Mathematics discovered, invented, and inherited

TL;DR

The paper explores the philosophical question of whether mathematics is discovered, invented, or inherited, proposing inheritance as a third perspective and illustrating this with historical and personal examples.

Contribution

It introduces the concept of mathematical inheritance as a third way alongside discovery and invention, supported by historical analysis and personal insights.

Findings

Mathematics can be inherited, not just discovered or invented.

Historical example from W. Burnside illustrates inheritance in mathematics.

Personal account demonstrates inheritance as a valid mathematical process.

Abstract

The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is new mathematics discovered or invented? Using an example from my own mathematical life, I argue that there is also a third way: new mathematics can also be inherited -- and in the process briefly discuss a remarkable paper by W. Burnside of 1900.