The author discusses the importance of mathematical conjectures, emphasizing the diverse nature of these unproven claims. They argue that conjectures hold significance beyond just scientific discoveries, as they shape the direction of mathematical research and are often more celebrated than proofs. The author critiques the imbalance between efforts to prove and disprove conjectures in modern mathematics, suggesting that both outcomes should be equally rewarded. They also highlight controversial views on the value of conjectures versus theorems and provide anecdotes of their own work in disproving famous mathematical claims. The author challenges traditional beliefs and encourages a more balanced approach to conjecture research.
https://igorpak.wordpress.com/2020/12/10/what-if-they-are-all-wrong/