You probably won’t find Albert Einstein’s theory of relativity in the Easyjet operations manual, but a group of maths students at the Ben-Gurion University of Negev in Israel, have applied it to the problem of loading commercial aeroplanes. Setting up their own mathematical model called “passenger space-time”, it has allowed them to put forward a set of scenarios for shaving precious seconds off the time it takes passengers to board and belt up.
Passenger space-time determines whether passengers are in each other’s “past” or “future”. If someone is in your future, they are blocking your progress in the aisle. With everyone’s place in the aircraft cosmos determined, different variables—such as legroom, length of aisle, width of passengers’ bodies—and some extremely complicated mathematical formulae, can be used to calculate the effect of different boarding techniques on the total time it takes to fill the plane.
One of the team’s conclusions—that for “congested” seating arrangements, completely random boarding is more effective than controlled boarding—is certainly accurate. Many budget carriers, whose seats are usually crammed in as tightly as possible, use a first-come, first-served, random seat allocation. Some of the team’s other conclusions—for example, that boarding via row order is relatively useless without first designating the seat order within rows—are less popular within the airline industry, perhaps because there’s a limit to how much pre-boarding organisation passengers will accept.
But the Israeli students’ work serves as a clear illustration of a growing trend: business is starting to see mathematical problem-solving in a different light. In an age where data are ubiquitous, maths can help turn that data into valuable information, offering new perspectives to age-old business conundrums that, quite often, even experienced managers can’t see.
According to Professor Peter Grindrod, president of the Institute for Mathematics and its Applications (IMA), it’s only recently that business has recognised the importance of maths. “Increasingly, businesses want to have some facts on the table to make decisions with,” he says. “Until a few years ago this wasn’t the case: retailers were making decisions with very little hard data—it was done by gut feeling.” Maths, he says, offers a competitive advantage—allowing you to see what your competitors cannot. “What we’re trying to do is give people some insight that is actionable. It’s about fact-based opportunities.”
As the amount of database information grows, so does the need for reliable mathematical models to make sense of it all, be it Amazon’s efforts to build better relationships with its customers simply by analysing where they click, or marketing agency dunnhumby’s consumer behaviour models for Tesco. “Tesco started off just analysing the data for the benefit of the customers,” says Professor Grindrod. “Increasingly, it is using the data to try and drive the business, to feed back to the operational part of the company.”
Mathematical analysis is particularly useful for determining the optimum pricing structures for perishable goods, such as hotel rooms or theatre tickets—items that are worth nothing once they pass their sell-by date. “It’s all about yield management,” says Ian Rowley, the University of Southampton’s industrial liaison officer. “How many tickets should you make available for last-minute bookings, how many should you try and sell early on? How do you optimise sales with so much conflicting information? Maths can provide the best profile of ticket pricing to maximise revenue.”
Every year, postgraduates from Southampton University’s schools of mathematics and management embark on three-month commercial placements to see if they can apply their mathematical thinking to real business problems. The placements have been running since the 1970s, but recent successes, both in the quality of projects and in the number of maths graduates finding permanent industry placements, has helped the scheme to grow in stature.
Among the most successful projects from 2005 were Fiona Bolton’s computer model to increase the effectiveness of ticket kiosks at London’s South Bank Centre, and Honora Smith’s work with airline bmi to use market information to determine the optimal pricing structure for one-way ticket sales.
Rowley attributes the scheme’s success to the strong link between the maths and management schools—and excellent contacts with industry, part of what the university calls its “enterprise agenda”. British Airways, he says, “regularly recruits” Southampton maths graduates.
Mike Herd, director of business incubator the Sussex Innovation Centre, believes there is now a “far greater appreciation of the use of high-level maths in industry” as more people are willing to apply new techniques, particularly in the City. “A few years ago you’d see maths models being presented, which no-one understood,” he says. “Now you have far more science and maths people in the City and they appreciate the different techniques coming through. Once you break the chain of ‘like employing like’, you open up your industry to new ideas.”
Rowley identifies a variety of industries that are actively recruiting maths graduates, sometimes even ahead of business studies graduates. Supply-chain management, defence, health, internet businesses and consultancy all lend themselves to analysis by numbers, largely because they rely on the use of large databases. That makes marketing a huge growth area for mathematicians, too.
