It's an excellent bet that few of the buskers encountered on the streets of Europe's major cities have Ph.D.s in mathematics. But on this day in London, the woman doing card tricks for passersby -- coaxing a teenage girl to encode her birthday into binary, for example, and then quickly doing the reverse conversion to announce the date -- was expatriate Portuguese mathematician Sara Santos, who in her daytime job coordinates the Royal Institution of Great Britain's  Secondary Mathematics Masterclass Programme  for talented 12- to 14-year-olds.
It's a simple trick, but it works. Busking is one of the ways Santos has found to increase interest in mathematics among "those audiences that you cannot reach in any other way," she says. It's the basis for a new organization, Maths Busking , which Santos co-founded last year to convey "the surprising and fascinating side of mathematics through the medium of street performance," as the organization's Web site puts it.
Whatever the medium, Santos has a passion for "communicating the power and joy of mathematics as widely as possible," as Sue Pope, professor of education at Liverpool Hope University  in the United Kingdom, puts it in an e-mail to Science Careers. This passion has led Santos onto a unique career path.
While growing up in Portugal, Santos enjoyed drawing, but it wasn't the kind of drawing most kids do. "I enjoyed everything geometrical," she says. "I used to spend most of my spare time playing with paper and doing technical drawings." In high school, she picked the arts education track "because science didn't give me any art, but the arts package gave me some science," she says. She studied math, chemistry, and physics as well as technical drawing and descriptive geometry.
Santos decided to study math at university -- at the University of Porto  -- intending to pursue a teaching career. But soon she set aside education training to focus on her growing interest in pure mathematics. Meanwhile, to sustain herself financially, she gave private classes and took a teaching assistant position at her university. "She was not exactly born in a cradle of gold, and had to face some real hardships," one of her former lecturers in Porto, António Machiavelo, writes in an e-mail. But Santos "knew how to make the best of all the opportunities that happen to cross her way."
Santos took part in an Erasmus exchange program , studying at the University of Manchester  for one term and learning about hyperbolic geometry. She decided to continue for a Ph.D., with Charles Walkden, in Manchester, looking at an extension of the central limit theorem. When making observations of the world around us, the measurements we make are actually sums or means of absolute values that originate from random events, Santos explains. "As you take larger and larger sets of random variables, the means of the sets tend to the normal distribution" with a bell-shaped curve, also known as a Gaussian. "The central limit theorem gives conditions for when the means of random variables converge to the normal distribution." Santos looked at "an extension of that result in a context of dynamical systems and when things are not Gaussian-like."
Toward the end of her Ph.D., Santos was reminded of her passion for communicating the beauty of math. She answered a call from her university to volunteer in a math club at a school located in "a bit of a tough area" north of Manchester, she says. "That thought of becoming a math teacher that I had put aside came back." Soon, Santos says, she was "having more and more ideas about things I wanted do with education, or more on the wider side of communication."
Santos started volunteering with the Faculty of Engineering and Physical Sciences's Widening Participation  team. Upon finishing her Ph.D. at the end of 2005, she took a part-time job with the team, funded by the Ogden Trust . She provided support to Ph.D. students who were helping in physics classes in schools one day a week. She took part in outreach events at the University of Manchester like the Liverpool Fun Maths Roadshow  and the Physics Tricks program. This is when Santos realized the need to devise new ways to make math more appealing. "Maths doesn't have explosions … and all these things that kids like that science teachers can do to attract kids to science," Santos says.
When, that same year, online retailer Amazon asked for "a formula for the perfect Christmas present," Santos proposed a method  for wrapping presents so that the patterns on the wrapping paper line up nicely while using a minimal amount of paper. Her method made the newspapers and local and national television.
Through her broad involvement in education and outreach during this period, Santos got to know the community and how it worked. This knowledge, and those connections, led to the opportunities that followed, she says.
Upon graduating, Santos was offered a temporary position in Porto to work in an interactive math museum called Atractor . But "I was not ready to go back to Portugal," she says. So she taught a mathematics module at the University of Manchester and worked for a while as an e-learning consultant for the university's School of Mathematics. She also started training for a postgraduate certificate of education , but she didn't follow through. "What I really wanted to do was to develop engaging maths activities that both make you understand deep things about mathematics" and feel attracted to the subject, she says. She took a position teaching mathematics at Manchester Grammar School in 2006 and continued doing outreach on the side.
Santos took her current position, as a Clothworkers' Fellow in Mathematics at the Royal Institution of Great Britain, 2 years later. The Secondary Mathematics Masterclass Programme she coordinates takes talented students through a series of Saturday morning sessions, where they explore topics outside the standard curriculum. Students are encouraged to think deeply and critically about mathematics, Santos says. She manages the U.K.-wide network of volunteer masterclass organizers, creates new session material, and trains speakers. "It's extremely rewarding," she says.
But Santos aims to do more than just educate the best pupils. Mathematics "is a very delicate subject because it has such an abstract component, and people have had such painful experiences with maths in education," she says. Together with stand-up mathematician Matt Parker  and consultant and columnist  Steve Humble (a.k.a. Dr Maths), she launched Maths Busking, under the auspices of the University of Manchester, "to repackage maths that is already known in a way that attracts new audiences and [makes] people rethink their attitudes," she says. More people joined in to help develop math-trick performances or be trained  as volunteer buskers. (You can watch a Maths Busking session on YouTube .) The work won Santos a national "Seeds of Science 2011"  award in the communication category back in Portugal.
Santos and her colleagues have "gone against the grain," says Mike Abrahams, a brand designer in London who runs a series of events exploring how people from different backgrounds use creativity in their professional lives -- including one event that Santos participated in. Santos is "very affable. She's a good communicator" with a "deep knowledge that … she can call upon in order to spread the word."
Santos also works with schoolteachers. A couple of years ago, she took part in a project led by Pope, the Liverpool Hope University education professor, during which she helped teachers incorporate material from the Royal Institution's masterclasses into mainstream mathematics curricula. Santos's greatest reward so far came at the end of that project, when one of the teacher participants said, " 'You know, we thought you were crazy, that you had no idea what you were doing and what it is like to be in a classroom. But … now I feel that we have more confidence and that we can do this kind of stuff,' " Santos recalls. "Probably I have reached a lot more students by working with teachers."
Elisabeth Pain is Contributing Editor for Europe.