1. Problem statement: We have 17 scientists discussing three particular topics. 2. Given: Any two scientists only discuss one of the three topics with each other. 3. Goal: Prove there is a group of three scientists who only discuss a specific topic among each other. 4. Model the problem as a complete graph $K_{17}$ where vertices are scientists. 5. Each edge is colored with one of three colors (representing the three topics). 6. The condition means every edge is colored with exactly one color. 7. By Ramsey theory, the Ramsey number $R(3,3,3)=17$ means in any 3-coloring of edges of $K_{17}$, there must be a monochromatic triangle. 8. A monochromatic triangle of one color corresponds to three scientists all discussing only that one topic pairwise. 9. Therefore, there exists a group of three scientists who only discuss on the same specific topic among each other. 10. Conclusion: The problem is proved by Ramsey theory using $R(3,3,3)=17$.