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# The Enormous Theorem

## Details

**Authors** Gorenstein

**Year** 1985

**Publisher** Scientific American

**Discipline** Cognitive Science

[Read it at the publisher](https://doi.org/10.1038/scientificamerican1285-104) 
10.1038/scientificamerican1285-104

## In authors' words

### What they set out to do (purpose)

To explore how the idea of simplicity itself is complex.

### What they found (results)

Yet there it is: the proof that all finite, simple groups have been found has run to between 10,000 and 15,000 pages. Of course, no one person is responsible for the achievement, nor is the size of the proof attributable to lengthy computer calculations (although computers are used at one place in the analysis).

## Commentary

### In short

Gorenstein explains that, “One can now appreciate how the rules for combining the elements in a group are the basic laws of arithmetic in more abstract form.” The very basis of mathematics--arithmetic--is born of part-whole grouping.

### In more detail

Gorenstein (1985) recounts one of mathematics' most staggering part–whole achievements: the classification of the finite simple groups. Finite simple groups are the indivisible building blocks — the “parts” — from which every finite group is assembled, much as the primes compose the integers. Gorenstein observes that “the rules for combining the elements in a group are the basic laws of arithmetic in more abstract form,” locating part–whole systems at the very foundation of mathematics: even arithmetic is, at heart, an act of grouping parts into wholes.

The classification itself is a monument to the complexity that part–whole composition can generate. The complete proof runs to somewhere between 10,000 and 15,000 pages and is the collective work of many mathematicians rather than any single author — a vivid reminder that “simple” elements, combined and recombined, give rise to wholes of enormous intricacy. In this way the study illustrates the Systems pattern at its purest: wholes defined by their parts, and parts whose interactions produce far more than their sum.

**Patterns it shows** S

**How to cite this** Gorenstein (1985). The Enormous Theorem. Scientific American.