Is Beethoven the only one to see the connection between music and math?

There are many studies.  

It turns out that there is much evidence that supports the positive effects of music on one's ability to do math. Most research shows that when children are trained in music at a young age, they tend to improve in their math skills. The surprising thing in this research is not that music as a whole is enhancing math skills. It is certain aspects of music that are affecting mathematics ability in a big way. Studies done mostly in children of young age show that their academic performance increases after a certain period of music education and training. One particular study published in the journal 'Nature' showed that when groups of first graders were given music instruction that emphasized sequential skill development and musical games involving rhythmn and pitch, after six months, the students scored significantly better in math than students in groups that received traditional music instruction. (1)

The result of this study posed another important question. How does this type of music that emphasized sequential skills, rhythmn and pitch manage to improve children's ability to do math? It turned out that there are two distinguished types of reasoning, spatial temporal (ST) reasoning and Language analytical (LA) reasoning. LA reasoning would be involved in solving equations and obtaining a quantitative result. ST reasoning would be is utilized in activities like chess when one needs to think ahead several moves. The effect of music on math sometimes termed the Mozart effect. The Mozart effect gain its name after the discovery that listening to Mozart's compositions, which is very sequential, produces a short-termed enhancement of spatial-temporal reasoning. 

Some key reasoning features used in spatial temporal reasoning are

1. The transformation and relating of mental images in space and time

2. Symmetries of the inherent cortical firing patterns used to compare physical and mental images and 

3. Natural temporal sequences of those inherent cortical patterns 

(3).The same people who conducted the Mozart effect experiment also suggested that spatial-temporal reasoning is crucial in math. The areas of math that require ST reasoning are geometry and certain aspects of calculus, which require transformations of images in space and time. In higher mathematics, the ability to write mathematical proofs is also associated with ST reasoning because proof writing is a task that requires intuitive sense of natural sequences and the ability to think ahead several steps.

As to the question, what part of the brain controls the correlation between math and music, there are also many resources that provide answers. Dr. Gottfried Schlaug, found that certain regions of the brain such as the corpus callosum and the right motor cortex, were larger in musician who started their musical training before the age of 7 (2). As to what happens in that area of the brain when one listens to music, we turn to the experiment performed by Xiaodeng Leng and Gordon Shaw. Gordon and Leng developed a model of higher brain function, which is based on the trion model. 

The trion model is a highly structured mathematical realization of the Mountcastle organization principle, with the column as the basic neuronal network in mammalian cortex. The column comprises minicolumns called trions. One particular columnar network of trions has a large repertoire of spatial-temporal firing patterns, which can be excited and used in memory and higher brain functions (3). Shaw and Leng performed an experiment in which they mapped the trion model of firing patterns in that particular column onto various pitches and instruments producing recognizable styles of music. This mapping of the trions gaves insight to relate the neuronal processes involved in music and abstract spatial-temporal reasoning (3). It shows that the part of the cortex, which contains the repertoire of spatial-temporal firing patterns, can be excited by music and is utilized in higher brain functions such as spatial-temporal thinking in mathematics.

http://serendip.brynmawr.edu/exchange/node/1869

That was excellent. 

There's also the music-math connection in Godel Escher Bach:

http://quora.com/Book-Summaries/What-are-the-main-ideas-and-highlights-of-Gödel-Escher-Bach

I love this image:

Yeah, that's a great image. Have you read the book? It's amazing.

Yet ANOTHER book!  Sheesh!  :)

This is not just any book. This is an exceptional book.

http://www.nytimes.com/books/97/07/20/reviews/hofstadter-grodel.html

I shall read the book!  Thank you.

Happily!

"I always have a picture in my mind when composing, and follow its lines." ~Beethoven