Vedic Maths Books: Sixteen Simple Mathematical Formulas from The Vedas

Today, we are going to discuss the Vedic Maths Books. Nowadays, everyone claims they have the original Vedic Math Book, but the fact of the matter is that all 16 volumes of Vedic Mathematics Book were lost and irrecoverable.

To know more about the Vedic maths Books, what was inside, what are the things available as of now, and how you can learn Vedic maths online with us, we will discuss everything in detail in this article.

Let’s begin…

Table of Contents

About the Vedic Maths Books

His Holiness Jagadguru Sankaracharya Sri Bharati Krishna Tirthji Maharaja of Govardhana Matha, Puri (1884-1960) wrote the monumental work Vedic Mathematics, or Sixteen Simple Mathematical Formulae From the Vedas.

After assiduous research and tapas, he reconstructed these sixteen arithmetic formulae from the Parisita (Bibliography) of the Atharvaveda for about eight years in the forests surrounding Sringeri. These methods are not found in the present recensions of the Atharvaveda; they were reconstructed by natural revelation from materials scattered here and there in the Atharvaveda.

Vedic Mathematics Book: 16 Volumes of 16 Vedic Maths Formulas

His Holiness Jagadguru Sankaracharya Sri Bharati Krishna Tirthji Maharaja wrote a Vedic Maths Books with 16 volumes, Based on 16 Vedic formulae between the years 1911 and 1918, after his assiduous research in Sringeri, and deposited them with one of his disciples. Unfortunately, the said manuscripts were lost. This enormous loss was finally confirmed in 1956.

Gurudeva was not much disturbed over this irretrievable loss and used to say that everything was there in his memory and that he could rewrite the 16 volumes Vedic Mathematics Book. Here are those 16 Vedic Formulae by His Holiness Jagadguru Sankaracharya Sri Bharati Krishna Tirthji Maharaja but the Separate 16 Volume of Vedic Mathematics Book is not Available now.

Sutra	Meaning	Real-World Application
Ekadhikena Purvena (By one more than the previous one)	One more than the previous one	Used to calculate the square of numbers ending in 5 efficiently.
Nikhilam Navatashcaramam Dashatah (All from 9 and the last from 10)	All from 9 and the last from 10	Simplifies multiplication of numbers close to powers of 10.
Urdhva-Tiryagbyham (Vertically and crosswise)	Criss-cross (vertically and crosswise)	Provides a general method for the multiplication of any two numbers.
Paravartya Yojayet (Transpose and Adjust)	Transpose and adjust (or apply)	Simplifies division by transforming the divisor.
Shunyam Saamyasamuccaye (When the sum is the same, it is zero)	When the samuccaya (combination) is the same, it is zero	Used in solving equations where expressions balance out.
Anurupye Shunyamanyat (If one ratio is zero, the other is zero)	If one ratio is in proportion, the other ratio is zero	This sutra is applied in proportional equations where one term becomes zero when proportions are identified.
Sankalana-vyavakalanabhyam (By addition and subtraction)	By addition and subtraction	This sutra is particularly useful in simultaneous equations.
Puranapuranabhyam (By the completion or non-completion)	By the completion or non-completion	This sutra simplifies calculations by completing numbers to a base like 10, 100, etc.
Chalana-Kalanabyham (Differences and similarities)	By calculus (or differentiation)	This sutra is used to derive results by a methodical approach, often involving changes in successive values.
Yavadunam (By the deficiency)	By the deficiency	This sutra simplifies multiplication by working with the deficiency from the base.
Vyashtisamasthi (Part and whole)	Specific and General	This sutra helps solve problems by analyzing parts (specific) and their totality (general).
Shesanyankena Charamena	The remainder by the last digit	Convert a fraction as a decimal
Sopaantyadvayamantyam (The ultimate and twice the penultimate)	The ultimate and twice the penultimate	This sutra is used for finding certain products or sums, particularly when there’s a clear relation between the ultimate and penultimate digits or terms.
Ekanyunena Purvena (By one less than the previous one)	By one less than the previous one	This sutra is used for simplifying multiplication when the numbers involved are close to a base (like 10, 100, 1000) and involve one less than a previously calculated number.
Gunitasamuccdyah (The product of the sum of coefficients in the factors.)	The product of the sum is equal to the sum of the product	This sutra is useful for simplifying the multiplication of binomials, especially
Gunakasamuchyah (Set of multipliers)	The factors of the sum is equal to the sum of the factors	Factorization and Differential Calculus

