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.

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