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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 motive for the conference was the celebration of the 100th birthday of Casimir and the 150th birthday of the Riemann hypothesis. 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 The latter topic was inspired both by the call for innovation in industry worldwide and by the fact that Casimir, who was the director of Philips research for a long time in his career, had an outspoken opinion on the importance of fundamental science for industry. These proceedings are of interest both to research mathematicians and to those interested in the role science, and in particular mathematics, can play in innovation in industry.

Casimir effect --- Research --- Research, Industrial --- Technological innovations --- Breakthroughs, Technological --- Innovations, Industrial --- Innovations, Technological --- Technical innovations --- Technological breakthroughs --- Technological change --- Creative ability in technology --- Inventions --- Domestication of technology --- Innovation relay centers --- Technology transfer --- Contract research --- Industrial research --- Engineering experiment stations --- Science --- Science research --- Scientific research --- Information services --- Learning and scholarship --- Methodology --- Research teams --- Casimir force --- Casimir forces --- Effect, Casimir --- Force, Casimir --- Electric fields --- Vacuum polarization --- Zero-point field --- Mathematical models --- Fukuoka <2009> --- Casimir Operators. --- Mathematical Biology. --- Mathematics in Industry. --- Number Theory.