An Attempt to Retrieve Lost Vedic Formulas

In 1957, before he toured the USA and the UK, he wrote the present volume, giving the first account of the sixteen formulae he had reconstructed. This volume of the book was written in his old age, within one and a half months, despite his failing health and weak eyesight.

He had planned to write subsequent volumes, but his deteriorating health and cataracts in both eyes prevented him from fulfilling this plan. So, we have just one volume of the Vedic Maths Books in Very Conise and Limited Capacity. It all depends on your interest and capacity in how you decode these formulas and make the maximum application from there. If you have limited capacity, you can start with our Details Course on vedic Maths, Where Our team of more than 20

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What People Say about the Vedic Maths Books

Swami Pratyagatmananda Saraswati on Vedic Mathematics

Swami Pratyagatmananda Saraswati Says,

“Vedic Mathematics By The Late Gurudev is a great work in the field of mathematics, and this is the result of his Deep-Layer Explorations of hidden Vedic Secrets, Especially Their Calculus Of Shorthand Formulae And Their Neat And Ready Application To Practical Problems.

The Late Sankaracharya Show The Rare Combination Of The Probing Insight And Revealing Intuition Of Yogi With The Analytical Acumen And Synthetics Talent Of A Mathematician.”

This Great Piece of Work is the result of the intuitive visualisation of fundamental mathematical truths and principles during eight years of highly concentrated mental endeavour of Gurudeva.

Gurudev always said, “Vedic Mathematics is the science which is widely used and was given by the ancient sages of India.”

“Vedic Mathematics is the ancient system of computation,” Believed Gurudev

According to Gurudev,

Vedic Mathematics is the ancient system of computation rediscovered by him from the Parishit of the Atharvaveda, which is also called Sulbha Sutras or Ganit Sutra and was primarily written in Sanskrit.

Books, which you can buy from our website:

Book Title	Read on Amazon	Buy the Book from our Website
India’s Great Mathematicians: Which you don’t know	Buy Amazon	https://learn.vedicmathschool.org/product/indias-great-mathematicians-which-you-dont-know/
Shakuntala Devi: The Human Computer	Buy Amazon	https://learn.vedicmathschool.org/product/shakuntala-devi-the-human-computer/
Srinivasa Ramanujan: The Great Mathematician	Buy Amazon	https://learn.vedicmathschool.org/product/srinivasa-ramanujan-the-great-mathematician/
The World Famous Mathematicians: Which You Don’t Know	Buy Amazon	https://learn.vedicmathschool.org/product/the-world-famous-mathematicians-which-you-dont-know/

Vedic Maths Books and Chapter-Wise Short Analysis:

So, here we are going to discuss all the chapters of the Vedic Maths Books and its short commentary to give you ideas about what it is all about…

I. Actual Applications of the Vedic Sutras

Explore the application of the Vedic Sutra “Ekadhikena Purvena” to simplify converting vulgar fractions into decimals. It contrasts conventional methods with the Vedic one-line approach, showcasing its efficiency and simplicity. Detailed examples highlight its practicality and ease for learners.

II. Arithmetical Computations

Explore the application of the Vedic Sutra “Nikhilam Sutra” for simplifying multiplication and squaring. This method leverages base-centric calculations to replace complex traditional processes, offering swift and intuitive solutions. Step-by-step examples illustrate its practicality and versatility for learners.

