Mathematical, Historical and Philosophical Perspectives on Problem Solving in Mathematics

Explore the fundamental question of what makes a mathematical problem worthwhile through this conference talk that examines problem-solving from mathematical, historical, and philosophical viewpoints. Discover how mathematics is fundamentally driven by problem-solving activities as two speakers present concrete mathematical examples to identify the key ingredients that characterize good mathematical problems. Analyze whether these essential components are shared across different mathematical contexts or remain distinct, and examine whether their similarities and differences stem from mathematical, historical, or philosophical motivations. Engage with thought-provoking questions about the nature of mathematical problem-solving, including whether concepts like "fruitfulness" should be considered mathematical or aesthetic notions. Recorded during the thematic meeting "History of mathematics, Philosophy of mathematics, and mathematics: which interactions?" at the Centre International de Rencontres Mathématiques in Marseille, France, this presentation offers insights into the intersection of mathematical practice, historical development, and philosophical inquiry into the nature of mathematical knowledge and discovery.