Universities are many things to many people ¨C shapeshifters in the public consciousness, which leaves them open to an endless, often conflicting, set of critiques.

They do too much research, not enough research or the wrong research. They teach too many students, not enough students, or the wrong students. They do not focus enough on vocational skills, or they have dumbed down unforgivably.

The thing about this kaleidoscope of views is that it¡¯s based on a truth: that universities are many different things at the same time, and this can make it hard to get agreement about where the value lies, or a general understanding of how the parts interlink.

Universities talk about the importance of research-led teaching, for example, but does that mean much to the man or woman on the street? More specifically, does it mean enough for them to view the subsidy that tuition fees provide for research as acceptable?

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These are the sorts of questions that swirl around the ¡°impenetrable puzzle in a box¡± (to quote the ever-quotable Universities UK chief executive Vivienne Stern) of how to reform university funding in England.

After seven years of frozen tuition fees, high inflation, and, more recently, a downturn in international students, the financial crisis is not a debating point.

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That Labour identified this as an early priority (one of a small number of items on Downing Street chief of staff Sue Gray¡¯s famous ¡°shit list¡±) was promising, but the ball seems to have been left firmly in the sector¡¯s court to come up with proposals that could work.

In the past few weeks, Universities UK has begun to do that ¨C with understandable caution about stepping on the multiple landmines that litter the debate.

At the UUK conference, it fell to Shitij Kapur, vice-chancellor of King¡¯s College London, to?put a number on the deficit that universities currently face ¨C he pointed out that had the fee paid by students been linked to inflation, it would be worth about ?12-13,000 today. This purely factual observation sparked some panic that it would be interpreted as a call for fees at that level, something that Kapur firmly refutes in our news pages this week.

Rather, the blueprint UUK is edging towards seems to be a level of public subsidy that secures the quantity and quality of university provision the country needs, with a more modest return to annual inflation-linked fee increases from the current level.

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While such an approach would be less incendiary to the public than a big hike in the headline fee, it does not defuse the wider problem, which is that the pressure on what to prioritise for public investment is acute.

Universities will continue to find competing demands from, say, early years education, or the health service, a major challenge.

The main asset at their disposal is the case that they are crucial to the growth and prosperity that the government is banking on to overhaul and rehabilitate a country in the doldrums, but for this argument to carry the day universities must offer more than simply more of the same.

With that caveat in mind, it was heartening to hear no less a Labour figure than Tony Blair voice his belief in the power that universities have to deliver for the country at a time of rapid change.

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In an , he pointed to the UK¡¯s strong showing in the upper reaches of the Times Higher Education World University Rankings, and called for universities to be nurtured.

¡°They are the engine for economic growth, they are places where you incubate innovation and we are second in the world on universities. There is this anti-university sentiment now, but no one is forcing children; they want to go¡­That is a huge strength,¡± he said.

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So has the impenetrable puzzle in a box been solved? Clearly not. But sector leaders have started to remove the cellophane, and cautiously accept that if no one is coming to put it together for them, they had better start trying to piece together what they can.

john.gill@timeshighereducation.com