III. Multiplication

Discover the “Urdhva Tiryak Sutra,” a versatile Vedic method for simplifying all multiplication cases through vertical and crosswise calculations. This approach streamlines complex arithmetic into a structured, intuitive process. Practical examples showcase its efficiency in general and compound multiplications.

IV. Division by the Nikhilam method

V. Division by the Parevartpa method

Explore the “Paravartya Sutra,” a versatile Vedic formula for division, particularly effective with small divisors. It simplifies the process using transposition and sign changes, extending applications to algebraic division and arithmetic. Detailed examples showcase its practicality and adaptability.

VI. Argumental Division

Based on the Urdhva Tiryak Sutra, the Argumental Division method simplifies division using logical reasoning and complements the Nikhilam and Paravartya methods. It excels in algebraic cases but is less intuitive for arithmetic. This sets the foundation for the advanced “Straight Division” technique.

VII. Factorisation (of simple quadratics)

The Vedic Sutras simplify quadratic factorisation using sub-sutras like “Anurupyena” for proportional splitting and “Adyamadyenantya mantyena” for direct factorisation. These methods make the process intuitive and efficient. Verification is enhanced by checking coefficient sums in factors and products.

VIII. Factorisation (of harder quadratics)

The “Lopana-Sthapana” Sutra simplifies complex quadratic expressions by alternately eliminating and retaining variables, enabling stepwise factorisation. It transforms challenging cases into manageable tasks using partial eliminations and the Adyam Sutra. This approach is also applicable in advanced geometry and algebraic concepts.

IX. Factorisation of Cubics, etc

Chapter IX simplifies cubic factorisation by identifying one factor using methods like the Remainder Theorem. The remaining factors are derived through division and techniques like “Adyamadyena” and “Gunita Samuccaya.” This approach also extends to biquadratics for streamlined solutions.

X. Highest Common Factor

The Vedic method for finding the HCF of algebraic expressions simplifies traditional approaches by using Lopana-Sthapana and Sankalana-Vyavakalan Sutras. It alternates the elimination of the highest and lowest powers, quickly revealing the HCF. This approach is efficient, and reliable, and avoids lengthy factorisation or division processes.

XI. Simple Equations (First Principles)

Vedic methods for solving equations using the Paravartya Yojayet Sutra, emphasising mental arithmetic and simplified formulas. Techniques cover transpositions, binomial products, and LCM-based equations. These intuitive approaches streamline complex solutions and set the stage for special equation

XII. Simple Equations (by Sunyam etc.)

Chapter XII introduces the Sunyam Samyasamuccaya Sutra, enabling quick solutions by equating the “Samuccaya” (sum, product, or total) to zero in specific cases. It simplifies linear, quadratic, and disguised equations, avoiding lengthy calculations. This method offers efficiency and clarity in solving even seemingly complex equations.

XIII. Merger Type of Easy Simple Equations

The Merger Type equations use the Paravartya Sutra to simplify equations by merging terms on the left-hand side with the right-hand side. This involves subtracting constants and multiplying numerators to reduce the equation systematically. The method is versatile, efficient, and unaffected by changes in term sequence.

XIV. Complex Mergers

The Complex Mergers chapter applies the Paravartya Sutra to solve intricate equations efficiently by aligning numerators and denominators through transposition and simplification. It uses mental shortcuts like LCMs and cross-multiplication for quick solutions. Even complex or disguised cases become manageable, showcasing the Sutra’s power.

XV. Simultaneous Simple Equations

The chapter presents quick methods like the Paravartya Sutra for solving simultaneous equations using cross-multiplication, and Sunyam Anyat for proportional coefficients. Special cases with swapped coefficients use Sankalana-Vyavakalanibhyum, simplifying complex problems efficiently.

XVI. Miscellaneous (Simple) Equations

This chapter demonstrates solving linear equations with Vedic Sutras. Cyclic fractions simplify using “Paravartya,” while “Sopcintyadvayamantyam” addresses arithmetic progression. “Antyayoreva” resolves series and ratio-based equations, enabling quick solutions by identifying patterns and critical terms. The methods streamline complex calculations with minimal effort.

