About
A cartographer of the integers
I am a mathematician based in Ulaanbaatar, working at the meeting point of number theory and dynamical systems. I believe mathematics is not a wall of formulas but a landscape — and my work is drawing maps of it.
Beyond research, I teach, write, and build small interactive tools that let anyone see a theorem before they prove it. This page is one of those tools: everything moving below is mathematics, computed live in your browser.
12+Publications
15Years teaching
∞Curiosity
Research
Three threads, one fabric
ℤ
Number theory
Prime distribution, quadratic forms, and the stubborn beauty of the integers.
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Dynamical systems
Iteration, chaos, and the long-term behaviour of simple rules.
∴
Mathematical education
Interactive visualisation as a first language for mathematical ideas.
Interactive
Four small universes
Everything below is computed live in your browser — no images, no libraries. Touch it.
The Mandelbrot set z → z² + c
The set of points c for which iterating z → z² + c never escapes to infinity. Click anywhere on the boundary to dive deeper.
zoom ×1
Fourier epicycles ∑ sin((2k−1)t)/(2k−1)
A square wave assembled from rotating circles — the heart of signal processing. Add harmonics and watch the corners sharpen.
4
Ulam’s prime spiral 1, 2, 3, 5, 7, 11 …
Write the integers in a square spiral and light up the primes: diagonal streaks appear that nobody fully understands.
0 primes
The golden angle θ = n · 137.508°
Sunflowers place each seed 137.5° from the last — the golden angle. Nudge it even slightly and the pattern collapses.
137.51°
Writing
Selected notes
Iteration of the logistic family at the edge of chaos
Teaching Euler’s identity with moving pictures
The Basel problem, three ways
Contact
Let’s talk mathematics
Questions, collaborations, or a pattern you can’t explain — my inbox is open.
hello@amarsanaa.com