The “Father of Algebra”: Muhammad ibn Musa al-Khwarizmi

He is the person most widely given the title “Father of Algebra.”

Why? He was the first to treat algebra as its own independent subject, separate from arithmetic and geometry.
His Key Work: His 9th-century book, Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala (“The Compendious Book on Calculation by Completion and Balancing”), is where we get the word algebra (from al-jabr).
His Contribution: He provided systematic, step-by-step methods for solving linear and quadratic equations, which is why the word “algorithm” is derived from his name (al-Khwarizmi). As you noted, his work was translated into Latin and introduced these systematic concepts to the Western world.

🏛️ The “Father of Greek Algebra”: Diophantus

He is often called the “Father of Greek Algebra” or a “father of algebra” by some, but his work was different.

His Key Work: His book Arithmetica (c. 250 AD) was a collection of problems that he solved using a form of “syncopated” algebra—using symbolic abbreviations for unknowns.
His Contribution: He was a pioneer in moving mathematics from purely verbal descriptions of problems to a more symbolic representation. His work focused on finding specific (rational) solutions to equations, which are now called Diophantine equations.

🇮🇳 The “Father of Indian Algebra”: Brahmagupta

Brahmagupta made fundamental contributions that are essential to the algebra we use today.

His Key Work: Brāhmasphuṭasiddhānta (c. 628 AD).
His Contribution: He was the first mathematician to provide systematic rules for operating with zero and negative numbers (which he called “debts” and “fortunes”). He also gave the general solution for the quadratic equation (the $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ formula), a cornerstone of algebra.

In summary:

Diophantus was a pioneer of using symbolic abbreviations to solve equations.
Brahmagupta provided the crucial rules for zero and negative numbers and solved the general quadratic equation.
Al-Khwarizmi is considered the “Father of Algebra” because he was the first to formalize it as a distinct, systematic discipline and gave it its name.

Indian Mathematicians

A Journey Through Indian Mathematics

Ancient & Medieval Mathematicians

Baudhayana (c. 800 BCE)

Wrote the *Shrauta Sutras* & *Sulba Sutra*.
The *Sulba Sutra* includes an early formulation of the Pythagorean Theorem.

Katyayana (c. 300 BCE)

Commented on Sanskrit grammar and the *Sulba Sutras*.
Contributed to geometry and the study of Pythagorean triples.

Pingala (c. 500 BCE)

Developed the **binary number system**, crucial for modern computing.
Introduced Pascal’s triangle (as *Meru-prastaara*), foundational to combinatorics.

Aryabhata (476-529 CE)

Transformed astronomy and mathematics.
Accurately computed **Pi ($\pi$) as 3.1416** and developed properties of trigonometric functions (sine).
Explained Earth’s rotation and lunar/solar eclipses, challenging myths.
Invented one of the first decimal number systems and algorithms for algebraic equations.
Estimated Earth’s circumference within 99 miles of the actual value.
Key Work: *Aryabhatiya*, consolidating Indian mathematics with models on astronomy, arithmetic, and algebra.

Varahamihira (505–587 CE)

Renowned astronomer who published encyclopedias on astronomy, astrology, and other sciences.
Key Works: *Brihat Samhita* and *Pancha Siddhantika*.
Contributions in combinatorics, predicting eclipses, trigonometry, and mathematical astrology.
Pioneer of the East Indian school of astronomy after Aryabhata.

Brahmagupta (598–670 CE)

Revolutionized arithmetic and algebra in medieval India.
Explained rules for operations with **negative numbers and zero**.
Developed methods for solving indeterminate and quadratic equations.
Contributed to residue mathematics, a precursor to modern number theory.
Improved geometry, with accurate formulas for triangles, circles, and more.
Solved linear equations using matrices, laying groundwork for linear algebra.
Key Work: *Brahma-sphuta-Siddhanta*.

Bhaskara I (c. 600–680 CE)

Expanded Aryabhata’s work in astronomy and mathematics.
Derived an approximation formula for the sine function.
Key Work: *Mahabhaskariya*—a key contribution to arithmetic and geometry.

