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Mathematics is a powerful tool in physics, describing everything from the shapes of planetary
orbits to the properties of atoms. Math was used to predict the existence of the planet
Neptune, radio waves and the Higgs Boson. Some\hthink it means nothing profound, or
that math is simply something we've made up to be useful. Others think it means\hthat
there's something\hfundamentally\hmathematical about nature.\hThe most extreme possibility
is that our universe is completely mathematical, in the sense that it has no properties\hexcept
mathematical properties.\h
But\hat first glance, our universe doesn't seem very mathematical at all. A sheep\hhas
properties such as cuteness and\hfluffiness — not mathematical properties. Yet we know
that this sheep - and everything else in our universe — is\hultimately made of elementary
particles such as electrons and quarks. And what properties does an electron have?\hSmell?\hColor?
Texture? No, only properties like -1, ½ and 1! We physicists call these properties electric\hcharge,
spin and lepton number, but the electron doesn't\hcare what we call them: the fundamental properties
that\han electron has are just numbers, mathematical properties. As far as we know, all elementary
particles, the building blocks of everything\haround, are purely mathematical objects in the sense
that they don't have any properties\hexcept for mathematical\hproperties. The same goes
for the space that these particles are in\h- for\hexample, it has the property 3, the number
of dimensions. If space is mathematical and everything in space is also mathematical,
then\hthe idea that everything is mathematical doesn't sound as crazy anymore.\h
Quantum mechanics and string theory introduce even more mathematical structures, with nerdy
names like Hilbert space, linear operators and\hCalabi-Yau manifolds.\hWe physicists
still haven't found any\hproperties of nature that we can prove are non-mathematical,\hwhich
is why some of us - including me - think that perhaps there just isn't anything else out
there, other than math.\hAnd that thought makes me one positively awestruck
mathematical object.