I don't envy anyone running a university these days. Just thinking about it makes me queasy: hustling for "customers" as if they were airlines or insurance companies; trying to keep their vital numbers of fee-paying foreign students up at the same time as the government is saying, rather clearly, that foreigners are no longer welcome; persuading their staff not to emigrate when academics' pay is rubbish; and navigating a Kafkaesque system for awarding research funds that would give anyone trained in logic a nervous breakdown.

Forget those little headaches. There are some more fundamental problems rumbling underground, most of them triggered by the onward march of the digital world.

For a start there's the question of how to respond to the dinner-party truism that we're educating kids for jobs that haven't been invented yet. For 20 years smart folks like Ken Robinson have been saying there has to be much less emphasis on passing on knowledge and skills – much of which will be redundant by the time a student graduates – and much more on creativity, flexibility, teamwork and learning to learn.

That seems screamingly obvious to me, but education ministers of all stripes remain stubbornly committed to marching off in the opposite direction, and many in the education world, perhaps not unreasonably, see it as a direct threat to their intellectual empires – not to mention their departments, status and pensions.

The science/humanities division is redundant

And beyond the question "What are we educating them for?" lies a related bit of tricky swampland. The neat division of the world into skills and disciplines, grouped as "sciences" and "humanities", is being rendered redundant by the digital revolution.

Everything is suddenly converging in a gigantic open-plan office of the mind. The techniques, technologies and mindset of the world of arts and digital entertainment are now being brought into service across whole swathes of the economy, from hi-tech manufacturing to systems analysis and healthcare.

Three years ago Google's CEO, Eric Schmidt, admonished Britain for its failure to bridge the gap between what he called the "luvvies" and the "boffins".

We needed to get back to the great days of British dynamism in the industrial revolution when "the same people wrote poetry and built bridges". Of course, he's got to be right, but the world is a more complicated and sophisticated place than when Brunel was a young man so how, in the 21st century, does higher education respond to that call?

Unsurprisingly, and with that compelling need for "customers" in mind, some universities are serving up the academic equivalent of smoothies – chucking bits of arts, humanities, business skills and a couple of techie modules into the blender and giving the resulting course an attractive, low-calorie, career–oriented title. But there may be a better way to go.

As one leading venture capitalist is fond of saying, instead of trying to teach art students the skills they need to run a business, it would be more practical to teach them the social skills they need to make friends with accountants and lawyers.

The goal shouldn't be the production of mini Robinson Crusoes, (or, more accurately, half-arsed jacks-of-all-trades), but team players who can regard the need for intellectual, creative technical and business skills with mutual and equal respect.

Give equal weight to arts graduates and technology graduates

Research into 500 digital media businesses in Brighton found – surprise surprise – that the companies that gave equal weight to the role of arts graduates and technology graduates were growing three times faster than the ones that didn't, even though the skills of the staff in what the researchers called "superfused" companies were no better than in the "unfused". That seems like an important lesson.

True to their reputation of being the smartest people in Europe, the Finns are already ahead of the game – watching their economy disappear down the pan with the rapid collapse of Nokia, the Finnish government pushed an engineering university, an art school and a leading business school into bed together and rebranded it as Aalto University – the University of Creativity. The idea was not to homogenise them but to get them collaborating as equals. And it's working.

Meanwhile our very own Arts and Humanities Research Council is running a four-year programme looking at how to build more robust and productive relationships between universities and the clusters of creative, mainly digital, businesses that are located in the communities around them. It's looking at the interface between the generation of knowledge that goes on in a university, and the generation of ideas and wealth that goes on in an innovative business.

One component of this programme, Creativeworks London, is doing some really simple stuff like offering entrepreneurs short-term placements in university research departments and academic researchers equivalent placements in companies. There are very modest funds for specific projects that explore that interface between the knowledge-generating capacity of the university and the business-generating capacity of the small company. Results are beginning to flow and be analysed. It's looking good.

At a time when ideological and financial pressures on universities are threatening to degrade many of them into broken-backed servants of the labour market, hawking easily digestible courses of limited rigour and value, this is a small step towards recognising that the convergence of skills and disciplines triggered by the digital revolution doesn't mean abandoning the need for academic rigour and specialisation; it means we need to learn from the superfused companies of Brighton and the bloody obvious lessons that Ken Robinson has been preaching for a couple of decades. And if it's good enough for the Finns, it's probably good enough for us.

John Newbigin is the chair of Creative England and a member of the Arts and Humanities Research Council oversight group for knowledge exchange.

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