The Classification of Finite Simple Groups

1. Front Matter

   Pages i-x

   PDF

2. Introduction

   • Daniel Gorenstein

   Pages 1-11

3. Simple Groups of 2-Rank ≤ 2

   • Daniel Gorenstein

   Pages 13-72

4. Simple Groups of Low 2-Rank

   • Daniel Gorenstein

   Pages 73-170

5. Centralizers of Involutions in Simple Groups

   • Daniel Gorenstein

   Pages 171-261

6. The B-Theorem and Locally Unbalanced Groups

   • Daniel Gorenstein

   Pages 263-334

7. The Classification of Groups of Component Type

   • Daniel Gorenstein

   Pages 335-474

8. Conclusion

   • Daniel Gorenstein

   Pages 475-475

9. Back Matter

   Pages 477-487

   PDF

Never before in the history of mathematics has there been an individual theorem whose proof has required 10,000 journal pages of closely reasoned argument. Who could read such a proof, let alone communicate it to others? But the classification of all finite simple groups is such a theorem-its complete proof, developed over a 30-year period by about 100 group theorists, is the union of some 500 journal articles covering approximately 10,000 printed pages. How then is one who has lived through it all to convey the richness and variety of this monumental achievement? Yet such an attempt must be made, for without the existence of a coherent exposition of the total proof, there is a very real danger that it will gradually become lost to the living world of mathematics, buried within the dusty pages of forgotten journals. For it is almost impossible for the uninitiated to find the way through the tangled proof without an experienced guide; even the 500 papers themselves require careful selection from among some 2,000 articles on simple group theory, which together include often attractive byways, but which serve only to delay the journey.

• Finite
• group theory
• history of mathematics
• mathematics
• proof
• theorem

• Rutgers, The State University of New Jersey, New Brunswick, USA

  Daniel Gorenstein

Policies and ethics