I met a pair of 20-year-old insurrectionaries last week. They were gently spoken and as slight as kittens, yet only recently the vice-chancellor at their elite university claimed they and their friends had threatened his life.

The story of how Dibyokamal Mitra, Nabottama Pal and a bunch of undergraduates drove one of the grandest institutions in Kolkata into meltdown needs to be heard far outside India. It’s an extraordinary blend of traditional protest rituals and social media, alleged police beatings and a march that brought an entire city to a standstill. But it also highlights one of our most important, yet under-remarked, geopolitical truths: in its megacities and towns, across campuses and workplaces, urban India is breeding a generation of angry young men and women.

In a report last year, the UN dropped its usual diplomat-ese to warn: “In every sphere – education, work and play – there is a mix of disenchantment, resentment and hope. With growth has not come equity. The cost of urbanisation is beginning to tell in a way that if left unattended could plunge society into fragments.”

Numbers alone make that globally significant: there are 433 million people aged between 15 and 34 living in Indian towns and cities. Imagine an army bigger than the combined populations of the US, the UK and Canada.

To see how quickly they might be mobilised, follow what happened with Mitra, Pal and their friends at Jadavpur university. At the end of August, a female undergraduate and her male companion were reportedly accosted on campus by a group of male students. She was allegedly dragged into a hostel and sexually molested, while her friend’s face was pulped. University authorities began investigating, but made no real progress. Instead, according to a charge the woman has lodged with police, senior academics came to her home to ask how she had been dressed.

By mid-September, frustrated students were protesting every evening outside the vice-chancellor’s office. It was peaceful. Violinist Mitra would do jazz renditions of We Shall Overcome. Then, one night, the students decided to block the journey home of their vice-chancellor, Abhijit Chakrabarti, by lying on the ground. The lights went out – and they were set upon by police. I couldn’t reach Jadavpur authorities for comment, but Chakrabarti has publicly said that he called police because he feared for his life – an odd anxiety to have about some teenagers and twentysomethings lying on the ground. Likewise, the police claim they used “minimum lawful force”. But video footage suggests that canes were used to beat students. Dozens were beaten and arrested, several ended up in hospital, women claim to have been groped.

As evidence of the beatings was uploaded to Facebook, then broadcast on TV, outrage spread. Three days later, central Kolkata was shut down for a rally by students from Jadavpur, other colleges and the public. Estimates of turnout vary from 30,000 to 100,000. Marches and protests were held in other cities across India. Jadavpur campus is still wallpapered with posters of its titular boss, Chakrabarti, that read “Resignation, no negotiation”.

Jadavpur is not an isolated example of youth protest. In past weeks, female students at Aligarh Muslim University in Uttar Pradesh have led successful protests to gain access to the main library (officials worried they would distract the boys); while at Benares Hindu University, also in Uttar Pradesh, parts of the campus have even been torched following protests over student representation.

These protests are linked by one thing. None of them are especially radical: young Indians are merely pointing out the failures of authority – to investigate an assault, to provide equal library access for women, to allow a student union. This is an old tale in India, of officials not living up to their promises. Even the use of physical repression in Kolkata is familiar. The only twist is that such an assault would be carried out at an elite university.

But what makes Jadavpur especially interesting is that familiar grievances were met with a new form of resistance: the movement is one of the first in India to use the internet to spread information and bring together activists.

Even as the police turned up that September night, Mitra was texting his friend who was putting status updates on a Facebook page. The rallies became known by a hashtag: #hokkolorob (in Bengali: make noise), after a song of the same name. After the beatings, an artist recorded a cover which is still doing the rounds on YouTube. As Mitra’s English professor, Abhijit Gupta, said: “The Indian authorities can and do police physical space; but they cannot hope to monitor virtual space.”

The point is, I can’t see India’s physical political space changing much: officials and politicians will continue to make promises that they extravagantly fail to meet. That UN report is stuffed full of graphs and figures, but the most telling is a piechart asking young people in Mumbai and two other Indian cities how they’d landed their job. Just under 45% came by it through contacts or family. Look at Patrick French’s research on the last Indian parliament, which found that two-thirds of MPs under the age of 45 already had a near relative in politics, while every MP under 30 had inherited her or (usually) his seat.

The gulf is between the pledges offered about the opportunities to be made in the new India, and the persistence of the old scratch-my-back system. Put yourself in the shoes of a middle-class Indian: for 20 years you’ve been told of the rewards of liberalisation; yet your position in no way reflects those promises. If you went to an English-medium school, then to university and now work in one of the growth industries, then the infrastructure doesn’t work, the transport system is a joke and you need to grease palms for government services, a decent school place for your kids, and so on. Meanwhile, the top jobs and offices go to the same faces. And you, my friend, are one of the lucky ones.

And that’s the point about the frustrations being voiced by India’s urban youth: they’re shared by their parents; it’s just that they’ve got less to lose by expressing them.

Aditya Chakrabortty is in Mumbai as part of Guardian Cities’ live week