The university recently partnered Southampton FC to help the football club market itself to a wider fan base. “They wanted help with statistical analysis to understand where to concentrate their marketing resources,” says Rowley.
In newer companies, maths is often integral to their existence and central to recruitment. The complex algorithms required to build internet companies mean that many are created by the mathematicians themselves—the best known being Google founders Sergey Brin and Larry Page. Brin and Page recently paid for an anonymous billboard poster on Silicon Valley’s highway 101 that featured nothing but a complex logarithmic problem, inviting those clever enough to solve it to post the answer on a website. The few that managed were given another puzzle, and then a link to a page inviting the candidate to send Google their CV.
Richard Duvall, who runs UK peer-to-peer money-lending website Zopa, says that although his company would rather recruit based on experience, intelligence, dynamism and entrepreneurialism, “if all things were equal”, in reality, he’d be likely to favour maths graduates. “Zopa involves complex matching algorithms and risk assessment techniques, and a maths degree would indicate a rigour of thinking and analysis that would be a helpful foundation,” he says. “In general, we would view a maths major very positively.”
Sally Brookes, responsible for graduate recruitment at Accenture, says the consultancy prefers not to differentiate between degrees too heavily, but admits to a rise in the demand for technically-minded graduates. “Technical graduates may have better problem-solving abilities,” she says. Just under half of Accenture graduates have maths or technical degrees. “There is a high proportion both applying and getting through,” she says.
But although the demand for maths graduates is increasing, the supply is falling short. “The sad fact is that we have about 4,500 maths grads a year, and that’s not enough,” says the IMA’s Grindrod. Many link the poor supply to the deterioration of the subject at A-level, where numbers of available teachers, and willing pupils, are dwindling.
A January 2006 report by the National Foundation for Educational Research concluded that one out of every four maths teachers was not a specialist in the subject. Without qualified teachers it can be tricky to persuade pupils that maths is a subject worth taking.
In July, Conservative MP Boris Johnson lamented that the graduate shortage had become so severe that Rolls Royce which, for security reasons, must employ UK scientists to build nuclear submarines, was seriously concerned there wouldn’t be enough manpower to handle the next government contract.
The Department for Education’s statistics bear out Johnson’s fears. In the past 20 years, the number of students taking all A-levels has risen by 100,000 yet, over the same period, the number of students taking maths has fallen from 71,608 to 58,830. Entries were up this year by 5.8 per cent, but considerably larger drops in recent years—in 2002 the number of pupils taking the subject fell by 18 per cent—mean there is some way to go.
Last month, Martin Read, CEO of one of Europe’s largest IT firms, LogicaCMG, hinted the firm would have to shift its headquarters out of the UK if the supply of maths and science graduates continued to fall.
Attempts have been made to reverse the trend. Computer giant IBM’s UK division, for example, has offered to ape a scheme it first trialled in the US, where experienced staff at the end of their careers volunteer as maths and science teachers in exchange for more lucrative pensions. Whether or not the idea goes ahead, it appears to be little more than a stopgap measure.
As Chris Howls, Southampton University’s senior lecturer in applied mathematics, points out, maths has the lowest proportion of high-achievers in teacher training in the country, because maths graduates can earn more in other professions. The reason earning power is high is because there are fewer graduates capable of filling those positions.
But with universities such as Birmingham, Liverpool John Moores and Oxford Brookes having strengthened their maths courses by adding business modules, and other institutions, such as Warwick and Lancaster, improving internal links between their maths and business schools, the overall “employability” of maths graduates is improving. And as Hardwin Jones, publicity officer for graduate website Milkround.com, says: “Maths in business studies degrees varies significantly. In areas where maths proficiency is required, it’s entirely feasible that employers would favour candidates with a pure maths training. [Maths] has greater intellectual pedigree.”
It is widely applicable, too. As Herd explains, there are far more scientists moving into business than vice versa, often to the “detriment of science” he says. “Taking scientists and giving them a better understanding of how to build a business is quite easy, whereas you can’t necessarily do that with business studies students. In that sense, mathematicians can become great business people.”
