Fill in each blank with an appropriate preposition: in, to, among, of, for, into, at. One preposition may be used several times. 1. Mathematics ranks … the highest cultural developments … man. 2. Mathematical reasoning is … the highest level known …man. 3. Mathematical style aims … brevity and perfection. 4. Arithmetic, geometry, and astronomy were to the classical Greece music … the soul and art … the mind. 5. Most mathematicians claim that there is great beauty … their science. 6. …1933, George Birkhoff, one … the most distinguished mathematicians … his generation, attempted to apply mathematics … art. 7. Joseph Fourier showed that all sounds, vocal and instrumental, simple and com- plex, are completely describable … mathematical terms. 8. Each musical sound, however complex, is merely a combination … simple sounds. 9. Thus, thanks … Fourier, the nature … musical sounds is now clear … us. 10. The role of mathematics … music stretches even …the composition itself. 11. Masters, such as Bach, constructed and advocated vast mathematical theories … the composition … music. 12. … such theories, cold reason rather than feeling and emotions produce the crea- tive pattern. 13. Through Fourier’s theorem, music leads itself perfectly … mathematical descrip- tion. 14. Hence, the most abstract … the arts can be transcribed … the most abstract … the sciences.