This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis– Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka (Japan). The conference focused on the following topics:

• Casimir operators in harmonic analysis and representation theory
• Number theory, in particular zeta functions and cryptography
• Casimir force in physics and its relation with nano-science
• Mathematical biology
• Importance of mathematics for innovation in industry