# When does a 'visual proof by induction' serve a proof-like function in mathematics?

- Josephine Relaford-Doyle,
*University of California, San Diego*
- Rafael Nunez,
*University of California, San Diego*

## Abstract

A proof by mathematical induction demonstrates that a general
theorem is necessarily true for all natural numbers. It has been suggested that
some theorems may also be proven by a ‘visual proof by induction’
(Brown, 2010), despite the fact that the image only displays particular cases of
the general theorem. In this study we examine the nature of the conclusions drawn
from a visual proof by induction. We find that, while most university-educated
viewers demonstrate a willingness to generalize the statement to nearby cases not
depicted in the image, only viewers who have been trained in formal proof
strategies show significantly higher resistance to the suggestion of
large-magnitude counterexamples to the theorem. We conclude that for most
university-educated adults without proof-training the image serves as the basis
of a standard inductive generalization and does not provide the degree of
certainty required for mathematical proof.

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