Rachel Wolf is a director of Public First. She was the education and innovation adviser in David Cameron’s Downing Street Policy Unit, and was founding director  of the New Schools Network.

Grammars, less immigration, a new industrial strategy. This does not instinctively sound like a modern government.

That is why Theresa May’s speech to the CBI last week was so important. Not only did it explain what a proper industrial strategy might look like, but it showed that this Government believes the future can be greater than the past.

Britain was once the most innovative country in the world. Ideas that propelled the West to prosperity originated here: the steam engine and Brunel’s grand projects; evolution, antiseptics and penicillin. We no longer have that ambition. How do we regain it?

Innovation requires a dynamic and long-termist private sector. It needs world class universities and labs. It also requires the right kind of public investment. We have some of those conditions. There is an increasingly impressive ecosystem of investors and entrepreneurs in the UK. We have learned many of the lessons of Silicon Valley, and undone much of the damage of the post-war period.

Our universities are still remarkably good, particularly given their funding. But we do not give them the kind of research support that the best US universities enjoy. And the way in which we fund research supports incremental quality, but not transformation: It is hard to imagine Darwin or Einstein doing well under our funding regime. We haven’t founded a new top-quality institution in decades, focusing instead on university expansion for less able students.

Worst, our public sector is unambitious and short-sighted. When I was advising the Government we fiddled at the margins – crafting announcements that appeased stakeholders and were somewhat useful, but hardly game-changing.

Often, the reason given was money. We are not as big as the US, nor do we spend much in comparison on R & D. America has become, post war, the great driver of innovation and the consensus view is that we cannot compete (although Israel has managed to become astonishingly innovative under much tougher circumstances with far fewer people and less money).  This is a bad attitude.

We are all facing stagnating living standards in the West. While there are short-term policies on productivity and redistribution that can make a modest difference, we are only going to transform living standards by another wave of innovation. It is ideas that made us rich in the first place, and only ideas can solve our long-term challenges. What are we supposed to do – just hope America sorts it for us? The relative size of Britain means we should be focused, rather than unambitious. David Willetts briefly achieved this through his “eight great technologies”, but by the time I arrived they were largely ignored.

Some of the answer does indeed lie in the US. We hear a lot about Silicon Valley, but far less about the importance of the government in innovation. Institutions such as DARPA (the Defence Advanced Research Projects Agency) are responsible for many of the most significant scientific and technological inventions of the last 70 years.

DARPA is an unusual organisation. It has an incredibly simple mission: “prevent technological surprise”. Its program managers are top scientists and engineers. They only stay for a few years – because anyone, no matter how good, becomes hidebound. It funds projects with a very high risk of failure. Their budget is tiny compared with the rest of the Department of Defense ($2.9 billion). It actually lobbied to shrink its budget during the 1990s because size breeds bureaucracy.

Once DARPA decides to back your project, you are given freedom. They believe in ‘people, not projects’. If you are funding one of the world’s brightest, leaving them alone is the most sensible thing to do. And then DARPA judges results, not method. It pits teams against each other, using competitions with a clear goal to spur ideas and figure out what works.

The result? In recent decades, DARPA projects have underpinned cloud computing, GPS, speech recognition, satellite imagery, unmanned autonomous aerial vehicles, and interplanetary rocket engines. DARPA is so successful it has spawned many imitations in the US – such as IARPA, which focuses on intelligence.

This is not how we work. Our institutions are timid. Innovate UK, for example, is under pressure to rapidly bring in private investment. This means it promotes low risk, and lower potential, innovations.

Which brings me to May’s speech. She made clear that her industrial strategy was an innovation strategy, and put real money behind the rhetoric – with £2 billion more a year for R&D by 2020. She also announced an industrial strategy ‘challenge’ fund to back emerging technologies.

This challenge fund has enormous potential, but only if we deliver it in the right way. We need to learn from what works:

First, successful institutions align action with self-interest. DARPA’s mission is about national security. Its aim is to improve the US’s long-term position in something that is clearly the Government’s job – not the private sector’s. The spillovers have created enormous wealth, but that’s not how the projects were conceived. If we want government to drive innovation, we need to align its interests with its funding. In our case that could mean security (including cyber), health technologies and drugs, and AI: all areas where we have both technological strength and clear governmental interests.

Second, people matter. The people who fund DARPA projects are the best, and the people who work on them are the best. You can’t have junior procurement officers doing ‘innovative funding’, or civil servants trying to create competitions for innovation. You need a completely different cadre of people. And when you fund projects, you need to trust the people who are doing them. The best are self-motivated. If the people you’re funding can’t be left alone, they’re the wrong people.

Third, there’s no point in the Government getting involved if the risk is not high. The private sector can sort low risk. If government innovation funding has too high a success rate, it is probably doing the wrong thing

Fourth, don’t dissipate the money everywhere. We are too prone to £5 million funds that achieve nothing. Yes, we are smaller than the States: so we should choose what we really care about.

If we use May’s new industrial strategy to create a genuinely ambitious innovation program, we can create a modern national agenda that everyone – Leavers and Remainers alike – can get behind. To do that, we need to radically rethink how the state should act.