G.H. Hardy was one of the greatest mathematicians of the 20th century. In 1913, while working at the University of Cambridge, he received a package consisting of closely written pages of mathematical analysis from an untutored Indian, Srinivasa Ramanujan. Hardy was not the first mathematician to receive a package from Ramanujan: a number of other prominent English mathematicians had also been recipients, but they had ignored it. Hardy did not. He showed the work to a colleague, J.E. Littlewood, and both came to the conclusion that the work was produced by a highly talented mathematician.

Ramanujan was invited to come to the UK and he collaborated with Hardy on a number of landmark publications. In 1918, at the age of 30, Ramanujan was elected to the Royal Society, becoming one of its youngest-ever Fellows. Despite his short lifespan - he died aged 32 - today he is regarded as a major figure in pure mathematics. When Hardy was asked about his greatest contribution to maths, he did not list his own achievements. Instead, he stated that it was the discovery of Ramanujan.

Throughout the course of history, there are examples of citizens outside academia whose work has had major scientific impact. In the 19th century, for example, Mary Anning, the daughter of a cabinetmaker, discovered fossils on the Jurassic Coast that made a major contribution to our thinking about prehistoric life. Last year, the Royal Society named her one of the 10 British women who have most influenced the history of science.

More recently, Sharon Terry, a college chaplain with no scientific training, taught herself molecular biology after learning in 1994 that her two children had a rare condition called pseudoxanthoma elasticum, or PXE (see below). An inherited disorder that causes tissue in the body to become "mineralised" - calcium and other minerals are deposited in body tissue - PXE damages the skin, eyes, cardiovascular system and gastrointestinal system. So, together with her husband Patrick, a fire-sprinkler designer, Terry developed a research plan over a two-month period to attack PXE; one of the results from this plan was the sequencing of the gene responsible for the condition, ABCC6.

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Terry now co-directs a 33-lab research consortium, with the labs providing facilities for diagnostic tests for PXE using her work. She also manages 52 offices worldwide for PXE International, the not-for-profit organisation developed to further those efforts. PXE International's website highlights a unique collaboration between scientists, clinicians, advocacy groups and citizens who want to help with research. A major part of its effort has centred on organising an international collaboration of 36 scientists. This has helped to generate research findings far more quickly than would have been possible with smaller research teams.

Ramanujan, Anning and Terry are all examples of citizen scientists: individuals without formal scientific or mathematical training who have contributed at the highest level. All faced barriers - technical, financial and cultural. Anning faced prejudice against women, Ramanujan lived a poverty-stricken existence in India and Terry was not able to access the research literature to the extent that academics could; she had to pay for access to journals, for example. But virtually all the cultural barriers have now been removed and many of the technical barriers that still existed in the latter part of the last century are being diminished. The technical obstacles are being eroded by the computer and the internet.

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As a result, many internet-based projects have enlisted citizen scientists to help carry out research. The Cornell Lab of Ornithology, for example, has a project that involves amateur birdwatchers in the gathering and collating of data on bird life in the US. Meanwhile, Galaxy Zoo is a project, also in the US, that invites members of the public to observe and classify galaxies in the universe. And at my own university, 6,000 people in 15 European countries took part in a citizen science project to observe evolutionary change in snails. The results were published in the peer-reviewed, open-access journal PLoS ONE. In 2009, The Open University also created the Creative Climate project, a global diary that documents how human beings respond to climate change.

But there are two notable features of current citizen science projects. The first is that the vast majority are situated in the US, where there is a long tradition of engagement of US universities with schools and communities and of citizens generating useful science. A recent example was the discovery of a strange type of neutron star, called a rotating radio transient, by Lucas Bolyard, a high-school student from West Virginia.

The second is that many projects are "passive": citizens who participate largely carry out rather rudimentary observational activities, such as observing, counting and classifying. This is necessary and worthwhile, but I believe that we are now at the point where academics can encourage their non-academic collaborators to take a more active and in-depth approach.

It is now possible for citizens to explore science in a way that goes far beyond simple data collection. Scientists have used the internet to create a virtual laboratory of data that can be accessed by anyone with a browser, as well as a number of cutting-edge research tools. A good example of such a repository is the Australian National Data Service, which acts as a clearing house for materials generated by scientists.