XVII. Quadratic Equations

Vedic Sutras simplify quadratic equations by breaking them into first-degree pairs using calculus-based methods. Special techniques like reciprocals, Sunyam Samuccaye, and Merger Sutras enable swift solutions by identifying patterns and ratios, offering a faster and more intuitive approach than conventional methods.

XVIII. Cubic Equations

Cubic equations are solved using Vedic Sutras like Parcivartya, Lopana Sthapana, and Purana methods. These techniques involve completing the cube, transformations, and factorization for simplified solutions. Roots are derived through substitutions, providing efficient solutions even for complex equations.

XIX. Bi-quadratic Equations

Bi-quadratic equations are solved using Vedic Sutras like Purana and Vyasti Samasti, simplifying equations into quadratics through substitution and cancellation of powers. These methods enable quick solutions for standard and complex cases. Extensions for harder equations are addressed in advanced applications.

XX. Multiple Simultaneous Equations

Multiple simultaneous equations with three or more unknowns can be solved using Vedic Sutras like Lopam-Sthapana, Anurupya, and Paravartya. Techniques include substitution, elimination, and cross-multiplication. Advanced methods simplify calculations, offering efficient solutions, with more approaches to be discussed later.

XXI. Simultaneous quadratic Equations

Simultaneous quadratic equations can be solved using Vedic methods like Vilokanam (observation), Sunyam Anyat (zero remainders), and cross-multiplication. These techniques reveal paired solutions through symmetry and factorization. Complex cases will be addressed in advanced stages.

XXII. Factorisation & Differential Calculus

This chapter explores the Vedic Sutra Gunaka-Samuccaya, linking factorization and differentiation to simplify polynomial equations. Successive differentials reveal factors and repeat roots efficiently. Examples like E = (x-1)^5 and E = (x-2)^3(x+3)^2 illustrate its practical applications.

XXIII. Partial Fractions

The Paravartya Sutra simplifies partial fractions by directly substituting values to find coefficients, avoiding complex equations. This quick, mental method transforms fractions into simpler terms effortlessly. It’s a faster and more efficient alternative to traditional approaches.

XXIV. Integration by Partial Fractions

Integration by partial fractions simplifies complex expressions, breaking them into manageable terms. Using the Vedic Paravartya Sutra, we swiftly find coefficients for decomposition without tedious calculations. This method efficiently integrates challenging functions, enabling rapid and precise results, especially for polynomial ratios with distinct or repeated factors.

XXV. The Vedic Numerical Code

The Vedic Numerical Code replaces numbers with Sanskrit letters, making technical content easier to memorize in verse form. It integrates mathematics, poetry, and additional meanings for versatility and cultural enrichment. This system combines learning with creativity and historical significance.

XXVI. Recurring Decimals

This chapter explores converting vulgar fractions to recurring decimals using Vedic methods like the Ekadhika Process and Geometrical Progression. Techniques like the Complementary Halves Rule simplify predictions of quotient cycles and remainders. These methods make even complex decimal conversions intuitive and quick.

XXVII. Straight Division

Straight Division, based on the Urdhva Triyak Sutra, is a powerful Vedic technique for performing quick, mental one-line division, even with large numbers. It simplifies calculations by dividing using a single-digit divisor while handling remainders systematically. Examples demonstrate its efficiency, making it a versatile and intuitive method for arithmetic.

XXVIII. Auxiliary Fractions

Auxiliary Fractions simplify complex divisions using Vedic methods like Ekadhika Purva, replacing large denominators with manageable equivalents. For denominators ending in 9 or 1, unique rules streamline computations by prefixing remainders or complements to quotient digits. This technique transforms tedious calculations into swift, mental arithmetic.

