value and importance of maths through the perceptions of the west and
Hinduism
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Western and Hindu cultures both recognize the profound
importance of mathematics, but differ in emphasis: the West focuses heavily
on its practical utility and logical application in the physical world,
while Hinduism views mathematics (Ganita) as a fundamental, often
spiritually connected, branch of knowledge necessary for understanding both
the physical and metaphysical realms.
Western Perceptions of Mathematics
The Western perspective on mathematics largely emphasizes its role as
a universal,
objective language crucial for scientific and technological progress. Key
values include:
Practicality and Application: Mathematics is highly valued as an essential
tool for daily life (budgeting, cooking, time management), various
vocations (engineering, finance, computer science), and the backbone of
science and technology. [HOWEVER, THE AUTHOR DESPISES THE ECONOMIC ACTIVITY
THROUGH THE MATHS AS IRRELEVENT TO THE PROGRESSIVE COMMUNITY]
Problem Solving & Critical Thinking: The study of mathematics is seen as a
means to develop logical reasoning, analytical skills, and methodical
problem-solving abilities that are applicable across all aspects of life.
[that means mere living in nature may provide the happiness, but sitting
with nature may not even last a week; but progress is civilization; and the
civilization expands the know how through the maths in valuing the life]
Economic and Career Value: Mathematical proficiency is a key indicator of
career readiness and a prerequisite for success in high-growth STEM
(Science, Technology, Engineering, and Mathematics) fields, which drive
modern economic advancement. [And the science was in vedas and now in
physics]
Objectivity: While the social context of math education is acknowledged,
the truth of mathematical statements is considered universal and
independent of culture, a shared heritage for all mankind. [science and
maths compare the progresses and the determination for a yard stick]
Hindu Perceptions of Mathematics (Ganita)
In Hinduism, the tradition of Ganita (mathematics) is ancient, with seminal
contributions like the decimal system, the concept of zero, and early
calculus originating in the Indian subcontinent. Its importance is
perceived through a broader lens:
Spiritual and Philosophical Connection: Mathematics is deeply intertwined
with philosophy and culture. It is listed among the major branches of
knowledge (aparāvidyā) in ancient scriptures like the Upanishads and is
considered a path to mental abstraction and concentration of thought.[RICS
ARE METERED BY MATHS; SAMA IS TUNED BY SRUTI METERS; YAJUR REVEALED THE
MEASURES AND PATTERNS OF THE YAGNA PROCEES BY APPLICATIONS]
Aesthetic and Moral Value: Beyond utility, mathematics holds aesthetic
value, embodying beauty, symmetry, and harmony. Its study is also linked to
developing moral qualities like honesty, truthfulness, and systematic
organization, as there is no place for bias or half-truths in the subject.
[CHAMAKAM METERS REVEAL THE VALUES OF NUMBERS]
Aid to Scriptural Understanding: In ancient times, mathematical methods
were essential for practical applications like architecture (e.g.,
constructing Vedic altars with specific proportions) and astronomy, which
were vital for religious practices and timekeeping. [YAJURVEDAM IS SO
EXPANSIVE]
Holistic Cognitive Development: The system of Vedic Maths is believed to
enhance not just calculation speed but also general cognitive
functions, memory,
and mental agility, offering a "fun and interesting" approach to the
subject that alleviates the fear of numbers.
In essence, while the West prioritizes the utility and application of math
for external world advancement, Hinduism's perception integrates this
utility with internal, spiritual, and moral development, viewing Ganita as
an elevated pursuit that unifies the mind and points to underlying
universal truths.
https://youtu.be/CA6DkdlTr28 1 ½ HOURS ON Hindu maths by Prof
Somesh Kumar IIT Kharagpur
"The measure of the genius of Indian civilization, to which we owe
our modern (number) system, is all the greater in that it was the only one
in all history to have achieved this triumph. Some cultures succeeded,
earlier than the Indian, in discovering one or at best two of the
characteristics of this intellectual feat. But none of them managed to
bring together into a complete and coherent system the necessary and
sufficient conditions for a number-system with the same potential as our
own." "...our decimal system, which (by the agency of the Arabs) is derived
from Hindu mathematics, where its use is attested already from the first
centuries of our era. It must be noted moreover that the conception of zero
as a number and not as a simple symbol of separation) and its introduction
into calculations, also count amongst the original contribution of the
Hindus."
