David Thouless, Duncan Haldane and Michael Kosterlitz's research could lead to the development of materials for electronics and science.
It is a peek into a world rarely seen, where matter can take on unusual and strange states.
While the 2016 Nobel physics laureates' work took place in the 1970s and 1980s, it has scientists excited about the possibility of even more exotic phases of matter.
Awarding the honour, Nobel Committee for Physics acting chairman Nils Martensson says the findings could have innovative implications.
"Today's advanced technologies -- take, for instance, our computers -- rely on our ability to understand and control the properties of the matters, materials, involved. And this year's Nobel laureates have, in their theoretical work, discovered a set of totally unexpected regularities in the behaviour of matter, which can be described in terms of an established mathematical concept, namely, that of topology. This has paved the way for designing new materials with novel properties, and there is great hope that this will be important for many future technologies."
David Thouless, Duncan Haldane and Michael Kosterlitz's research centres on a branch of mathematics called topology.
It looks at making step-wise changes to an object.
While phases such as a matter changing from a liquid to a solid are obvious, other steps are less so.
For example, the men proved superconductivity could occur in thin layers, demonstrating it could happen at low temperatures before disappearing at higher temperatures.
Nobel committee member Thors Hans Hansson, a professor of theoretical physics, explains the complicated concept using a bagel, a cinnamon bun and a Swedish pretzel.
"Now for us, these things are very different -- this is sweet, this is perhaps salty, different shapes, et cetera. But if you're a topologist, if you're a topologist, it's only one thing that is really interesting with these things in which they differ: This thing has no holes, the bagel has one hole, the pretzel has two holes. The number of holes is what a topologist would call a topological invariant. And, just as you cannot have half a hole, or two and two thirds holes, you can, for a topological invariant, only have integer numbers, only in digits."
Professor Hansson says, for example, a doughnut and a coffee cup have the same topological number, because they both have one hole.
He says changing that number requires radical action.
"And another thing which is very important for the following with topological invariants is that it takes something to change the topological number. I take this thing, you see, I can bend it a little bit, compress it, but, in order to change the number of holes, I have to do something drastic, I have to break it apart. And this stability of the topological invariance is going to be important."
The discovery could have applications for super fast quantum computers, with insulating matters being able to carry electrical currents at the surface.
In theory, those machines will be able to store data in compressed forms and solve problems in record time, eclipsing current traditional computing devices.
The three men sharing the prize all now work at universities in the United States.
They join the ranks of greats such as Albert Einstein and Marie Curie.
Addressing the Nobel ceremony via phone, Mr Haldane says he never thought their work would have such an impact.
"Like most discoveries, you stumble onto them and you ... you just have to realise there's something very interesting there. And one never realises the full implications of these things until other people have started thinking it's true and one realises the big picture. So most of the big discoveries are really that way, I think, at least in theoretical things. You don't ... you never kind of set out to discover something new. You stumble on it, and you have the luck to recognise what you've found is something very interesting."
