on. Even though the financial sector hires a large number of people with strong mathematical science expertise, he thinks the level of mathematical knowledge in the finance world is still lower than it should be. As an example, he said that many people do not know the distinction between beta (the difference between an instrument’s performance and that of a relevant market) and volatility; they are related but different. He thinks finance will continue to be permeated by quantitative methods. Some of the skills that are necessary, in Dr. Simons’s view, include statistics (though not normally at the level of new research) and optimization, and good programming skill is essential.

Dr. Simons is concerned about the pool of U.S.-born people with strong skills in the mathematical sciences. The majority of people hired by Renaissance are non-Americans. Most are from Europe, China, and India, though most have gone through a U.S. graduate program, and the fraction of U.S.-born people hired is declining. He thinks he probably could have found an adequate number of U.S.-born people if pressed, but it would have required a lot of work. He worries that high school teaching in the United States is simply not good enough, even though our economy is increasingly dependent on mathematical models and data analysis.

Dr. Dietrich described the kinds of mathematical science opportunities she sees and the kind of people IBM-Watson would like to hire. She said that much of IBM’s business has become data-intensive, and numerical literacy is needed throughout the corporation. The mathematical sciences are increasingly central to economics, finance, business, and marketing, including areas such as risk assessment, game theory, and machine learning for marketing. But she noted that it is difficult to find enough people who have the ability to deal with large numerical data sets plus the ability to understand simple concepts such as range and variability. Many mathematical scientists at IBM must also operate as software developers, and they must be flexible enough to move from topic to topic.

She listed some qualifications that are especially valuable in her division, which employs over 300 people worldwide. It needs people with statistical expertise who are also are very computational. They should not rely on existing models and toolkits and should be comfortable working with messy data. The division needs people who are strong in discrete mathematics and able to extract understanding from big data sets. In her experience, most employees do not need to know calculus, and she would like to see more emphasis in the undergraduate curriculum on stochastic processes and large data. Programming ability is essential.

Mr. Bin Zafar presented impressions about the mathematical science skills that are important to the movie industry. (Similar skills are presumably important for the creation of computer games and computer-based training and simulation systems.) He showed the committee an example of

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