Mapping the human genome showed how the internet can play a vital part in collective scientific research. Now more scientists are collaborating – and inviting amateurs and colleagues from other disciplines to get involved

On the surface, it looked as if there was nothing in mathematics that Timothy Gowers couldn't achieve. He held a prestigious professorship at Cambridge. He had been a recipient of the Fields Medal, the highest honour in mathematics. He had even acted as a scientific consultant on Hollywood movies. Yet there were a few complex mathematical problems that he had struggled to solve. "In most cases, I just ran out of steam," he explains.

So one day he took one of these – finding a mathematical proof about the properties of multidimensional objects – and put his thoughts on his blog. How would other people go about solving this conundrum? Would somebody else have any useful insights? Would mathematicians, notoriously competitive, be prepared to collaborate? "It was an experiment," he admits. "I thought it would be interesting to try."

He called it the Polymath Project and it rapidly took on a life of its own. Within days, readers, including high-ranking academics, had chipped in vital pieces of information or new ideas. In just a few weeks, the number of contributors had reached more than 40 and a result was on the horizon. Since then, the joint effort has led to several papers published in journals under the collective pseudonym DHJ Polymath. It was an astonishing and unexpected result.

"If you set out to solve a problem, there's no guarantee you will succeed," says Gowers. "But different people have different aptitudes and they know different tricks… it turned out their combined efforts can be much quicker."

This ability to collaborate quickly and transparently online is just one facet of a growing movement in research known as open science.

There are many interpretations of what open science means, with different motivations across different disciplines. Some are driven by the backlash against corporate-funded science, with its profit-driven research agenda. Others are internet radicals who take the "information wants to be free" slogan literally. Others want to make important discoveries more likely to happen. But for all their differences, the ambition remains roughly the same: to try and revolutionise the way research is performed by unlocking it and making it more public.

"What we try to do is get people to organise differently," says Joseph Jackson, the organiser of the Open Science Summit, a meeting of advocates that was held for the first time last summer at the University of California, Berkeley.

Jackson is a young bioscientist who, like many others, has discovered that the technologies used in genetics and molecular biology, once the preserve of only the most well-funded labs, are now cheap enough to allow experimental work to take place in their garages. For many, this means that they can conduct genetic experiments in a new way, adopting the so-called "hacker ethic" – the desire to tinker, deconstruct, rebuild.

The rise of this group is entertainingly documented in a new book by science writer Marcus Wohlsen, Biopunk (Current £18.99), which describes the parallels between today's generation of biological innovators and the rise of computer software pioneers of the 1980s and 1990s. Indeed, Bill Gates has said that if he were a teenager today, he would be working on biotechnology, not computer software.

Spurred on by the new-found ability to work outside the system, these rebel biologists believe that the traditional way of doing science is not the most efficient and could even be holding back important developments.

"Institutions, typically, are the slowest and have the most amount of inertia lagging behind the technology," says Jackson. "We have a lot of things that made sense once, or never made sense, that are clogging up the works."

Those sound like fighting words to a traditional scientist. After all, ask any lab director and they'll tell you the same thing – doing real science is tough. It takes time, energy and money to conduct serious research. Institutes manage vast budgets, operate huge, hi-tech labs and call upon armies of graduate students to sift for evidence in great oceans of data. Real science is a slow, expensive process that has been hewn into shape over centuries of experimentation, false starts and the occasional success.

But open scientists suggest that it doesn't have to be that way. Their arguments are propelled by a number of different factors that are making transparency more viable than ever.

The first and most powerful change has been the use of the web to connect people and collect information. The internet, now an indelible part of our lives, allows like-minded individuals to seek one another out and share vast amounts of raw data. Researchers can lay claim to an idea not by publishing first in a journal (a process that can take many months) but by sharing their work online in an instant.

And while the rapidly decreasing cost of previously expensive technical procedures has opened up new directions for research, there is also increasing pressure for researchers to cut costs and deliver results. The economic crisis left many budgets in tatters and governments around the world are cutting back on investment in science as they try to balance the books. Open science can, sometimes, make the process faster and cheaper, showing what one advocate, Cameron Neylon, calls "an obligation and responsibility to the public purse".

At the same time, moves are afoot to disrupt the closed world of academic journals and make high-level teaching materials available to the public. The Public Library of Science, based in San Francisco, is working to make journals more freely accessible, while the Massachusetts Institute of Technology currently boasts that material for almost 2,000 courses is now available on the web.

"The litmus test of openness is whether you can have access to the data," says Dr Rufus Pollock, a co-founder of the Open Knowledge Foundation, a group that promotes broader access to information and data. "If you have access to the data, then anyone can get it, use it, reuse it and redistribute it… we've always built on the work of others, stood on the shoulders of giants and learned from those who have gone before."

In the seven years since he started the organisation, Pollock, now in his early 30s, has helped build communities and tools around everything from economics data to Shakespeare's sonnets. He says that it is increasingly vital for many scientists to adopt an open approach.

"We have found ourselves in a weird dead end," he says – where publicly funded science does not produce publicly accessible information. That leads to all kinds of problems, not least controversies such as the leaked climate change emails from the University of East Anglia, which led to claims of bias among the research team.

But it's more than just politics at stake – it's also a fundamental right to share knowledge, rather than hide it. The best example of open science in action, he suggests, is the Human Genome Project, which successfully mapped our DNA and then made the data public. In doing so, it outflanked J Craig Venter's proprietary attempt to patent the human genome, opening up the very essence of human life for science, rather than handing our biological information over to corporate interests.

"It was a very large project in one of the most organised and information-rich areas of science, but it faced genuine competition from a closed model," says Dr Pollock. "It is basically an extraordinary example and it could have gone in a very different way."

Unsurprisingly, the rise of open science does not please everyone. Critics have argued that while it benefits those at either end of the scientific chain – the well-established at the top of the academic tree or the outsiders who have nothing to lose – it hurts those in the middle. Most professional scientists rely on the current system for funding and reputation. Others suggest it is throwing out some of the most important elements of science and making deep, long-term research more difficult.

Open science proponents say that they do not want to make the current system a thing of the past, but that it shouldn't be seen as immutable either. In fact, they say, the way most people conceive of science – as a highly specialised academic discipline conducted by white-coated professionals in universities or commercial laboratories – is a very modern construction.

It is only over the last century that scientific disciplines became industrialised and compartmentalised. Some of history's most influential scientists and polymaths – people such as Robert Hooke, Charles Darwin and Benjamin Franklin – started as gentleman scholars and helped pioneer the foundations for modern inquiry at a time when the line between citizen and scientist was blurred.

In attempting to recapture some of this feeling, open scientists say they don't want to throw scientists to the wolves: they just want to help answer questions that, in many cases, are seen as insurmountable. This means breaking down barriers by using the tools at our disposal – whether it's abundant biological data, inexpensive lab equipment or the internet. It might not be the way we think of science, but it is still science.

"Some people are naturally sympathetic to this sort of idea," says Professor Gowers. "Some people, very straightforwardly, said that they didn't like the idea because it undermined the concept of the romantic, lone genius." Even the most dedicated open scientists understand that appeal. "I do plan to keep going at them," he says of collaborative projects. "But I haven't given up on solitary thinking about problems entirely."