“Mathematics is the Queen of sciences”, mathematics own a mysterious powerful charm Once you enter the world of numbers and shapes there is plenty of opportunities .Numerous challenges awaits you there .For most of the people one way or other mathematics means fun, Hobby and A great Passion ,and it has a great beauty like any art form and an abstract beauty that can only be perceived by mathematical genius , Symmetry is one of the factors that figure beauty .We love symmetric objects so does nature, it creates symmetric objects .Mathematical problems have great significance , a solution means something great .Our understanding about this universe is based on mathematics otherwise it's an incomprehensible mystery.
A Pen and Paper is enough for a mathematics lab .there you can begin exploring things .Nowadays there are lots of computer packages available .some of them are targeting applied mathematicians while some target pure mathematicians. Visualizations and data analysis have become a simple task with these packages .Analyzing data and plotting it in 1D ,2D and 3D are possible with these packages .Commercial as well as Open source packages are available .Most often people rely on this software beyond a level, they forget one important question ,how it works ? Or what's the logic behind that beautiful plot? this question may sound insignificant for some people .But the fact is that most of the people forget this question, they never ask this question .It's significant because the method and solution are correlated moreover it’s all mathematical wonders . To produce better result we need to know how it works .So using open source tools provides you with an opportunity to comprehend the fundamentals of computer math.
Independent mathematical thinking is essential for our society ,all the technological advances we made in the 20th Century had its roots In the powerful mathematics laid out by the extraordinary and prolific mathematicians of the past as well as present .Physics depends on mathematics to express its ideas .visualizing physics is possible with math tools ,Pictures have a greater effect than Lectures .Pictures can convey immense information within a short span of time .Whenever you want to introduce something new a picture can do much more .An animated sequence of picture has even greater effect .Including more Graphical Data improves efficiency and it can have a wide spectrum of Audience than a most of those simple equation
Many mathematical theories at first seemed to have no meaning rather they seemed subtle and strange to a larger section of the society .Usually many mathematical concepts do not have any existence outside the abstract world .But in future they may be the corner-stone upon which some physical theories are formulated .but that’s beyond prediction but often it has occurred in the past. Is there any intelligent beings in universe other than humans .If they exist do they have an abstract language like mathematics or is mathematics everywhere the same ,Often physicists have a Question ,”Are the laws of Physics valid ” .Similarly there is just one Question ,are the laws of the mathematics same for all intelligent entities or else is there something that’s beyond our comprehension .physicist predict that our universe is multidimensional .so mathematics is in a stage to describe a multidimensional Universe but actually the physics lags behind .intuitively one Would suggest mathematics is valid anywhere in the universe .But even mathematics is built on certain axioms so a better Question should be -are all the Axioms of mathematics valid anywhere in the universe ,it’s for sure valid everywhere until now and hope it will! .IF the laws of physics are not same as our universe then all those physical limits and life forms any if , would be significantly different .Black hole is one such entity where the Laws physics may be different ! ,Physics Also predicts we may be living in a multiverse ,that’s there may be even parallel universes .so it’s possible that many intriguing questions are there to explore both for physicists and mathematicians
Mathematics can describe multidimensional entities .if a multidimensional entity exists then it should have greater degrees of freedom . so it will be superior to us. Can mathematics prove the existence of any superior entity? It’s an unusual question .There is one hypothesis called simulation hypothesis which states that we are actually living in a computer simulation created and ran by some other intelligent civilization and also intelligent civilizations always creates simulations so that actually there is a chain of simulations .Currently that simulation hypothesis says that it’s possible to pack so much information into a Quantum computer and the visible universe could be simulated and it’s metrics are only limited by Quantum bits packing limitation ,but it’s possible to do that simulation .But no one has produced any proof .so it remains a hypothesis and not theory. if it’s valid and could proved some time in future ,there arises an some important questions .In order to do precise simulation ,the entity performing simulation must have some exact mathematical modeling .so again mathematics is the key .How does the simulation describes our visible universe ? Usually an N dimensional thing can live in a larger N dimensional entity or in a higher dimensional entity .If multiple simulations exists and all of them are in separate dimensions. Can we ever contact them; if we have to contact we need to travel across an extra dimension .It could be proved by mathematics .In a three dimensional Analogy, an entity locked inside a torus can penetrate the wall and travel through another dimension to reach its destination .So there must some mechanism to prove the transportation between lower and higher dimension
A point Equidistant from a set of points of a plane describes a circle .Similarly a set of points equidistant from a point in 3D describes a Sphere .So It must have counter parts in higher dimensions .For a given perimeter circle encloses largest area in 2D .Similarly for a given surface area Sphere Encloses greatest volume, where volume shows the size of existence if it could be called so! , Again there must be something in 4D that has best existence in 4D for a given Volume measure! On the other hand the analogies are also built from the perspective of 3D beings it may or may not be valid for higher Dimensional world or most probably it might some other description that shows the similarity. Symmetry is one of the concepts that seems intuitively extensible in to higher dimensions.
What seemed absurd and impossible in the past have become a reality in present .3D printing remained in the dreams of weird people for years ,then suddenly one day it becomes a reality .Our perception of reality is also dependent on dimensions .We think ,talk, Sense ,smell, taste in 3 Dimensions, anything outside these 3D dimensions means fantasy . Therefore the reality may be different for each dimensional being. Like Einstein’s Relativity Reality may be based on some factors that may be different for Different entities
Mathematics is a tool as well a format for Describing our universe .so it essentially represents the human efforts until now .To Better understand the universe and ourselves we need this invaluable tool. The pursuit for mathematical beauty never converges it extends into far and beyond the obvious