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 writeup 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 spacetime
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 spacetime continuum, while
the latter retain this hope, trying to find the most reasonable speculations for
modeling the whole of spacetime, 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 realvalued 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
infinitedimensional) 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 threedimensional space, but
later also generalized to nonEuclidean 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 wellbeing:
 : 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 lifegiving or healthgiving 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 manmade character
 real and objective existence : the world of mind and matter external
to an observer : reality as observed
 the aspect of outofdoors (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, padic 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 subdivision
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
(18721970) who made groundbreaking 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.)