Modern arithmetic was known during medieval times as "Modus Indorum"
or method of the Indians. Leonardo of Pisa wrote that compared to method of
the Indians all other methods is a mistake. This method of the Indians is
none other than our very simple arithmetic of addition, subtraction,
multiplication and division. Rules for these four simple procedures was
first written down by Brahmagupta during the 7th century AD. "On this
point, the Hindus are already conscious of the interpretation that negative
numbers must have in certain cases (a debt in a commercial problem, for
instance). In the following centuries, as there is a diffusion into the
West (by intermediary of the Arabs) of the methods and results of Greek and
Hindu mathematics, one becomes more used to the handling of these numbers,
and one begins to have other "representation" for them which are geometric
or dynamic." "Geometry, and its branch trigonometry, was the mathematics
Indian astronomers used most frequently. Greek mathematicians used the full
chord and never imagined the half chord that we use today. Half chord was
first used by Aryabhata which made trigonometry much simpler.
In fact, the Indian astronomers in the third or fourth century, using
a pre-Ptolemaic Greek table of chords, produced tables of sines and
versines, from which it was trivial to derive cosines. This new system of
trigonometry, produced in India, was transmitted to the Arabs in the late
eighth century and by them, in an expanded form, to the Latin West and the
Byzantine East in the twelfth century." "As for trigonometry, it is
disdained by geometers and abandoned to surveyors and astronomers; it is
these latter (Aristarchus, Hipparchus, Ptolemy) who establish the
fundamental relations between the sides and angles of a right angled
triangle (plane or spherical) and draw up the first tables (they consist of
tables giving the chord of the arc cut out by an angle θ<π {\displaystyle
\theta <\pi } on a circle of radius r, in other words the number
2rsin(θ/2){\display style 2r\sin \left(\theta /2\right)}; the introduction
of the sine, more easily handled, is due to Hindu mathematicians of the
Middle Ages)."
"It is not unusual to encounter in discussions of Indian
mathematics such assertions as that "the concept of differentiation was
understood [in India] from the time of Manjula (... in the 10th century)"
[Joseph 1991, 300], or that "we may consider Madhava to have been the
founder of mathematical analysis" (Joseph 1991, 293), or that Bhaskara II
may claim to be "the precursor of Newton and Leibniz in the discovery of
the principle of the differential calculus" (Bag 1979, 294). ... The points
of resemblance, particularly between early European calculus and the
Karalee work on power series, have even inspired suggestions of a possible
transmission of mathematical ideas from the Malabar coast in or after the
15th century to the Latin scholarly world (e.g., in (Bag 1979, 285)). ...
It should be borne in mind, however, that such an emphasis on the
similarity of Sanskrit (or Malayalam) and Latin mathematics risks
diminishing our ability fully to see and comprehend the former. To speak of
the Indian "discovery of the principle of the differential calculus"
somewhat obscures the fact that Indian techniques for expressing changes in
the Sine by means of the Cosine or vice versa, as in the examples we have
seen, remained within that specific trigonometric context. The differential
"principle" was not generalised to arbitrary functions—in fact, the
explicit notion of an arbitrary function, not to mention that of its
derivative or an algorithm for taking the derivative, is irrelevant here"
"One example I can give you relates to the Indian Madhava’s
demonstration, in about 1400 A.D., of the infinite power series of
trigonometrical functions using geometrical and algebraic arguments. When
this was first described in English by Charles Matthew Whish, in the 1830s,
it was heralded as the Indians' discovery of the calculus. This claim and
Mādhava's achievements were ignored by Western historians, presumably at
first because they could not admit that an Indian discovered the calculus,
but later because no one read anymore the Transactions of the Royal Asiatic
Society, in which Whish's article was published. The matter resurfaced in
the 1950s, and now we have the Sanskrit texts properly edited, and we
understand the clever way that Madhava derived the series without the
calculus; but many historians still find it impossible to conceive of the
problem and its solution in terms of anything other than the calculus and
proclaim that the calculus is what Mādhava found. In this case the elegance
and brilliance of Madhava’s mathematics are being distorted as they are
buried under the current mathematical solution to a problem to which he
discovered an alternate and powerful solution."
