Years ago, Heliocentric theory was believed to be correct to the core. Ptolemy, Copernicus and Galileo rethought and by observation, they brought up Geocentric theory, after very great opposition from society it was proved to be true. Acceptance of the theory was something very much difficult for the humanity then, as their belief was hard and only upon that all other were build up.
Sir Issac Newton following the geocentric theory, started to describe the entire nature of universe by "The Theory of gravitation". His wonderful work "Pricipia Mathematica", Mathematical calculus (leibniz also has to attributed for calculus) has brought infinite number of changes to our perspective. There was a time, when it seemed that almost all about planetary motion were discovered. But when Einstein put up his theory of relativity, he found himself squaring with Newton's theory and all of a sudden, the entire planetary motions where rethought and Einstein's Special theory of relativity was put up to redefine the exact planetary motions.
It was a time when scientist waged wars with one another in the quest for describing the nature of atomic world.Today, we accept the existence of indivisible building block (Atoms) easily but that was time when people considered that there cannot be any building block, which could be of defined nature.Astonishingly steam engines and many innovations happened by the time did not considered existence of some indivisible block (atoms) . Arguments about atom was not given importance, Einstein rethought about the Brownian movement which was first observed by "Robert Brown", though most of the people at that time did not put their interest in the Jiggling pollen grains. Einstein rethought and was able to prove the existence of atoms mathematically. This proof of existence of atoms led to the development of Quantum theory after great fight between scientists.
By the time, James clerk Maxwell, put up his Electromagnetic theory, unifying both electricity and magnetism, the process of unification tickled Einstein and others, Everyone tried to unify all the four forces of nature known, weak nuclear, Strong nuclear, gravitational and electromagnetic. The unification of weak nuclear, strong nuclear and electromagnetic field was possible and people are able to describe them via quantum theory, But the gravitational forces remains apart. Anyhow the gravitational forces are being described through General theory of relativity.
To the latest many theory has been put to unify the mentioned two great theory, to make a "Theory of Everything". One of the theory which is believed to explain and predict the observations of our universe is "STRING THEORY". It has predicted many thing about our universe.
The world largest experiment (LHC built by CERN. By 2012, it will be started and experiments will be conducted) today is conducted to observe some of the prediction made by "STRING THEORY". Though String theory remains untestable, it unifies all the forces together, one of the bizarre thing is that there were around 5 different versions of STRING THEORY put up by different scholars. Initially Einstein theory of relativity defined the curved space and time, and made 3 dimensional world into a 4 dimensional taking time as its fourth dimension. People now have went beyond 4 dimensions, the mentioned all 5 versions of STRING THEORY make use of 10 dimensions to explain our universe. In order to unify the 5 versions of the STRING THEORY, one other scholar has put up a 11 dimensional unified STRING THEORY, which is now considered as the theory of everything. Out of the 11 dimensions 4 are those that i mentioned for theory of relativity other 6 are required to unify forces and the last 1 dimension for unifying the versions of STRING THEORY.
I am only aware of STRING THEORY as of now, but there are other theories that have been put up to unify forces.
On the other hand, in particle physics, apart from protons, electrons and neutron hundreds of particles have been observed. It is astonishing that atom was said to be indivisible, while trying to discover the structure of atoms people discovered the existence of protons, neutrons and electrons, actually it did not end up, all protons, neutrons and electrons are said to be made of particles called "quarks". These quarks has the ability to build up other particles too. The LHC is considered to produce more such particles for observation and even black holes too.
All the theory that have been described so far, has much to do with mathematics. I shall bring you more information about how mathematics has got changed with the proposal of these theories in next post.
My first post made some points on conundrum existing in the number system, we shall see more conundrum and difficulties we have got in the existing Mathematics in further posts.