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Math Majors in other Disciplines

We turn the page over to Professor of Music William Goldenberg.

Although I have been asked to write this paean on behalf of mathematics, for me it truly has been a sincerely felt path.  Without reservation, I would advise anyone who has a love for the field to pursue it for the sheer pleasure and fun you will enjoy.  Developing proofs, seeing new relationships, and discovering creative ways of thinking provides a real "aha"  or "eureka" experience!  As an undergraduate, I earned a Bachelor of Arts degree with a double major in mathematics and music, went on to earn a doctorate in music, and now teach piano at the NIU School of Music. 

 
Intrinsic love and the fun you can have is the best reason to work in any field, but mathematics certainly yields many fringe benefits.  As Plato might say, it deals with "eternal" truths at the highest level of abstraction; hence, it has applications to virtually every other field of endeavor known to mankind.  Applications to the sciences are myriad and obvious, but mathematics methodology contributes to numerous other areas of study including the social sciences, education, business, and  even the arts and humanities (every college at NIU!).  In music, for example, we often analyze groupings, patterns, and ordering of notes using set theory, and the mathematical "style of thinking" (e.g., recognizing patterns and parallel relationships) is very helpful in developing musical thinking. One of my previous music theory teachers, David Lewin (now Professor of Music at Harvard), worked almost exclusively with advanced mathematics in his music research and teaching. Technological advances in nearly every field now demand some facility with mathematics. 
 
Another fringe benefit I gained from studying mathematics was the opportunity to study with mathematics professor Samuel Goldberg who, in my opinion, was the clearest and most logical thinker (as well as teacher) I ever met in my life.  And you can learn new approaches to thinking.  When working on proof of a theorem, for example, one often works from a known premise through several logical steps and encounters a "roadblock," which precludes arriving at the desired conclusion.  At such moments, one path to follow could be to begin at the conclusion and work "backwards" toward the premise, trying to connect the strands into a unified line of reasoning (and, of course, another method is to go out for a walk and let your brain subconsciously solve the puzzle for you- or decide that your desired conclusion is a pipe-dream and change it!). 
 
At any rate, I had great fun with mathematics for many years and still use mathematical thinking with frequency in my work, in my daily life, and in simply trying to comprehend the unfathomable, amazing world in which we live!  If you have any inclination, it is a fine road to be taken.
 
Bill Goldenberg
Professor of Music