Mathematics & other curiosities

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curious thinking.

Explore mathematical ideas through problems, proofs, code, and experiments. Follow a question, test a pattern, and see where curiosity leads.

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What is the area of the shaded square?

Four congruent right triangles. Two marked lengths.

Obvious!

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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Problem Sep 2026 Solution included

Two expressions that cannot both be cubes

For a natural number n, prove that n + 2 and n² + n + 1 cannot both be perfect cubes.

number theoryperfect powers

Exploration Oct 2026

The magician’s problem

A coin, an audience, and a probability that seems to settle—until you magnify a ripple that never disappears.

probabilityoscillationslimits

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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

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