Mathematics · Research · Reflection

Finding the human side of mathematical thought.

I study structures, patterns, and the questions behind them. This is a growing record of my research, mathematical reflections, reading, and life beyond the desk.

Begin with an introduction

About

SDSZ · Class of 2027

Portrait / personal image Replace with a natural photograph

I'm Jiankun (Kevin) Xu, a Grade 12 student at The Experimental High School Attached to Beijing Normal University. My interests lie in mathematics and philosophy, especially model theory and the foundations of mathematics. Working through proofs led me to ask what I was trusting when I accepted their conclusions. Why do we adopt particular axioms? What does it mean for a mathematical statement to be true? These questions now guide much of my reading and writing.

More about me

Academic Work

Selected work across pure mathematics, scientific computing, applied problems, and mathematical exposition.

View the complete index

Pure mathematics 01

Can One Hear the Shape of a Drum?

Geometry and spectral data: what can the frequencies of a domain reveal about its shape?

View project

Scientific computing 02

Physics-Informed Neural Networks

Exploring how physical laws can be built into neural-network training and used to solve differential equations.

View project

Applied research 03

Flood Susceptibility Mapping

A LeNet-style CNN maps flood susceptibility in Fangshan District using verified insurance claims and eleven environmental factors.

View project

Expository mathematics 04

Ramanujan's Partition Formula

An expository Pioneer Academics paper that expands Newman's proof and traces integer partitions through generating functions, contour integration, and asymptotic analysis.

View paper

Mathematical Thinking

Notes on the foundations, language, and meaning of mathematics.

Axioms Formalization Mathematical truth Proof and intuition Philosophy of mathematics

“A theorem may end with a square, but thought rarely does.”

Future note

Axioms as beginnings

A short essay, reading note, or unfinished question can live here. The final structure will grow with the writing rather than dictate it in advance.

Enter Mathematical Thinking

Writing & Reading

Essays, reading notes, and links to writing published elsewhere.

Ongoing essay series

Axioms

Essays on the history and philosophy of mathematics, beginning with the question of how to measure infinity.

Explore the series

Reading note placeholder

A book, an idea, a margin note

Use this space for books that changed a question, rather than for a decorative reading list.

Explore reading notes

Book / article visual Optional image

Beyond the Desk

Movement, sport, and the parts of life that create a different kind of rhythm.

Movement photograph Sport, training, or life outside research

Space reserved

The body also learns through repetition.

This section is intentionally open for now. It can later become a story about a sport, a visual diary, or a few moments that show another side of the person behind the work.

Résumé

A concise reference for education, research, projects, and activities.