorld, τ-bench, MLE-bench, TheAgentCompany), the contrarian compute-fair-comparison literature (Stop Overvaluing MAD, Agentless, Mixture-of-Agents rethinks), and safety/control (AI Control, debate, collusion, AgentHarm). With negative results and the methodological crisis foregrounded.

An end-to-end research survey of the CPU and GPU chip supply chain in 2026 — from a single Appalachian quartz mine and Ukrainian neon plants up through 300mm wafers, EUV scanners, leading-edge foundries, HBM/DRAM/NAND, advanced packaging, design and EDA, ATE, the geopolitics of CHIPS Acts and export controls, and the hyperscaler demand wave that is now consuming most of it. With 130+ primary references — SEC filings, government reports, SEMI/SEMI Europe data, Yole/TrendForce/SemiAnalysis/CSIS, and company disclosures.

GPS jamming and spoofing are now routine in contested airspace, and indoor/underground operations have always lived without it. This post is a technical survey of GPS-denied drone navigation in 2026 — VIO, visual SLAM, terrain-relative navigation, satellite image matching, magnetic anomaly navigation (MagNav), LiDAR SLAM, and multi-modal factor-graph fusion. Deep dives into satellite image matching (the most promising daytime approach) and MagNav (the dark horse that works at night, in fog, and is unjammable). With lessons from Ukraine, the open problems, and a practical stack for builders.

A subfield-by-subfield survey of the mathematics research frontier, grounded in specific papers from Annals, Inventiones, JAMS, Acta, Publications of the IHÉS, and the work of recent Fields medalists. Covers number theory, algebraic geometry, topology, geometric analysis, PDE, probability, combinatorics, logic, representation theory, harmonic analysis, dynamics, mathematical physics, and the rise of formalization. The through-line: mathematics in the 2020s is fusing — Langlands now spans number theory, geometry, and physics; condensed and prismatic methods unify analysis and arithmetic; and Lean is starting to absorb the load-bearing proofs.

A domain-by-domain survey of the artificial intelligence research frontier, grounded in specific papers from ICML, ICLR, NeurIPS, and adjacent venues (CoRL, CVPR, Nature). Covers natural language processing, speech, video, sound, robotics/VLA, biology, 3D generation, diffusion architecture, and the renaissance of reinforcement learning and world models. The through-line: pretraining is no longer the frontier — test-time compute, generative simulators, and embodied grounding are.

A technical survey of where visual perception and planning research actually stands in 2026. Pixel-level perception is largely solved at the representation layer, but perception-for-action — geometry, physics, dexterity, long-horizon control — is not. Reading the recent literature on JEPA, DreamerV3, Sora-as-world-model, RT-2 / OpenVLA / π0, Helix, Gemini Robotics, DUSt3R / MASt3R / VGGT, and the world-model evaluation papers (WorldModelBench, Physion, IntPhys 2), the through-line is the same: we have strong representations and architectural ideas, but the data, evaluation, and physical-grounding infrastructure to validate them is what's missing.

The Luddites were not anti-technology. They were protesting a bundle of wage collapse, skill devaluation, and lost autonomy that mechanization triggered but did not constitute. Reading the modern economics literature — Acemoglu & Restrepo, Allen on the Engels' Pause, Caprettini & Voth on Captain Swing, Autor on polarization, Brynjolfsson on the productivity J-curve — the question for the age of perception-aware and lingual robotics is not whether the reinstatement effect will eventually arrive. It is whether the adjustment window has been compressed past the point where the historical safety valves can open in time.

A historical analogy: the US-China rivalry rhymes with the original Cold War in ways that go far beyond the obvious. Espionage on defense contractors, proxy conflicts through Iran, semiconductors as the new uranium, and ASML as the chokepoint nobody can replicate. The thesis I'm trying to defend: this ends without a hot war, and the defense-industrial complex on both sides is the long-term beneficiary, just as it was from 1947 to 1991. With references from Politico, Bloomberg, The Economist, CSIS, RAND, CFR, CNAS, SemiAnalysis, MIT Technology Review, the Quincy Institute, War on the Rocks, the Stimson Center, and Chris Miller's Chip War.

A beginner-friendly tour of the mathematics behind Rand Protocol — a privacy-preserving, post-quantum blockchain that combines BFT consensus with GPU-driven zero-knowledge proving. We unpack the cryptographic primitives, the consensus protocol, and the security proofs in language a first-year graduate student in mathematics can follow.

If GPU compute becomes a proper commodity market — with spot indices, futures, perpetuals, and basis trades — what changes for everyone who doesn't run an exchange? Peak-off-peak AI for consumers, swap books for neoclouds, watts as the binding constraint, and why your phone bill might start looking like your electric bill. Part 2 of a two-part series.

GPU compute is being financialized the way oil was in the 1980s, but the correct commodity analogue is electricity, not oil. A rigorous look at the microstructure: perishability, locational marginal pricing, basis risk, standardized units, forward curves, and why the math breaks where the electricity analogy breaks. Part 1 of a two-part series.

Hard-won lessons from raising capital across continents -- from the geographic bias of investors to the timing of markets, venture debt traps, and why your competitors in emerging markets might be your best exit.

Nearly all public discourse on Artificial Super Intelligence fixates on how it might destroy us. Almost nobody writes concretely about what happens if we get it right. Here is that essay.

Oxford physicist Tim Palmer claims quantum computers face a hard 1,000-qubit ceiling that would protect RSA and ECC forever. A careful reading of the physics and the math says otherwise---and your migration timeline should not wait to find out.

Bitcoin's price isn't just driven by supply and demand. A \$507 million invisible hand -- dealer gamma exposure -- now dwarfs ETF flows by 13x and mechanically pins, repels, or accelerates price through options hedging dynamics. A deep dive into the math, the market structure, and the Q1 2026 gamma trap.

Can quantum models train as efficiently as classical neural networks? Abbas et al. prove backpropagation scaling is impossible without multiple copies of a quantum state, then show how shadow tomography gets you most of the way there. A deep dive into the paper that defines the trainability frontier for quantum machine learning.

Google Quantum AI, the Ethereum Foundation, and Stanford published a 57-page whitepaper showing <500,000 physical qubits and ~9 minutes suffice to break Bitcoin and Ethereum's elliptic curve cryptography---a 20x reduction over prior estimates. This is not FUD. It is an engineering specification.

A unified mathematical framework for entrepreneurial decision-making, drawing on options theory, game theory, information theory, and regulatory economics.

A deep dive into the most important quantum algorithms papers from Q1 2026, analyzing what each result means for real-world applications once fault-tolerant quantum computers arrive.

Welcome to my blog — Adventures and Amusings of a Mathematician.