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From the reflected light, as well as the room’s geometry and mathematical modeling, he deduces the structure of the hidden objects. “If you modify your camera and add sophisticated processing,” he said, “the camera can look around objects and see what’s beyond

The impact of data abundance extends well beyond business. Justin Grimmer, for example, is one of the new breed of political scientists. A 28-year-old assistant professor at Stanford, he combined math with political science in his undergraduate and graduate studies, seeing “an opportunity because the discipline is becoming increasingly data-intensive.” His research involves the computer-automated analysis of blog postings, Congressional speeches and press releases, and news articles, looking for insights into how political ideas spread.

But the computer tools for gleaning knowledge and insights from the Internet era’s vast trove of unstructured data are fast gaining ground. At the forefront are the rapidly advancing techniques of artificial intelligence like natural-language processing, pattern recognition and machine learning.

If you had asked them, most of my high school teachers would have called me an unmotivated student or said that I lacked discipline and didn't take learning seriously. And yet, that abandoned storage bin told another story: with the aid of my calculator, I'd crafted narratives, drawn storyboards, visualized foreign and familiar environments and coded them into existence. I'd learned two programming languages and developed an online network of support from experienced programmers. I'd honed heuristics for research and discovered workarounds when I ran into obstacles. I'd found outlets to share my creations and used feedback from others to revise and refine my work. The TI-83 Plus had helped me cultivate many of the overt and discrete habits of mind necessary for autonomous, self-directed learning. And even more, it did this without resorting to grades, rewards, or other extrinsic motivators that schools often use to coerce student engagement.

I've now begun to see Texas Instruments graphing calculators as unique among educational technologies in that they enable learning that is couched in discovery more than formal teaching.

take the notion of "correctness." School typically assumes that answers fall neatly into categories of "right" and "wrong." As a conventional tool for computing "right" answers, calculators often legitimize this idea; the calculator solves problems, gives answers. But once an endorsed, conventional calculator becomes a subversive, programmable computer it destabilizes this polarity. Programming undermines the distinction between "right" and "wrong" by emphasizing the fluidity between the two. In programming, there is no "right" answer. Sure, a program might not compile or run, but making it offers multiple pathways to success, many of which are only discovered through a series of generative failures. Programming does not reify "rightness;" instead, it orients the programmer toward intentional reading, debugging, and refining of language to ensure clarity. This is a form of learning that privileges the process of discovery over the interventions of formal teaching. It can fuel an intrinsic desire to pursue similar learning experiences, but even more, it gradually transforms the outlook of the student

his view of mathematics has utterly changed since childhood.

he ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians.

Many years ago, people learned to weld in a high school shop class or in a family business or farm, and they came up through the ranks and capped out at a certain skill level. They did not know the science behind welding,” so could not meet the new standards of the U.S. military and aerospace industry. “They could make beautiful welds,” she said, “but they did not understand metallurgy, modern cleaning and brushing techniques” and how different metals and gases, pressures and temperatures had to be combined.

Welding “is a $20-an-hour job with health care, paid vacations and full benefits,” said Tapani, but “you have to have science and math. I can’t think of any job in my sheet metal fabrication company where math is not important. If you work in a manufacturing facility, you use math every day; you need to compute angles and understand what happens to a piece of metal when it’s bent to a certain angle.” Who knew? Welding is now a STEM job — that is, a job that requires knowledge of science, technology, engineering and math.

even before the Great Recession we had a mounting skills problem as a result of 25 years of U.S. education failing to keep up with rising skills demands, and it’s getting worse.

Corrypt, upon proper exploration, revealed itself to be a brilliantly designed puzzle game, unforgiving and unwilling to accommodate players who refuse to give it their full attention. Peel back one layer, and it reveals another more surprising one.

After completing a degree in math and computer science at the University of Auckland, Brough moved to London and began working towards a Ph.D. He landed a decent-paying programming job while continuing his scholastic work, but continued making games, including the beautiful, abstract strategy game Vertex Dispenser, which even Brough admits may have been too esoteric. It combined elements of shooters and real-time strategy games with a complex puzzle system, and many players felt overwhelmed. “I just could not get my head around those concepts at the same time,” said one.

Well-designed games, he believes, can teach people how to do some things better. By simulating challenging situations, games can teach us about “managing unexpected situations… making good decisions, thinking about the costs of our actions and dealing with the consequences,” he says.

This approach can even be useful for applications that are not, strictly speaking, compressed sensing problems, such as the Netflix prize.

Given the enormous popularity of Netflix, even an incremental improvement in the predictive algorithm results in a substantial boost to the company’s bottom line. Recht found that he could accurately predict which movies customers might be interested in purchasing, provided he saw enough products per person. Between 25 and 100 products were sufficient to complete the matrix.

Across every discipline, data sets are getting bigger and more complex, whether one is dealing with medical records, genomic sequencing, neural networks in the brain, astrophysics, historical archives, or social networks. Alessandro Vespignani, a physicist at Northeastern University who specializes in harnessing the power of social networking to model disease outbreaks, stock market behavior, collective social dynamics, and election outcomes, has collected many terabytes of data from social networks such as Twitter, nearly all of it raw and unstructured. “We didn’t define the conditions of the experiments, so we don’t know what we are capturing,” he said.

There are three formal AIMS undertakings: a master’s degree program in Mathematical Sciences, research, and teacher training. The master’s program offers free tuition to accepted students and trains them in both general principles – problem formulation, the scientific method, communication – and cutting-edge math in subjects including computer science, biomathematics, and financial mathematics. Research will allow for international collaborations and advanced student training.

Traditionally, classrooms were led by an authoritative teacher who disseminated information to silent students, but Zomahoun hopes to turn that paradigm on its head. “We train people who can challenge the status quo,” he explains, “not just people who learn from books, listen to lectures, and just repeat it.” Rather, he hopes to instill qualities like “critical thinking, independent thinking, and problem solving” in order to prepare students for real-world problems.