Indian scholars, on the other hand, were by 1600 able to use ibn
al-Haytham's sum formula for arbitrary integral powers in calculating power
series for the functions in which they were interested. By the same time,
they also knew how to calculate the differentials of these functions. So
some of the basic ideas of calculus were known in Egypt and India many
centuries before Newton. It does not appear, however, that either Islamic
or Indian mathematicians saw the necessity of connecting some of the
disparate ideas that we include under the name calculus. They were
apparently only interested in specific cases in which these ideas were
needed. ... There is no danger, therefore, that we will have to rewrite the
history texts to remove the statement that Newton and Leibniz invented
calculus. They were certainly the ones who were able to combine many
differing ideas under the two unifying themes of the derivative and the
integral, show the connection between them, and turn the calculus into the
great problem-solving tool we have today."
The arithmetic content of the Sulva Sutras consists of rules
for finding Pythagorean triples such as (3, 4, 5), (5, 12, 13), (8, 15,
17), and (12, 35, 37). It is not certain what practical use these
arithmetic rules had. The best conjecture is that they were part of
religious ritual. A Hindu home was required to have three fires burning at
three different altars. The three altars were to be of different shapes,
but all three were to have the same area. These conditions led to certain
"Diophantine" problems, a particular case of which is the generation of
Pythagorean triples, so as to make one square integer equal to the sum of
two others." "The requirement of three altars of equal areas but different
shapes would explain the interest in transformation of areas. Among other
transformation of area problems the Hindus considered in particular the
problem of squaring the circle. The Baudhayana Sutra states the converse
problem of constructing a circle equal to a given square. The following
approximate construction is given as the solution.... this result is only
approximate. The authors, however, made no distinction between the two
results. In terms that we can appreciate, this construction gives a value
for π of 18 (3 − 2√2), which is about 3.088."
The Decimal System in Harappa
In India a decimal system was already in place during the Harappan
period, as indicated by an analysis of Harappan weights and measures.
Weights corresponding to ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20,
50, 100, 200, and 500 have been identified, as have scales with decimal
divisions. A particularly notable characteristic of Harappan weights and
measures is their remarkable accuracy. A bronze rod marked in units of
0.367 inches points to the degree of precision demanded in those times.
Such scales were particularly important in ensuring proper implementation
of town planning rules that required roads of fixed widths to run at right
angles to each other, for drains to be constructed of precise measurements,
and for homes to be constructed according to specified guidelines. The
existence of a gradated system of accurately marked weights points to the
development of trade and commerce in Harappan society.
Mathematical Activity in the Vedic Period
In the Vedic period, records of mathematical activity are mostly to be
found in Vedic texts associated with ritual activities. However, as in many
other early agricultural civilizations, the study of arithmetic and
geometry was also impelled by secular considerations. Thus, to some extent
early mathematical developments in India mirrored the developments in
Egypt, Babylon and China . The system of land grants and agricultural tax
assessments required accurate measurement of cultivated areas. As land was
redistributed or consolidated, problems of mensuration came up that
required solutions. In order to ensure that all cultivators had equivalent
amounts of irrigated and non-irrigated lands and tracts of equivalent
fertility - individual farmers in a village often had their holdings broken
up in several parcels to ensure fairness. Since plots could not all be of
the same shape - local administrators were required to convert rectangular
plots or triangular plots to squares of equivalent sizes and so on. Tax
assessments were based on fixed proportions of annual or seasonal crop
incomes, but could be adjusted upwards or downwards based on a variety of
factors. This meant that an understanding of geometry and arithmetic was
virtually essential for revenue administrators. Mathematics was thus
brought into the service of both the secular and the ritual domains.
Arithmetic operations (Ganita) such as addition, subtraction,
multiplication, fractions, squares, cubes and roots are enumerated in the
Narada Vishnu Purana attributed to Ved Vyas (pre-1000 BC). Examples of
geometric knowledge (rekha-ganit) are to be found in the Sulva-Sutras of
Baudhayana (800 BC) and Apastamba (600 BC) which describe techniques for
the construction of ritual altars in use during the Vedic era. It is likely
that these texts tapped geometric knowledge that may have been acquired
much earlier, possibly in the Harappan period. Boudhayan’s Sutra displays
an understanding of basic geometric shapes and techniques of converting one
geometric shape (such as a rectangle) to another of equivalent (or
multiple, or fractional) area (such as a square). While some of the
formulations are approximations, others are accurate and reveal a certain
degree of practical ingenuity as well as some theoretical understanding of
basic geometric principles. Modern methods of multiplication and addition
probably emerged from the techniques described in the Sulva-Sutras.
