First rare-earth element discovered by Finnish chemist Johan Gadolin in 1792 after receiving a heavy mineral from Swedish village of Ytterby. Subsequent rare-earth elements identified and isolated over a period of about 150 years.
The core group of 15 rare earths are known as lanthanides. These have an atomic number from 57 to 71 and are grouped together in the periodic table.
Scandium and yttrium - making the total number 17 - are also considered rare earths as they exhibit similar chemical properties to lanthanides. Final one to be discovered, in 1945, was the radioactive promethium, which is the rarest.
Wide range of uses such as in camera and telescope lenses, catalytic converters, refining crude oil, magnets and X-ray scanning systems.
Its loud ticking is impossible to ignore. He is delighted when I ask about it. It is, he says, an original example of a synchronome clock.
"I bought it to inspire, and because sometimes I feel the need to rub my colleagues' noses in the fact that there are simple solutions to engineering problems people have struggled with for centuries."
The synchronome, designed more than a century ago in Britain, is the most accurate pendulum clock ever built - correct, according to recent studies, to one second every 12 years.
It represents, he explains, an exceptionally elegant answer to the challenge for horologists down the centuries - by reducing the mechanism down to a single gear wheel.
Until very recently Stiesdal and his colleagues faced a similar challenge. They wanted to strip out the gear systems in their turbines.
Wind turbines need gears because the blades turn at about 10 revolutions a minute but the generators that convert that rotation into electricity operate at more like 1,500 revs.
The problem is that - just as with clocks - the more complex a mechanism becomes, the more things can go wrong. And, in the world of wind turbines - particularly offshore turbines - mechanical failure is very expensive. You need specialist crane ships, engineers and good weather. The bill very rapidly runs to hundreds of thousands of dollars.
So how could Stiesdal and his team get rid of all those gears? The industry's solution - as you will have guessed - involves the rare earths.
In his laboratory in University College London, Prof Andrea Sella's face lights up when I ask him about them. Clearly this family of elements is particularly close to the chemist's heart.
"The first thing you need to know is they are neither rare nor earths," he tells me.
They are known as "rare" because it is very unusual to find them in a pure form, but it turns out there are deposits of some of them all over the world - cerium, for example, is the 25th most common element on the planet. The term "earth" is simply an archaic term for something you can dissolve in acid.
They are grouped together as a family because of their incredible chemical similarities - the reason it took a century of chemical investigation to finally isolate them all.
But the rare earths' chemical similarity belies all sorts of fascinating and often very useful electro-magnetic and optical differences.
To demonstrate, Andrea produces a rack of test tubes containing a selection of the rare-earth elements, each one a different pastel shade - there are gentle pinks, purples, blues and greens.
The radioactive element promethium, is missing from his collection. Andrea calls it the "cuckoo in the nest".
Promethium isn't found naturally on earth, but is formed in nuclear reactors. You may be carrying a tiny trace of promethium now because it has been used in the luminous paint on some watches.
Andrea waves an ultraviolet light over his collection. Some suddenly light up in vivid fluorescent colours.
"One of the incredible properties of the rare-earth elements is that they produce different wavelengths of light - specific colours - exactly on demand," he explains.
It turns out this property forms part of the anti-counterfeiting system used in euro notes.
Andrea takes a 50-euro note from his wallet and places this under the UV light. Bright green and blue stripes and shapes appear together with a constellation of beautiful blue and pinky-purple stars.
"Those stars contain europium," he says, grinning broadly. "This tells me that there is someone with a sense of humour at the beating heart of the European Union."
But the optical properties of the rare earths do more than just deter forgers. The distinctive green light in a television or computer screen is generated using terbium, while the red colour is produced by a combination of europium and yttrium (which is often treated as an honorary member of the rare earths).
But the most useful rare earth - in optical terms - is probably erbium.
The light produced by erbium is out in the near-infrared spectrum and is invisible to the human eye.
But it can send signals down optical fibres for many kilometres, which is why most of the optical fibre applications around the world use signal amplifiers made with erbium.
Rare earths are also essential for the catalytic converters that scrub the exhaust gases of cars clean and in glass polishing.
But it is the incredible magnetic properties of some of the rare earths that most of us - unwittingly - exploit most often.
Andrea passes me a rectangular lump of dark grey metal a few centimetres long.
"Hold this," he orders. I clutch it in my fist.
He produces a two pence coin and places it on the back of my hand.
Even through the thickness of my hand I can feel the magnet tugging at the disk of metal.
"That is a magnet made with neodymium," he explains. "It is 10 times as powerful as a normal iron magnet and can hold 1,000 times its own weight."
It is no exaggeration to say that the miniaturisation of technology would not be possible without these incredible magnets.
They are a surprisingly recent breakthrough. The first magnets using the rare earths neodymium and scandium were developed only in 1982, but their discovery has revolutionised all sorts of technologies.
The tiny motors that power computer hard drives and the miniature speakers on mobile phones and laptops depend on rare-earth magnets.
Neodymium magnets are used in electric guitar pickups, MRI scanners and microwave ovens. You can even buy cufflinks that link up with neodymium magnets.
And they also hold the key to Mr Stiesdal's challenge - getting rid of the huge gear mechanism in wind turbines.
The stronger the magnets, the easier it is to generate power at lower speeds.
An electric current is generated by induction - the electrons are driven as a magnet moves past a coil of wire. The stronger the magnet, the more the electrons move.
Down in one of Siemens' huge engineering sheds below Stiesdal's office, I was shown one of the company's new gearless turbines.
It is much more compact than its forebears. The core is a ring about five metres in diameter, like a giant doughnut, which encloses the axle.
This ring is packed with 648 22cm-long neodymium magnets laced with another rare-earth element, dysprosium, which makes them much less liable to become demagnetised.
It means, Henrik Stiesdal tells me with evident pride, that the same power can be generated without any gear system at all.
The problem is getting hold of the rare earths that make this possible. More than 85% of the world's supply of rare-earth metals comes from China.
And practically 100% of the "heavy" rare earths - at the farther end of the periodic table - come from China, including Stiesdal's dysprosium.
China has some very rich deposits of rare earths in Inner Mongolia. And, until recently, China has not been very squeamish about the consequences of rare-earth extraction.
It is a very dirty business. Rare earths are often found with radioactive elements like thorium and uranium, and separating them out requires a lot of toxic chemicals.
Jack Lifton, founder of Technology Metals Research and an expert on rare earths, describes how, in China, the process of extraction involves leaching out the elements. They flood the high ground with chemicals, he says, and then precipitate out the metals, leaving behind a lake of carcinogenic waste fluids.
In recent years China has been trying to clean the industry up. But it can't actually stop production, because many of the hi-tech industries at the heart of the Chinese economy rely on rare-earth supplies.
Just how dependent the entire world is on Chinese rare earths became very clear at the end of 2010 when China threatened to restrict supplies. The spike in rare-earth prices was very dramatic - up to 3,000% for some of them.
Prices have since fallen back, but the shock was enough to prompt companies to begin to explore producing and refining rare earths elsewhere in the world.
And how did Stiesdal respond to this shock?
"The neodymium exists in large abundance outside China. There are a couple of companies outside China that could keep us running for thousands of years."
And the dysprosium?
"It turns out you can tweak the way you deal with your alloy so you need less. In today's magnets we have 0.7% dysprosium, and in a few years it will be all gone."