# What is a Theorem?

## TL;DR

This paper questions the criteria for accepting mathematical theorems and explores the parallels between proof evidence and randomized computation evidence, challenging traditional standards of mathematical proof.

## Contribution

It introduces a novel perspective by comparing accepted proof evidence with evidence from randomized computations, questioning the consistency of current standards.

## Key findings

- Highlights the inconsistency in accepting evidence for the existence of proofs.
- Draws parallels between proof evidence and randomized computation evidence.
- Proposes reconsideration of what constitutes convincing evidence in mathematics.

## Abstract

General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes "convincing evidence?" I will argue that, given the types of evidence that are currently accepted as convincing, it is inconsistent to deny similar acceptance to the evidence provided for the existence of proofs by certain randomized computations.