Software developers have also created a number of research tools that are freely available online at no cost. (Two good examples are Gnuplot, a fantastic graphic and plotting package for displaying research results, and the R programming language, used for developing statistical software and data analysis.) And the internet allows researchers and citizen scientists to work together via collaborative websites such as wikis.

But why should a busy academic researcher consider getting involved in, and doing more to encourage, citizen science? There is a core reason: that it promotes science. There is also a very strong pragmatic reason. The two communities - academics and citizens who want to carry out science - have complementary skills. Academics have a high degree of professional training and education in science, but face career pressures arising from the research excellence framework, citation indexes and metrics that measure an academic's research; all this can lead to a degree of conservatism. On the other hand, citizen scientists have raw skills but do science for non-career reasons, often with a huge enthusiasm for creating new knowledge.

The expertise of those outside the academy is becoming increasingly important as science becomes more complicated. This complexity is a result of modern computing technology and the nature of data that is now collected. At this very moment, computers attached to ships are gathering data from the oceans for climate researchers. Meanwhile, computers deployed in projects such as the Large Hadron Collider provide huge quantities of data for physicists, and computers attached to sequencing technology generate and collect data that can be used for the sort of research that Sharon Terry carried out.

This type of computer-generated scientific data has a number of unpleasant features. There is a lot of it, it contains errors, it is stochastic, it requires complex software for its analysis, it can be biased between different runs of the same piece of equipment; it is very difficult to look at the results from experiments and establish research relationships between elements of the data because of the size of the datasets and the large number of variables; and it is often resistant to the analysis that statistical methods of the last millennium provided.

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Potential citizen scientists have data-processing skills that are often in short supply within science departments: for example, programmers in industry have advanced software skills and statisticians in the commercial and business worlds often have statistical expertise in excess of those found in a science department.

Imagine if a scientist could gather a team of citizen statisticians, computer programmers and, indeed, managers to organise and manage the research. They would have at their fingertips resources they could never hope to obtain from research funding organisations such as the Medical Research Council.

Some academics might worry that there is a danger that academics engaging citizen scientists could be seen in the same negative light as that of companies taking on unpaid interns. But provided there is an implicit contract between the academic and the citizen in which the academic promises to teach skills, such as research methods, and to include collaborators as authors on research articles, a professional and mutually beneficial relationship can be established.

There are a number of things academics can do to encourage citizens to engage in science.

The first is to engage in reproducible research. All the products of a research publication - software, data and the research article itself - should be packaged up in such a way that the work described can be downloaded, repeated and extended. In a recent article in Journal of Science Communication (JCOM), Victoria Stodden, an assistant professor in the department of statistics at Columbia University and a leading cheerleader for reproducible research, argued that citizen science could be hugely enhanced by attention to reproducibility and that it would lead to major increases in public science engagement.

Increasingly, research data are being made available. From the beginning of the last decade, more and more journals and research funding bodies began to insist that data supporting published research should be made available on request. The trend was accelerated by the release of emails from the Climatic Research Unit at the University of East Anglia. Whatever the rights and wrongs of this incident, it and subsequent rulings from the Information Commissioner have made science departments much more aware of the imperatives of publishing research data, protocols and program code on their websites.

Increasingly, academic journals and funding organisations are also demanding access to relevant software. Science, the US competitor to Nature, recently asked authors to make program code available on request. A good example of a journal at the forefront of this development is Biostatistics, which has appointed an associate editor for reproducibility. Academics should lobby journals to have explicit policies on reproducibility.

The second thing that academics can do is to proselytise science more - not just by writing about their specific discipline but more generically. When I was young, I bought a book with the title Mathematics for the Million: How to Master the Magic of Numbers. Written by Lancelot Hogben, it was first published in 1936 and reprinted many times - and it was an example of the sort of material that my university develops for open-learning students. Hogben was an academic zoologist and statistician; his book, together with a 1938 companion volume Science for the Citizen: A Self-Educator Based on the Social Background of Scientific Discovery, sold over half a million copies. It was the inspiration for a whole generation of mathematicians and scientists - including me. There is a need for someone to do the same for science in the internet age. After all, as well as being a passport to impact metrics, research assessment exercise ratings and personal citation metrics, science is an enjoyable, challenging and rewarding activity that is akin to completing a puzzle or even solving a crime.

