Hereford, some local folk say, could have had a university in the early Middle Ages and become like Oxford or Cambridge. But it was then considered a dangerous frontier town, a war zone between England and Wales, and today Herefordshire is one of the few English counties lacking a university. Next year, however, some seven centuries later, Hereford will have a brand new university. There will be just 50 students at first, 200 in 2020 and 5,000 in a decade. It will be Britain’s first new “greenfield” university – one not upgraded from an existing institution – in 40 years.

The university, we are promised, will be like no other. For one thing, it will focus, at least initially, entirely on engineering. (Until it gets a royal charter, it will be known, not very snappily, as New Model in Technology and Engineering, or NMiTE.) For another, it won’t have lectures, syllabuses, exams, or academic terms. Even the engineers who emerge won’t be engineers as we know them. They will, it is said, be “humanist” or “Renaissance” engineers who have dabbled in poetry, music or philosophy.

Presiding over this, as chief executive officer and provost, will be a slightly improbable figure: Elena Rodriguez-Falcon, a female gay Mexican mechanical engineer. There are probably not many such people in the UK, let alone in Hereford.

In her homeland, she tells me at her office in Hereford’s historical centre, women account for 35% of engineers, while in the UK it’s only 11%. NMiTE aims to recruit equal numbers of men and women, she says. “Women seem to want to choose what they perceive as a caring profession. Engineering is a caring profession. An engineer is nothing other than someone who solves the problems of the world.” She pulls a blister pack of tablets out of her desk. “An engineer may be asked to make this pack child-proof. That’s caring. It’s the kind of problem we shall ask our students to solve.”

She blames the specialised A-level system for the paucity of female engineers. Teenagers without A-level maths and physics are not usually admitted to engineering courses but her solution is to drop such requirements. “We shall want GCSE maths at a high level so we know there’s an aptitude. Then we can bring people up to speed when they require a specific kind of maths. We shall have toolkits.”

Toolkits? It takes time to master the new university’s language. It will have no open days for prospective students. Mobile “ingenuity studios” will tour schools, inviting pupils to try the equipment they will use at the university. Instead of courses or modules, NMiTE will have “sprints”, lasting three-and-a-half weeks, during which students tackle problems and projects brought by employers. They will develop not only engineering skills but personal and communication skills needed to satisfy customers and sell products. In place of exams, they will compile “portfolios” showing evidence of the skills acquired.

The “sprints” will be interrupted by “disruptors” – accountants, perhaps, philosophers, sociologists, even poets – who arrive unannounced to ask awkward questions such as “is what you’re doing ethical?”, or “should this be or not be?”. Learning will be “accelerated”, allowing students to gain a degree in two years instead of three, a master’s in three and, crucially, pay lower tuition fees (£6,000 instead of £9,250). The toolkits, in the brief periods between sprints, are the bits where students mug up on maths and other basics.

Where do the poetry and music come in? “Engineering is nothing if not creative,” says Rodriguez-Falcon. “We want students with diverse skills outside their subject and we want them to carry on with those skills because they help them to think in diverse ways. We may have scholarship programmes for those who want to develop violin-playing, or singing, or painting. An engineer with a different skill set will be a better engineer.” It sounds like a far more thrilling way to get a degree than the heavily theoretical lectures that characterise most traditional engineering courses.

Before she moved to Hereford this year, Rodriguez-Falcon was professor of engineering education (a chair in how to teach engineering rather than in engineering itself) at Sheffield University. She doesn’t criticise Sheffield – courses based on theory have a place, she agrees – but she says: “So many times in the past 20 years, I have said ‘if only I could start my own university’. Because I could get right things which are impossible to get right in universities that are so well established.”

She was born in Monterrey, one of Mexico’s wealthier cities, the only child of working-class parents. At first, she wanted to be a doctor “but then I realised I didn’t like blood”. She decided on engineering because it was relatively well paid. After graduation, she worked in industry and moved to England to take an MBA at Sheffield University. She intended to go back to Mexico but when the university advertised for a mechanical engineer with a business background to help design a new course, she applied.

“It wasn’t an academic job, it involved market research. But someone who taught business planning left and the department asked me to teach the module. I was asked to stay another year and, by then, I was hooked. I loved creating things with young people.” Twenty years later, she was still at Sheffield.

Hereford, chiefly noted for cider-making and military bases (the SAS has its headquarters there), isn’t an obvious place for an engineering university. But as Rodriguez-Falcon tells me: “People think engineering is only to do with cars, machines, buildings and bridges but everything around us – your glasses, your clothes, the chair you’re sitting on – has had intervention from some kind of engineer.” Local leaders developed plans for Hereford’s university but it became evident that government money would be available only for a vocational venture offering the two-year degrees that many Tory politicians favour.

Here, doubts creep in. The university’s four principal themes, according to its website, will be “feeding the world”, “shaping the future”, “living in harmony” and “a healthy planet”. Cynics might dismiss this as clever marketing – pitched at what Rodriguez-Falcon calls “a generation of young people who want to make a difference to the world” – and argue that NMiTE’s programme will be dominated by industry’s needs.

Concerns have been raised, she admits, about links to the defence industry. Students will follow an “integrated” engineering programme, not one divided into the usual mechanical, civil and electronic tracks. I ask if students will follow tracks linked to particular industries, with defence among them. “Not explicitly,” she replies. “Students will tailor their learning as they wish and, yes, they could select projects that follow one industry, such as security. But it’s not a path we will set out specifically.”

Cynics may wonder whether the poetry, the disruptors, and the other quirky, if attractive, ideas, along with the relaxed A-level requirements, can survive the scrutiny of engineering’s notoriously conservative professional institutions, without whose imprimatur any course is doomed.

But Rodriguez-Falcon’s engagement and sincerity are hard to resist. “I know this kind of course isn’t for everyone,” she says. “We need to find the kinesthetic learners for whom this model is right. I came here to see this through. I imagine that, a hundred years from now, this university will be flourishing, producing wonderful engineers. I don’t have children. This will be my legacy.”