The "Horgan Surface" and "The Death of Proof"

John Horgan, a science writer, discusses the concept of the "Horgan surface" in mathematics, which was named after him in a somewhat derogatory manner. The surface was initially thought to contradict the idea that computer modeling could replace traditional proofs. However, mathematician Matthias Weber later provided a nonexistence proof for the "Horgan surface." Despite the controversy surrounding his work, Horgan remains proud of the recognition, even if it was sarcastic. The discussion on the evolving nature of mathematics, the role of proofs, and the impact of technology like computers and artificial intelligence on the field continues to be relevant. Horgan reflects on the ongoing developments in mathematics, including the discovery of new mathematical objects like the Horgan surfaces, both real and pseudo. The debate around the mechanization of mathematics and the implications for human understanding and discovery remains a topic of interest in the field.