Pythagoras - the Greek mathematician and philosopher who lived in the
6th C B.C was familiar with the Upanishads and learnt his basic geometry
from the Sulva Sutras. An early statement of what is commonly known as the
Pythagoras theorem is to be found in Boudhayan’s Sutra: The chord which is
stretched across the diagonal of a square produces an area of double the
size. A similar observation pertaining to oblongs is also noted. His Sutra
also contains geometric solutions of a linear equation in a single unknown.
Examples of quadratic equations also appear. Apasthamba's sutra (an
expansion of Boudhayan’s with several original contributions) provides a
value for the square root of 2 that is accurate to the fifth decimal place.
Apastamba also looked at the problems of squaring a circle, dividing a
segment into seven equal parts, and a solution to the general linear
equation. Jain texts from the 6th C BC such as the Surya Pragyapti describe
ellipses.
Modern-day commentators are divided on how some of the results were
generated. Some believe that these results came about through hit and trial
- as rules of thumb, or as generalizations of observed examples. Others
believe that once the scientific method came to be formalized in the
Nyaya-Sutras - proofs for such results must have been provided, but these
have either been lost or destroyed, or else were transmitted orally through
the Gurukul system, and only the final results were tabulated in the texts.
In any case, the study of Ganita i.e. mathematics was given considerable
importance in the Vedic period. The Vedang Jyodisha (1000 BC) includes the
statement: "Just as the feathers of a peacock and the jewel-stone of a
snake are placed at the highest point of the body (at the forehead),
similarly, the position of Ganita is the highest amongst all branches of
the Vedas and the Shastras."
Now say whether the Maths rendered anew the life or marred it to
exist only with the nature?
K Rajaram IRS 131225
On Sat, 13 Dec 2025 at 06:20, Markendeya Yeddanapudi <
[email protected]> wrote:
>
>
> --
> *Mar*
>
> Emotional Expansionism-Vs-Mathematical Reductionism
>
>
>
> Free and Healthy nature relates you emotionally, creating wonderful
> feelings as symbiotic lessons. Ageing actually is expansion of the reach of
> emotions. One gets over the limitations of the 3D based language, based
> mainly on the visible spectrum. One enters the gigantic 99.9965% of the
> totality or reality via sensing and feeling of the invisible spectrum. The
> troposphere provides the musical language of sounds and the resulting
> message laden smells, the language of free and healthy nature. That
> language enables you to live in the fact that you are part of nature, part
> of the planet earth, so the planet earth itself functioning as its limb,
> serving your own macro body, earth. In the Biosphere thoughts and feelings
> of the organisms’ converse mainly in smells and sounds. The free and
> healthy nature keeps you conscious of the fact that you are the planet
> earth as every part has claim as the whole. And every day all the five
> senses, the Panchangams, smelling, hearing, touching, seeing and tasting
> become stronger and sharper. They become the macro sensings expanding into
> you.
>
> Definitions actually expand via diverse scope paths. The definitions do
> not stagnate and arrest. One’s life synchronizes with the life of the
> planet earth, Gaia or Bhoodevi. One becomes a word, then a phrase and then
> a clause of the great expanding sentence, nature which lives and expands
> eternally in the present perfect continuous tense. May be one’s births and
> deaths are participations in the gigantic complex sentence, the universe in
> the present perfect continuous tense, which big banged 13 billion years ago
> from Singularity. The Singularity did not stagnate in the tiny definition,
> less than the size of an electron. And you are part of that big bang
> continuously expanding in perception and understanding.
>
> Perception and understanding are simply noting creating feeling. If
> mathematical representations expand into eternal equations, embellishing
> understanding, via participating in nature, mathematics serves the meaning
> and purpose of life.
