WHAT MATHEMATICS TODAY MEANS  TO HUMANKIND
 ON THIS PLANET EARTH

In the article "PROOF OF MATHEMATICS EXISTS IN veD ETERNALLY",  a brief history of MATHEMATICS from the Dark Ages to the end of Middle Ages in Europe and the rest of the world was presented. Further development in the understanding of MATHEMATICS as understood by the humankind on this planet earth in the last 500 years of human history on this planet earth is presented below. The write-up is compilations from various encyclopedic sources and verbatim extracts have been incorporated herein in order not to corrupt the knowledge of the specialized fields. Such verbatim extracts has been identified with quotation marks. After understanding this development in understanding MATHEMATICS we will review some very specific cases of inclusion of MATHEMATICS in the currently available sNskrut texts of veD = SCIENCES OF CREATION AND LIFE.

Mathematics  is defined as the study of patterns of STRUCTURE, CHANGE and SPACE in this universe. The word UNIVERSE means the whole space-time continuum in which we find ourselves, together with all the matter and energy within it. Attempts to understand the Universe in this sense using MATHEMATICS, have been made in cosmology, a science that has grown from astronomy and physics. During the second half of the 20th century, the development of observational cosmology, also called physical cosmology, led to a split in the meaning of the word Universe between observational cosmologists and theoretical cosmologists, where the former (usually) abandon the hope of observing the whole space-time continuum, while the latter retain this hope, trying to find the most reasonable speculations for modeling the whole of space-time, despite the extreme difficulty in imagining any empirical constraints on these speculations and the risk of sliding into metaphysics which is veD = SCIENCES OF CREATION AND LIFE.

MATHEMATICS tries to explain STRUCTURE, CHANGE and SPACE through the knowledge of the following topics in MATHEMATICS:

• Change is explained by: Arithmetic, Calculus, Vector calculus, Analysis, Differential equations, Dynamical systems and chaos theory, Fractional calculus, List of functions......Understanding and describing change in measurable quantities is the common theme of the natural sciences, and calculus was developed as a most useful tool for doing just that. The central concept used to describe a changing variable is that of a function. Many problems lead quite naturally to relations between a quantity and its rate of change, and the methods to solve these are studied in the field of differential equations. The numbers used to represent continuous quantities are the real numbers, and the detailed study of their properties and the properties of real-valued functions is known as real analysis. For several reasons, it is convenient to generalize to the complex numbers which are studied in complex analysis. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions, laying the groundwork for quantum mechanics among many other things. Many phenomena in nature can be described by dynamical systems and chaos theory deals with the fact that many of these systems exhibit unpredictable yet deterministic behavior. (from www.wikipedia.org)
   
• Structure is explained by:  Abstract algebra,  Number theory, Algebraic geometry, Group theory, Monoids, Analysis, Topology, Linear algebra, Graph theory, Universal algebra, Category theory...."The study of structure starts with numbers, firstly the familiar natural numbers and integers and their arithmetical operations, which are recorded in elementary algebra. The deeper properties of whole numbers are studied in number theory. The investigation of methods to solve equations leads to the field of abstract algebra, which, among other things, studies rings and fields, structures that generalize the properties possessed by the familiar numbers. The physically important concept of vector, generalized to vector spaces and studied in linear algebra, belongs to the two branches of structure and space." (from www.wikipedia.org)
   
• Space is explained by: Topology, Geometry, Trigonometry, Algebraic geometry, Differential geometry, Differential topology, Algebraic topology, Linear algebra, Fractal geometry......."The study of space originates with geometry, first the Euclidean geometry and trigonometry of familiar three-dimensional space, but later also generalized to non-Euclidean geometries which play a central role in general relativity. Several long standing questions about ruler and compass constructions were finally settled by Galois theory. The modern fields of differential geometry and algebraic geometry generalize geometry in different directions: differential geometry emphasizes the concepts of coordinate system, smoothness and direction, while in algebraic geometry geometrical objects are described as solution sets of polynomial equations. Group theory investigates the concept of symmetry abstractly and provides a link between the studies of space and structure. Topology connects the study of space and the study of change by focusing on the concept of continuity. "(from www.wikipedia.org)

