Mathematical Modelling
A Beginner’s Guide to Modeling Technical Systems
How to describe everything with mathematics
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Symmetry
The Many Symmetries of Tessellations ft. Harry’s Tiles
Tessellations
Light
The Michelson-Morley Experiment
Light, you are the strangest thing I have ever “seen.”
Number Theory
Perfect Numbers
An ancient riddle
Light
The Physics of Rainbows
How and why they appear in the sky.
Probability Theory
Transforming Scores Into Probability
How to show what subjective scores do and do not tell you about probability of success on the basis of their past performance
Geometry
Visualizing Mathematical Equations and Operations
Capture the Essence of an Equation and Solve it Visually by Using Mathematical Graphs
Philosophy
Mathematics as Fiction: A Common Sense Approach
The following essay was written in 2014 when I was an undergraduate student at the University of Florida; it was the winner of the mathematics department’s Robert Long Prize for writing in the history and/or philosophy of mathematics. In the intervening time, my views on ontological/epistemological status
Philosophy
The Backstage of Mathematical Thinking: How Our Brains Bring About the Abstract
A brief survey of recent insights from cognitive science
Prime Numbers
Mersenne Primes
Number Mysteries and the Hunt for Large Primes
Relativity
How to Compute the General Relativistic Correction to Time
General relativity is one of the most technically difficult physics theories, as it requires uncommon knowledge and mathematical skills. However, it is possible to calculate the relativistic effects induced by the curvature of space-time with good precision, and even to derive its formula, with a few simple arguments. We know
Philosophy
Mathematical Intuitionism and Anti-Realism Compared and Contrasted
Mathematical intuitionism (which is a subset of mathematical constructivism) has it (or had it) that mathematics is purely the result of the mental activities of human beings; not the discovery of mathematical entities which exist in an “objective” (or Platonic) realm. In terms of L. E. J. Brouwer’s original