Why should a student major in mathematics? Duke University declares that the joy of attacking "the intellect's most extreme sport" is sufficient justification. But in addition to being the most demanding of all intellectual pursuits, math is also one of the highest paying majors. Engineering and math reigned supreme in pay and job opportunities, when PayScale compared its massive compensation database with 120 college majors and job growth projections through 2020 from the U.S. Bureau of Labor Statistics.

On Wall Street, the math geeks are known as quants. They're the ones who create sophisticated trading algorithms that can ingest vast amounts of market data and then form buy and sell decisions in milliseconds. When hiring a quant, most firms look for at least a Master's degree or preferably a PhD in a "quantitative" subject, such as mathematics, economics, finance or statistics.

Quantitative analysts design and implement complex models that allow financial firms to price and trade securities. They are employed by investment banks and hedge funds, but sometimes also by commercial banks, insurance companies and management consultancies, in addition to financial software and information providers.

Due to the challenging work — a blend of mathematics, finance and computer skills — quants are in great demand and able to command high salaries. Compensation in the field of finance tends to be very high, and it's not uncommon to find quantitative analyst positions with posted salaries of $250,000 or more and with bonuses, $500,000+ is achievable.

When math wizards redirect their quant proclivities toward consumer technology they become, as it were, a Want. For instance, at social networking companies like Facebook, Wants may sit among the computer scientists and engineers, but theirs is the central mission: to poke around in data, hunt for trends, and figure out formulas that will put the right ad in front of the right person. They gauge the personality types of customers, measure their desire for certain products, and discern what will motivate people to act on ads.

"The most coveted employee in Silicon Valley today is not a software engineer. It is a mathematician," says Glenn Kelman, CEO of Redfin, who graduated summa cum laude from the University of California, Berkeley. "The mathematicians are trying to tickle your fancy long enough to see one more ad."

The new data-driven market makes math skills, particularly statistics, very valuable to employers. Statisticians use statistical methods to collect and analyze data and help solve real-world problems in business, engineering, the sciences, and other fields. The average annual salary for statisticians was $95,170 in 2014.