In 2021, I started thinking about mathematical assumptions from first principles. I came to some less than conventional conclusions and so wrote 3 papers to describe my findings.
Why I hesitated to publish these
- I was uncertain they had validity.
- If valid, I wanted to protect attribution.
I have recently had the opportunity to discuss these concepts with a senior mathematician and so I publish them here to make them available to the world and to protect attribution.
Mixed Bases
Division producing repeating decimals in base 10 can yield clean, exact results when we choose a more appropriate base — like base 12.
Read the PDF →Division by Zero
Dividing by zero (nothing) means nothing changes. Zero is a special case — distinct from the notion of infinity that classical division produces.
Read the PDF →Clarifying Bases
An exercise in notational hygiene — tidying up the conventions that arise naturally when adopting mixed-base arithmetic.
Read the PDF →Who these papers are for
- Mathematicians interested in challenging foundational assumptions
- Engineers and scientists who work with number-base conversions
- Curious minds drawn to first-principles thinking in arithmetic
Want to discuss or challenge these ideas? Get in touch →