With these 3 parameters of STRUCTURE, CHANGE and SPACE the current evolutions of humans have tried  to define pRkruti = nature and its existence with its mechanics, processes and purposes. pRkruti = nature is defined in current science as follows in the Webster's Third International Dictionary:

• the essential character or constitution of something
• the essence or ultimate form of something
• the distinguishing qualities or properties of something
• the fundamental character, disposition, or temperament of a living being usually innate and unchangeable
• the fundamental character, disposition, or temperament of mankind as a whole : HUMAN NATURE
• a creative and controlling agent, force, or principle operating in something and determining wholly or chiefly its constitution, development, and well-being: 
  • : such a force or agency in the universe acting as a creative guiding intelligence : a set of principles held to be established for the regulation of the universe or observed in its operation
  • an inner driving or prompting force (as instinct, appetite, desire) or the sum of such forces in an individual
  •  a life-giving or health-giving force in an animate being
• the qualities, characteristics, properties, organs, and functions that together make up the vital being of a human being or other organism: a : such organs or functions requiring nourishment
• feeling (as kindliness or affection) that is genuine, spontaneous, or unstudied
• the created world in its entirety:
  •  the totality of physical reality exclusive of things mental;
  • the total system of spatiotemporal phenomena and events that can be explained by other occurrences in the same system
• the state of an unregenerate soul
•  a theoretical condition or stage of existence usually held to reveal man in his original or proper state
• substance or essence that is the principle of specific proper acts or operations as in the union of two natures in Christ or in the Trinity, three persons in one divine nature
• the genetically controlled qualities of an organism
• a particular order of existence or of existing things that is the subject matter of art: as in
  • one having an unchanged as contrasted with a developed, ordered, perfected, or man-made character
  • real and objective existence : the world of mind and matter external to an observer : reality as observed
  • the aspect of out-of-doors (as a landscape)
  • natural scenery

As per veD all living beings including we humans are made of pRkruti plus aatmaa (soul)......

MATHEMATICS as known today also deals with the following topics of pRkruti = nature in addition to explaining STRUCTURE, CHANGE and SPACE:

• Quantity explained by:  Numbers, Natural numbers, Integers, Rational numbers, Real numbers, Complex numbers, Hypercomplex numbers, Quaternions, Octonions, Sedenions, Hyperreal numbers, Surreal numbers, Ordinal numbers, Cardinal numbers, p-adic numbers, Integer sequences,  Mathematical constants, Number names, Infinity......
   
•  Discrete mathematics is explained by: Combinatorics, Naive set theory, Probability, Theory of computation, Finite mathematics, Cryptography, Graph theory, Game theory.......
   
• Applied Mathematics is explained by: Mechanics, Numerical analysis, Optimization, Probability, Statistics....
   

The word "mathematics" comes from the Greek μάθημα (máthema) which means "science, knowledge, or learning"; μαθηματικός (mathematikós) means "fond of learning".

Historically, the major disciplines as noted above within mathematics arose out of the need of humans to do calculations in commerce, to measure land and to predict astronomical events. These three needs can be roughly related to the broad subdivision of mathematics into the study of structure, space and change. And then each sub-division evolved as mankind started understanding more and more about  pRkruti = nature.

When computers were first conceived, several essential theoretical concepts were shaped by mathematicians, leading to the fields of computability theory, computational complexity theory, information theory and algorithmic information theory. Many of these questions are now investigated in theoretical computer science. Discrete mathematics is the common name for those fields of mathematics useful in computer science.
 

From a layman's point of view, Bertrand Russell (1872-1970) who made ground-breaking contributions to the foundations of mathematics and to the development of contemporary formal logic, as well as to analytic philosophy said.

"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

The above is so true when one tries to understand MATHEMATICS in the current texts of veD which we are trying to decipher and understand from physical and spiritual aspects of our existence....

With the blessing of creator BRH`m we will continue reviewing the meaning of MATHEMATICS in current search for knowledge called science and also the mystery of MATHEMATICS in veD = SCIENCES OF CREATION AND LIFE.....

(This posting as a sharing of veD = SCIENCES OF CREATIONS AND LIFE will continue as the information is compiled by SRii chmpklaal daajibhaai misTRii ...who prays that our creator bRH`m will bestow His grace on us for all of us to continue to learn through this topic in days to come....
.om tt st......om bRH`mye nmh......our guru...our creator.)