>
> Unfortunately today mathematics is enabling mechanics and technology
> perverting life into economic life. Economics simply is based on the
> destruction of naure.It destroys ecology. It promotes the proliferation of
> machines, which have no feelings and emotions. Economics has created the
> economic man the mechanized human as the monster who continuously destroys
> nature. And every university lost the basic objective of education and is
> now a subject of the economic and commercial interests. The economic man
> lives in the false notion, commercial profit. When my income is your
> expenditure, incomes and expenses can only be equal and there can be no
> profit or loss. But we are using technology to get this profit, the basic
> falsehood.
>
> It is time for every University to start a ‘Free Nature Park ‘without
> human tampering, so that the meaning and purpose of life gets revived.
>
> YM Sarma
>
> As edited by chat gpt
>
>
>
> Here is an edited and improved version that preserves your philosophical
> voice while strengthening clarity, flow, and coherence. I’ve kept your
> metaphors and intent intact, but refined structure, grammar, and
> readability.
> ------------------------------
>
> *Emotional Expansionism vs. Mathematical Reductionism*
>
> *Edited and Improved Version*
>
> Free and healthy nature relates to us emotionally, offering symbiotic
> lessons through the wonderful feelings it evokes. Ageing, in this sense, is
> the gradual expansion of emotional reach. As we grow, we begin to move
> beyond the limitations of our three-dimensional, visually dominated
> language—rooted largely in the narrow band of the visible spectrum. We
> start to enter the vast 99.9965% of reality that lies beyond visibility,
> accessed through sensing and feeling.
>
> The troposphere provides a musical language of sounds and the
> message-laden language of smells—the true language of free and healthy
> nature. Through this language we experience, not merely understand, that we
> are part of nature and part of the Earth. The planet itself functions as a
> limb of our macro-body: the Earth. Within the biosphere, the thoughts and
> feelings of organisms converse primarily through smells and sounds. Healthy
> nature keeps us conscious of our identity as expressions of the Earth, each
> part having a claim to the whole. In such a life, all five senses—the
> Panchangams of smelling, hearing, touching, seeing, and tasting—grow
> stronger and sharper. They become macro-sensibilities expanding through us.
>
> Definitions, too, expand along diverse paths of meaning; they do not
> stagnate or imprison understanding. A person’s life becomes synchronized
> with the life of the Earth—Gaia or Bhoodevi. One becomes first a word, then
> a phrase, and eventually a clause in the great expanding sentence of
> nature, which lives eternally in the present perfect continuous tense. Our
> births and deaths may be nothing more than participations in the gigantic,
> ever-unfolding sentence of the universe, which has been expanding since the
> Big Bang 13 billion years ago. The primordial Singularity did not remain
> confined to its infinitesimal definition—smaller than an electron—but
> expanded continuously. We, too, are part of that ceaseless expansion in
> perception and understanding.
>
> Perception and understanding are simply acts of noticing that generate
> feeling. When mathematical representations grow into ever-evolving
> equations that adorn our understanding, then mathematics can indeed serve
> the meaning and purpose of life by helping us participate more deeply in
> nature.
>
> Unfortunately, today mathematics is more often used to empower mechanics
> and technology, reducing life to economic life. Economics, in its current
> form, is built on the destruction of nature; it undermines ecology and
> fuels the proliferation of machines—entities without emotion or feeling. It
> has created the “economic man,” a mechanized human who becomes a monster
> through the continuous destruction of nature. Universities, once devoted to
> education’s deeper purpose, have largely become instruments of economic and
> commercial interests. The economic man lives by the illusion of commercial
> profit. When my income is your expenditure, they must be equal; profit and
> loss, in truth, cannot exist. Technology is used to sustain this falsehood.
>
> It is time for every university to establish a *Free Nature Park*,
> untouched by human manipulation, so that the meaning and purpose of life
> can be revived.
>
> *—Y. M. Sarma*
> ------------------------------
>
> If you'd like, I can also:
> • create a more academic version,
> • shorten it for publication,
> • expand it with references, or
> • adjust tone (more poetic, more scientific, etc.).
>
>
>
> --
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> <https://groups.google.com/d/msgid/thatha_patty/CACDCHCJzCyvtM%3DgZE8kD37gDZb6vPzrd%3DNmCn92DKUXHu66Xpg%40mail.gmail.com?utm_medium=email&utm_source=footer>
> .
>
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