Over centuries scientists have realised the power of mathematics to uncover invisible worlds previously unavailable to mankind. Advancements of these methods may lead to more profound understandings of nature and superior technology.

The man many believe to be the father of modern science Galileo, once said “nature is written in the language of mathematics.” A great insight for an individual living in the 16^{th} century and it spurred the search for patterns of nature which might be represented in the language of numbers.

Earlier, in 1202 performing experiments into rabbit breeding Leonardo da Pisa discovered the Fibonacci sequence. This may be a neat solution to the question of how many rabbits may be produced from an original pair under certain conditions. It is simply a series of numbers for example 1 1 2 3 5 8, where a number may be found by adding the two previous numbers. It has intrigued many scientists and appears in nature frequently. Many plants, fruits and even the family tree of bees have this sequence imbedded in their intrinsic makeup. An interesting component of the sequence seems to be the golden ratio. The patterns in nature described by the golden ratio appear to be universal and explain everything from chemistry to biology including the topology of space-time, hurricanes, the spiralling of galaxies and magnets. The double helix of the human genome follows the mathematical rules of the golden spiral.

At the atomic scale Einstein’s famous equation e=mc2 has been an important part of modern technology and in particular nuclear technology. It encapsulates the simple idea of how energy and mass are equivalent; e=m. The c2 element is the speed of light squared and is the exchange rate between mass and energy. This was fundamental in the development of the atomic bomb because c2 is such a large number, a tiny alteration in mass by radioactive decay or the collision of atoms results in an enormous amount of energy being released. The end result is a specific amount of mass is eliminated from an atom, hence mass equals energy.

Einstein’s insights were made possible by the groundwork laid by Galileo Galilei and Isaac Newton. Galileo discovered objects with different masses fell to Earth at the same rate, proven when two cannon balls were apparently dropped by Galileo from the leaning tower of Pisa. This gave a new view of the force of gravity, now believed to be an inherent attraction between all masses and a constant by nature.

Newton made the further distinction of how an object moves further away from a mass with a gravitational field the effects subside. Larger objects may have a greater attractive force, this is shown by planets like Earth having a much larger gravitational field than the Moon, which is 80 times smaller and has little gravity. These understandings on a macro scale seemed to have inspired Einstein’s insights at a microscopic (atomic) scale. The atomic bomb seemed to have brought real world proof to the equation. Other important technology advancements in the form of aircraft wings and artificial heart valves were made possible by the Navier-Stokes equations. This relied upon understandings in fluid dynamics and vector fields and has been extensively verified in many contexts. Having applications for car and aeroplane aerodynamics, it seemed to have made possible an appreciable benefit for these technologies.

In the future, the further development of science may rely on new mathematical practices or methods which allow new insights into nature. The interaction of the sciences and mathematics may enrich both fields leading to a simultaneous progression. It is believed biology may take the reigns from physics as the most likely to create new realms of mathematics as living nature is far more diverse. As with the nuclear advancements based on Einstein’s equations, new and appropriate mathematics may reveal new invisible worlds which were previously unknown. Many realms of knowledge are readily available to mankind it is how this information is decoded which might be the key. This knowledge may be stored, waiting to be discovered and may be solved with new equations. Or like e=mc2, be a product of imagination waiting to be proved.

**Why do numbers underlie the makeup of natural patterns?**

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