In 2002, three Indian mathematicians (Manindra Agrewal, and his two students Neeraj Kayal and Nitin Saxena) invented a faster algorithm for factoring large numbers — an advance that could be crucial for code-breaking. They posted their results on the Web. Such was the interest that within just a day, 20000 people had downloaded the work, which became the topic of hastily-convened discussions in many centres of mathematical research around the world.
This episode — offering instant global recognition to two young Indian students — offers a stark contrast with the struggles of a young Indian genius a hundred years ago. Srinivasa Ramanujan, a clerk in Bombay, mailed long screeds of of mathematical formulae to G H Hardy, a professor at Trinity College, Cambridge. Fortunately, Hardy had the percipience to recognise that Ramanujan was not the typical green-ink scribbler who finds numerical patterns in the bible or the pyramids, but that his writings betrayed preternatural insight. Hardy arranged for Ramanujan to come to Cambridge, and did all he could to foster his genius — sadly, however, culture shock and poor health led him to an early death.
The Internet enables far wider participation in front-line science; it levels the playing field between researchers in major centres and those in relative isolation, hitherto handicapped by inefficient communication. It has transformed the way science is communicated and debated. More fundamentally, it changes how research is done, what might be discovered, and how students learn.
And it  allows new styles of research. For example, in the old days, astronomical information, even if in principle publicly available, was stored on delicate photographic plates: these were not easily accessible, and tiresome to analyse. Now, such data (and, likewise, large datasets in genetics or particle physics) can be accessed and downloaded anywhere. Experiments, and natural events such as tropical storms or the impact of a comet on Jupiter, can be followed in real time by anyone who is interested. And the power of huge computing networks can be deployed on large data sets.
Indeed, scientific discoveries will increasingly be made by 'brute force' rather than by insight. IBM's 'Deep Blue' beat Kasparov not by thinking like him, but by exploiting its speed to explore a huge variety of options. There are some high-priority scientific quests — for instance, the recipe for a room-temperature superconductor, or the identification of key steps in the origin of life — which may yield most readily neither to insight nor to experiment, but to exhaustive computational searches.
Paul Ginsparg's arXiv.org archive transformed the literature of physics, establishing a new model for communication over the whole of science. Far fewer people today  read traditional journals. These have so far survived as guarantors of quality. But even this role may soon be trumped by a more informal system of quality control, signaled by the approbation of discerning readers (by analogy with the grading of restaurants by gastronomic critics), by blogs, or by Amazon-style reviews.
Clustering of experts in actual institutions will continue, for the same reason that  high-tech expertise congregates in Silicon Valley and elsewhere. But the actual progress of science will be driven by ever more immersive technology where propinquity is irrelevant. Traditional universities will survive insofar as they offer mentoring and personal contact to their students. But it's less clear that there will be a future for the 'mass university' where the students are offered little more than a passive role in lectures (generally of mediocre quality) with minimal feedback. Instead, the Internet will offer access to outstanding lectures — and in return will offer the star lecturers (and perhaps the best classroom teachers too) a potentially global reach.
And it's not just students, but those at the end of their career, whose lives the IInternet can transformatively enhance. We oldies, as we become less mobile, will be able to immerse ourselves — right up to until the final switch-off, or until we lose our wits completely — in an ever more sophisticated cyber-world allowing virtual travel and continuing engagement with the world