XXIX. Divisibility & Simple Osculators

This chapter introduces Vedic divisibility methods using positive (Ekadhika) and negative (Paravartya) osculators, simplifying checks for large numbers. By systematically multiplying and adding/subtracting digits, divisibility is determined without full division. These methods offer speed and precision, even for complex numbers.

XXX. Divisibility & Complex Multiplex Osculators

This chapter introduces complex multiplex osculators for divisibility tests with large divisors, using grouped digits and positive (P) or negative (Q) osculators. It demonstrates splitting numbers into groups, applying osculation rules, and transforming non-standard divisors into usable forms. This simplifies divisibility checks for even the largest numbers.

XXXI. Sum & Difference of Squares

Any number can be written as the difference of two squares, while the sum of squares works easily for odd numbers split into consecutive parts. For even numbers, adjustments like dividing by powers of 2 help achieve similar results, simplifying many calculations.

XXXII. Elementary Squaring, Cubing etc

Squaring and cubing numbers can be simplified using special sutras like Yavadanam for squaring and Anurupya for cubing. These methods use patterns or base numbers, enabling rapid calculations, even for larger powers like the fourth power, by breaking down the problem into manageable parts.

XXXIII. Straight Squaring

The Dwandwa-Yoga simplifies squaring by calculating contributions from individual digits using squaring and cross-multiplication. It works systematically, handling even and odd digits differently for clarity. This method is efficient for large numbers, making squaring straightforward and accurate.

XXXIV. Vargamula (square root)

The Vargamda or square root extraction employs a systematic approach similar to straight division, enhanced by Dwandwa-Yoga (Duplex) calculations. Numbers are grouped into two digits, and square root digits are derived progressively. This method ensures accuracy through simple divisors and checks for completeness, handling exact and incomplete squares efficiently.

XXXV. Cube Roots of Exact Cubes

To find cube roots of exact cubes, use the last digit rule to determine the cube root’s final digit and group digits in threes to estimate the number of root digits. Deduce intermediate digits using logical steps like subtracting cubes and applying algebraic expansions. For example, the cube root of 33,076,161 is 321.

XXXVI. Cube Roots (General)

The Vedic method for cube roots uses logical steps like identifying the number of digits and estimating the first digit based on inspection. Successive subtractions and divisions refine the root using known patterns for terms like a3a^3a3 and combinations of digits. For example, the cube root of 258,474,853 is determined as 637.

XXXVII. Pythagoras Theorem etc

Pythagoras’s Theorem relates the sides of a right-angled triangle, stating the square of the hypotenuse equals the sum of the squares of the other two sides. Though attributed to Pythagoras, ancient Indian scholars used this concept earlier. Its applications span geometry, trigonometry, and engineering, with simpler Vedic proofs enriching its legacy.

XXXVIII. Apollonius’ Theorem

Apollonius’ Theorem relates a triangle’s sides and medians, stating the sum of squares of two sides equals twice the sum of the square of the median and half the third side’s square. The Vedic proof offers a simpler, elegant approach using coordinate geometry.

XXXIX. Analytical Conics

Conic sections describe shapes formed by intersecting a cone with a plane. Analytical Conics, vital in geometry, use Vedic Sutras for simplified solutions, avoiding traditional, lengthy methods. These include equations for straight lines, hyperbolas, and asymptotes.

In the end: Vedic Maths Books

The Vedic Maths Books by Tirthaji Maharaja is a monumental work that unveils the simplicity and brilliance of ancient Indian mathematical wisdom. Through 16 profound sutras, this book offers a methodical, intuitive approach to solving complex mathematical problems with ease. Although the original 16 volumes were tragically lost, the surviving text stands as a testament to Gurudeva’s genius, bridging ancient knowledge with modern applications.

Whether you’re a student, teacher, competitive exam aspirant, or just curious about mathematics, Our Course based on this book provides mental ability and computational shortcuts to problem-solving techniques. What you learnt today, share your thoughts in the comments. Happy Reading.