A proof that if n is composite, 2^n − 1 cannot be prime — establishing a necessary (but not sufficient) condition that confines the Mersenne prime search to prime exponents.
Backward induction reveals that the first player wins the ‘1-to-50’ calling game by opening at 6 and maintaining positions congruent to 6 mod 11.
Three distinct approaches — concrete table, row-by-row summation, and ordered-pair symmetry — all converging on the formula n(n-1)/2.
A systematic count of all distinct triangles formed in a regular pentagram inscribed in a pentagon, using rotational symmetry and case analysis.
How to configure Quarto to render native TikZ diagrams as crisp SVGs using a local LaTeX engine and Inkscape — with a working example.
Ancient intellectual traditions — mathematics pursued for its own sake, poetry, philosophy — will thrive in the AI era precisely because their value was never tied to economic efficiency.
Selected passages from SICP on programmer responsibility, problem decomposition, proof methods, and the relationship between software and human thought.
Reconciling Visionary, Builder, and User perspectives through three question categories — Context+Problem, Solution+Deployment, and Pitfalls+Troubleshooting — to produce documentation that emerges organically.
A practical guide to inspecting pod status, reading logs, executing into containers, and using ephemeral containers to diagnose common Kubernetes failures.
Five concrete issues in BrowserStack’s documentation — verbosity, heading style, misused admonitions, unnecessary images, and poor UX — with LambdaTest as a counterexample.
A complete walkthrough for automating browser tests with Selenium and Python, running them on BrowserStack’s device grid, and wiring everything up with GitHub Actions CI.
Optimal play strategy for tic-tac-toe — center control, corner responses, and multi-threat recognition — showing that a well-played game always ends in a draw.
Step-by-step guide to setting up a Google Cloud project, configuring a service account, and writing a Python script that extracts landmark names from images using the Vision API.
A practical comparison of REST and SOAP architectures — when enterprise security and transactions favour SOAP, and when public-facing speed favours REST.
A code review of a multi-string search method in Java, identifying five improvements in readability and performance, with a revised implementation.
A personal compendium of principles across five domains: body, mind, profession, money, and relationships.
