Mathematics & other curiosities

Curiosity is
the new ingenuity.

When answers are abundant, the creative edge is knowing what to ask—and wanting to discover more.

What is the area of the shaded square?

Four congruent right triangles. Two marked lengths.

Solution

Slide the four triangles to leave a square of side a and another of side b. The same shaded area becomes a² + b².

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Problems to think about and explorations through mathematics, diagrams, code, and experiments.

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Puzzles

Games to play at your own pace. Slide a block, fit a tile, or find a path across Hex.

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Problem Oct 2026 Solution included

A set that shifts into its complement

Can arbitrarily small translations turn a subset of the real line into its complement?

real analysislinear algebraset theory

Exploration Oct 2026

Lagrange multipliers: follow the constraint

Explore the method of Lagrange multipliers for constrained optimization, with a visual perspective.

calculusoptimizationinformation theory

A little time to play

Puzzles, just for the fun of it.

Pick a game and settle in. Slide a block, fit a tile, or find a path across Hex.

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Everyday productivity

Gadgets for work and study.

Timers, ambient sound, and practical tools for everyday tasks.

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A window into research

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Paper / 2026

Strong Measurability and Adapted Approximations with Applications to Non-Markovian Control

Keivan Mirzaei, Jinniao Qiu

Measurability and adapted approximation tools for metric-space-valued maps, with applications to path-dependent stochastic control.

Preprint

University of Calgary

Explore this work