Academic outreach is an important part of this endeavour. Some of the professional societies do good work here, but much of it is drowned by the messages from university open days and other events that a degree in a particular science is a passport to better employment prospects.

A good model for outreach is the Pulsar Search Collaboratory, a joint project of the National Radio Astronomy Observatory and West Virginia University. Funded by a grant from the American National Science Foundation, the project provides training for teachers and student leaders and makes data from a major radio telescope available to those teams. Lucas Bolyard, the high-school student who made the discovery of the neutron star, was a member of one of the teams.

But some barriers to citizen scientist participation in research do remain, particularly in the area of publishing.

In 1982, Douglas Peters and Stephen Ceci published a controversial study of refereeing practice. They took 13 psychology research articles that had been written by staff at prestigious US universities and published in top-notch journals. They resubmitted them to the same journals that had published them previously, with fictitious author names and less prestigious author institutions such as the Tri-Valley Center for Human Development. The first surprising result was that in the non-blind refereeing process, only three of the papers were identified as having been previously published; of the 10 undetected manuscripts, nine were recommended for rejection resoundingly, with the grounds often being cited as "serious methodological flaws". The second was that none of the 20 reviewers who recommended rejection suggested that a paper would be acceptable for publication following revision. There is clearly a chance that a paper from someone living at 23 Acacia Avenue might receive the same treatment.

What is needed is a levelling of the playing field with more blind refereeing, where authors' identities are withheld from referees. Some journals do this already: I recently had a paper published in The British Journal of Social Work that rigorously enforced this policy, down to forbidding any acknowledgement to colleagues and other clues such that I had recently been a member of a government review into childcare.

There is also the important issue of access to journal papers. Sharon Terry had to pay to access scientific journals when she carried out her research on PXE. With the open-access movement, journal articles are beginning to be more readily available. For example, many research articles in medicine are publicly available at the PubMed Central website. But universities should consider supplementing such schemes by opening access to their digital resources and making only a minimum charge to subscribers outside academia. So there are challenges to be overcome, but there are also significant rewards to be won. Universities that adopt a more outward-facing view of the world would be doing a service to both academics and the public - and a service to science itself.

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'I didn't know a gene from a hubcap until my daughter became ill'

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Worried about a rash on the neck of her seven-year-old daughter Elizabeth, Sharon Terry took her to see a dermatologist just before Christmas in 1994.

It turned out not to be a typical skin condition. Elizabeth and her five-year-old brother Ian had a rare disease called pseudoxanthoma elasticum, or PXE, an incurable connective-tissue disease that can cause bleeding, skin lesions and blindness by the time sufferers are in their thirties.

At the time, "we didn't know a gene from a hubcap", Terry has written. But she and her husband Patrick were determined to do something and, working from their home in suburban Boston, they set out to find the gene responsible.

"We realised that if we got enough people's DNA, we could find the gene," Terry has said.

"So we decided to make a central repository. And we decided to keep the key to the repository ourselves."

The couple collected more than 1,000 DNA samples from people with the disease, and made the samples available to researchers interested in PXE. They managed to raise $500,000 to help fund research.

The grants they have awarded include a $10,000 grant to scientists at the Jackson Laboratories in Maine to create a genetically altered mouse whose condition mimicked PXE.

Terry has also worked to establish connections among laboratories from Hawaii to Italy.

Today, she is the co-director of a 33-lab research consortium and was involved in the cloning of the gene that is mutated in PXE patients.

She also worked to isolate the DNA and sequence the gene, ABCC6.

Terry is listed as a co-inventor on the gene patent and she is president and CEO of the Genetic Alliance, a not-for-profit health advocacy organisation committed to transforming health through genetic research.

Jack Grove

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Little stars making a big impact on astronomy

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Teenage astronomer Lucas Bolyard won international acclaim after he discovered a star of a particularly rare type.

The high-school student from West Virginia made the find as part of a school project in which pupils were trained to study data from one of the National Science Foundation's massive radio telescopes.

After many hours spent studying some 2,000 data plots in March 2009, Bolyard had found nothing.

But one weekend while bored at home, he turned his attention to the charts again and was drawn to an unusual blip on a data printout.

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"I saw a plot with a pulse, but there was a lot of radio interference, too," he told journalists.

