Imagine living four thousand years ago. What would you believe about you reality? You would believe that you live on the surface of a flat plain, with the stars and the sun rising and setting each day, moving predictably across the sky.

Your senses would tell you this is true. And in a limited way it was, in that to a mere human in that age the size of the Earth was so huge that the surface was flat to the extent such things could matter.

Then about two thousand three hundred years ago Aristotle used some clever reasoning to argue that the world was a sphere. This would have been contrary to reality as understood by those alive at the time.

Even after the shape of the Earth was established it was still the intuitive reality that Earth was at the centre of the everything. The stars and planets at this point understood to be nothing more than lights in the sky, revolving around the earth on a celestial sphere.

Then along came Galileo and used the invention of the telescope to observe the night sky. And in doing so he discovered that contrary to Orthodox understanding of reality that not everything went around the Earth. There were moons orbiting Jupiter. And so this meant that the Earth could orbit the Sun. And so our intuition about reality and our place in the universe had failed again.

After the turn of the twentieth century Einstein determined that the speed of light was a constant, and in the process determined our intuitive view of relative velocities was wrong. If you have one spacecraft moving toward Earth at two thirds the speed of light, and another spacecraft traveling toward Earth from the opposite direction also at two thirds the speed of light their total relative velocity does not exceed the speed of light. Space and time is warped.

The reality of solid objects evaporated when Rutherford and Bohr discovered how atoms are constructed, with electrons and their interactions primarily responsible for all the characteristics of the elements. There is no solidity, just the electric fields of electrons and interactions with photons.

Along with our understanding of elemental particles comes the realization that there might be multiple universes. There might be countless other versions of you, each having taken a slightly different course in life, all as real as you are sitting here today.

The reality you know and love, the one you find so intuitive, the understanding of the world that lets you get by day to day, is fundamentally flawed. It is a convenient illusion constructed to help you survive in a hostile universe. It has, I am afraid, very little to do with reality.

There is a common thread running through all the discoveries about the natural world; the scientific process. Science has allowed us to shed our preconceived illusions, to discover the cause of disease, to understand earthquakes and volcanoes, to see distant suns and galaxies, and to understand how our universe works at the smallest scale. It has even allowed us to understand ourselves more deeply than many would find comfortable.

But even science has limits. Science depends on the observable, the physical evidence and experimentation. Why does our universe look the way it does? Are there other universes? Will they have the same natural laws? Some even ask whether we live in a simulation being run on a huge computer. Sim Universe perhaps. Can we know anything of what is beyond our little corner of reality?

Is reality limited to whatever we can see in universe around us? Is it all contingent on some accident of fate that put us on this small rock orbiting an unremarkable star in an ordinary galaxy? Can we know anything is real? What does real even mean?

There is one thing we can know is real with absolute certainty. It is mathematics. There is a reason they call a proof a proof. While it takes a rational mind to understand mathematics it is also truly universal. The value of PI is the same everywhere, in any universe. Prime numbers are the same everywhere, from one side of the universe to the next. Carl Sagan said Mathematics is the only true universal language. This is true in two ways, being universally accessible to anyone capable of reason and also describing the laws of the universe itself.

The Universe follows a precise set of mathematical rules. That is reality. To peek behind the curtain of the Universe might then involve a deeper understanding of mathematics. And so we return to the thesis of Plato; that only through pure mathematics can we truly understand the nature of reality.