1+1=2 (2006)

The discussion revolves around the historical and mathematical significance of Whitehead and Russell's "Principia Mathematica," particularly its proof that 1+1=2. The work, published around 1910, is noted for its extensive length and complexity, taking a thousand pages to establish foundational mathematical concepts, including the simple arithmetic of addition. The author highlights how the notation and techniques used in the book are outdated compared to modern mathematical practices. For instance, the authors lacked the concept of ordered pairs, which simplifies many proofs today. The text also critiques the redundancy in the work, where similar concepts are repeated due to the authors' limited understanding of logical structures at the time. The proof of 1+1=2 is presented as a culmination of earlier theorems, demonstrating the evolution of mathematical logic and notation. The author suggests that contemporary mathematics would approach these concepts more efficiently, thanks to advancements in understanding sets and relations. Overall, the piece serves as both a historical reflection on mathematical logic and a commentary on the evolution of mathematical notation and proof techniques.

- "Principia Mathematica" took a thousand pages to prove basic arithmetic.

- The work reflects early 20th-century mathematical logic, which has since evolved.

- Redundancies in the text highlight the authors' limited techniques at the time.

- Modern mathematics simplifies proofs using concepts like ordered pairs.

- The proof of 1+1=2 illustrates the foundational nature of set theory in mathematics.