In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy.— Godfrey H. Hardy (1877-1947), English mathematician, from A Mathematician's Apology, London, Cambridge University Press, 1941
The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities.— G. Sarton
In many disciplines, the history of the twentieth century tells of the introduction of more and more mathematical techniques. Mathematics has been established as a universal ingredient in the understanding of the world, and is the language used in conveying this understanding. As we enter the twenty-first century, higher mathematics is not just a tool for physical scientists and engineers, but it is also of crucial importance in business, economics, and even the social sciences. Many mathematicians still delight in the aesthetic appeal of their subject; however, it is ultimately the application of mathematics that makes it a critical element in modern civilization.
Why declare a math major?
Undergraduate training in mathematics is an important step along many career paths. It is essential for those who intend to continue toward a graduate degree in Mathematics, Applied Mathematics, Statistics, or Computer Science. Admissions committees for graduate studies in Astronomy, Physics, Engineering, Economics, or Finance often prefer students with undergraduate mathematics majors (together with the proper minor) over students who have majored in their own subject. Some University of Arizona mathematics graduates have also used their degree as the first step toward professional degrees in law, medicine, and even divinity. 
The mathematics major is not just a path toward graduate education. Mathematics training is training in general problem solving. Many employers recognize this fact; they also recognize that a Bachelors degree in mathematics is proof of an ability and willingness to work hard. Many Mathematics majors have found success by completing more than one major. Double majors in Mathematics and Science, Mathematics and Business, or even Mathematics and a Social Science, prepare graduates with enhanced ability to compete well in the job market.
Mathematics majors are advised to develop both computing skills and communication skills during their time as a student. Computing skills are increasingly important in today's society. Experience using graphing calculators and standard mathematical software packages, programming experience, and experience using the Internet are extremely useful. And in virtually any type of position, the need for good communication skills is paramount.
More reasons to become a math major
The art of doing mathematics consists in finding that special case which contains all the germs of generality.— David Hilbert (1862-1943), from N. Rose (ed.), Mathematical Maxims and Minims
How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?— Albert Einstein (1879-1955), German-Swiss-American mathematical physicist, famous for his theories of relativity
Let us not forget one of the main reasons for becoming a mathematics major. It is fun! The mathematics program affords students plenty of time to link their mathematical interests to other intellectual endeavors. Students who combine mathematics, computer science, and another area will find themselves with many options when they graduate with an undergraduate degree.
The Department of Mathematics created the Math Center to ensure that our mathematics majors have a home base to turn to during their undergraduate studies. One of our goals is to integrate the undergraduate mathematics major into the intellectual life of this university and this nation. The working mathematician is involved in three areas: the creation of new mathematics, the application of mathematics to solve real-world problems, and the teaching of mathematics. Many of our undergraduate mathematics majors are able to perform these same activities during their undergraduate years through various research and teaching/tutoring opportunities and summer internship opportunities.