The pulse was almost dismissed as interference, but several months later, Bolyard's data was reprocessed by experts and confirmed as one of only 30 known rotating radio transient stars.

Similar to pulsar stars, these superdense neutron stars are the corpses of massive stars that exploded as supernovae, emitting radio waves sporadically.

Bolyard was invited to go stargazing with Barack Obama on the White House lawn in October 2009.

Other guests at the president's star party included Caroline Moore, who lives near New York, who in 2008, at the age of 14, became the youngest person to discover a supernova.

That record was broken by 10-year-old Kathryn Aurora Gray, from New Brunswick, Canada, in January 2011.

Jack Grove

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(A bit too) fired up by nuclear fusion

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Amateur scientist Richard Handl found himself in a spot of trouble with the authorities for trying to split the atom in his kitchen.

Unemployed Handl was arrested in July at his home in Angelholm, Sweden, after he admitted cooking up nuclear materials on his hob. He told officers he had acquired americium, radium and beryllium via mail order from Germany and mixed them up in a saucepan with 96 per cent sulphuric aid.

An explosion and mini-meltdown later, Handl, 31, decided to contact the Swedish Radiation Safety Authority to check if his project was legally permissible. Shortly afterwards, the police turned up.

"I have always been interested in physics and chemistry," he was reported as saying, adding he just wanted to "see if it's possible to split atoms at home".

Admitting that his experiment was "crazy", Handl has decided to put an end to future nuclear fusion attempts.

"From now on, I will stick to the theory," he has told the press.

Jack Grove

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How 'hobbyists' in the computer world can make a useful contribution to scientific research

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When James Gill began his PhD at the University of Edinburgh in 1998, his intention was to pursue a career as a particle physicist.

By the end of his doctorate, his fascination with the subject was undimmed, but the realities of life in academia had given him pause for thought.

In the end, he opted for a more stable existence as a computer programmer, moving to Cambridge where he now works for the software firm Autodesk.

"The main reason I chose not to pursue an academic career was the insecurity," he says. "It's hard to get a postdoctoral position and even harder to progress to a permanent position.

"I would have had to accept spending perhaps 10 years moving from postdoc to postdoc, which would have made it hard to settle. But I was sad when I left physics."

One development that enabled him to stay in touch with the field was its early adoption of open-access publishing.

"For several years afterwards I would keep an eye on what people were publishing," Gill says.

This habit has fallen by the wayside, but he believes that the accessibility of journal papers is key to keeping enthusiasts engaged, and he still uses research in his work.

"When I'm working on mathematical problems I will often try to survey the literature," he says.

Gill admits that, at this point in his life, he does not have the time to devote to a citizen science project.

"My life is pretty full with work and a young family," he explains. "But I can imagine many people wanting to do so.

"It's a bit like the free software movement, with people all over the world writing high-quality computer software for no personal gain."

Would he have been interested in it at another point in his life?

"Yes, I might have been, if I'd been approached by someone I'd worked with previously or an area I had a strong interest in," he says.

And he believes that in his field, non-academics would be able to make a useful contribution.

"Software development at university can be pretty chaotic - it certainly was when I was doing my PhD. If you brought in someone with industry experience it would be pretty helpful," he says.

Ten years after his PhD, he does not think he "could go back now and crack really hard physics problems".

But he could, he suggests, "write some pretty good software to help solve those problems".

Some of Gill's colleagues do donate their time to university research.

Until joining Autodesk seven years ago, Jean Flower was a researcher at the University of Brighton working on diagrammatic layout and reasoning.

She has kept in touch with former colleagues, regularly helping them by writing software to test their ideas.

"I'm really interested in the area and I wanted to keep up with the research.

"I'm glad I can contribute. It's exciting to see theoretical ideas tested and brought alive using prototype software."

She finds the time - around seven days a year - by taking time off from her day job and by working on projects in the evenings and at weekends.

"I think a lot of people who work in the commercial sector in software development are hobbyists in one way or another and they have pet projects that they do at home," says Flower, who also keeps abreast of newly published research.

"It's good to work in a different programming language or different framework from the one you deal with every day at work. I think it keeps your broader skills alive."

She says she does not expect to be paid for her contribution, as "universities don't have a lot of cash". But, she notes, voluntary contributions cannot replace more formal arrangements under which software developers are employed to work on university research projects.

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Rebecca Attwood