Toward a Comparative Cognitive History: Archimedes and D. H. J. Polymath

TL;DR

This paper explores the nature of collective versus individual intelligence through a cognitive history approach, comparing ancient Greek mathematical proofs with modern collaborative efforts using network science metrics.

Contribution

It introduces a novel cognitive history methodology and applies quantitative network analysis to compare individual and collective mathematical reasoning.

Findings

Differences in argument structure between individual and collective proofs

Network metrics reveal distinct patterns in collaborative versus individual work

Case study demonstrates potential of cognitive history in understanding intelligence types

Abstract

Is collective intelligence just individual intelligence writ large, or are there fundamental differences? This position paper argues that a cognitive history methodology can shed light into the nature of collective intelligence and its differences from individual intelligence. To advance this proposed area of research, a small case study on the structure of argument and proof is presented. Quantitative metrics from network science are used to compare the artifacts of deduction from two sources. The first is the work of Archimedes of Syracuse, putatively an individual, and of other ancient Greek mathematicians. The second is work of the Polymath Project, a massively collaborative mathematics project that used blog posts and comments to prove new results in combinatorics.