Shridhara (c. 650–850 CE)

Calculated the volume of the sphere, pioneering integral calculus.
Derived the sphere volume as two-thirds of the circumscribing cylinder’s volume.
Introduced early concepts of integral calculus before Kepler or Cavalieri.

Mahavira (9th century CE)

Jain mathematician.
Key Work: *Ganita Sara Sangraha*, the earliest surviving Sanskrit text on algebra.
Solved algebraic, quadratic equations, and problems involving fractions systematically.
Explored permutations, combinations, and progressions.

Bhaskara II (1114–1185 CE)

Developed principles of **differential calculus** and solved astronomical problems.
Derived Bhaskara’s Wheel formula for quadratic equations and an approximation of the sine function.
Key Work: *Lilavati*, focusing on arithmetic and algebra.

Narayana Pandit (1340–1400 CE)

Key Works: *Ganita Kaumudi* and *Bijaganita Vatamsa*.
Developed methods for finding integral solutions using the ‘kuttaka’ method.

The Kerala School of Astronomy & Mathematics

Madhava (c. 1340–1425 CE)

**Founder of the Kerala School** and a pioneer of calculus.
Developed the infinite Newton-Gauss series to calculate Pi ($\pi$) accurately to 11 decimal places.
Discovered Taylor series, power series, and analytical tools, pre-dating European discoveries.
Inspired mathematicians like Nilakantha Somayaji and Jyesthadeva.

Parameshvara (c. 1360–1455 CE)

A leading astronomer from the Kerala school.
Expanded on Madhava’s astronomical models, revising parameters.
Authored commentaries on works by Aryabhata, Bhaskara, and others.

Nilakantha Somayaji (1444-1545 CE)

Advanced infinite series in the Kerala school.
Computed Pi ($\pi$) accurate to 9 decimal places.
Improved trigonometric approximations using infinite series.
Key Work: *Tantra-sangraha*, a comprehensive treatise on his mathematical discoveries.

Jyeshtadeva (c. 1500 CE)

Authored **Yukti-bhāṣā**, the first calculus text based on Kerala school principles.
Derived properties of sine, cosine, and inverse tangent series.
Solved indeterminate equations using calculus techniques.
Pioneered a new problem-solving methodology.

Contemporary Mathematicians

Srinivasa Ramanujan (1887-1920)

Derived over 3,900 mathematical theorems in his short lifetime despite limited formal training.
Groundbreaking discoveries in analytic number theory, partitions, numerical series, and continued fractions.
Discovered mock theta functions, laying the foundation for a new research area.
Formulated influential theories in probabilistic number theory, combinatorics, Fourier analysis, and prime number theory.
Introduced Ramanujan prime, theta functions, and the Ramanujan conjecture.
Collaborated with G. H. Hardy, proving theorems related to partitions and analytic number theory.
His work impacted quantum entropy calculations in physics, particularly related to black holes.
Hardy-Ramanujan Number (1729): Smallest number representable as the sum of cubes of two numbers in two different ways.
First Indian to be chosen as a Fellow of Trinity College, Cambridge.
Named a Fellow of the Royal Society in 1918.
National Mathematics Day: Observed on his birth anniversary, December 22.
His life is famously depicted in the biopic “The Man Who Knew Infinity.”
His work is preserved in his “Frayed Notebooks.”
His love for mathematics was sparked by G. S. Carr’s book, “Synopsis of Elementary Results in Pure Mathematics.”

Harish Chandra (1923-1983)

Transformed representation theory of Lie groups.
Founded the Harish-Chandra Research Institute, promoting mathematical research and education in India.

C.R. Rao (1920-2023)

Pioneer in modern statistics and econometrics.
Econometrics is the use of statistical and mathematical methods to analyze economic data and test economic theories.

S. Varadhan (1940-)

Key contributor to probability theory and stochastic processes.
Awarded the Abel Prize and National Science Medal.

Historical Factors for Underrepresentation of Women

Fewer female mathematicians are documented historically due to persistent societal and structural barriers:

Stereotypes: Women were perceived as more emotional and less rational, leading to the belief that they were not suited for logical and abstract fields like mathematics.
Limited Exposure: In the past, women were excluded from trade, business, and formal education, reducing their opportunities to engage in mathematical calculations.
Time Constraints: Family responsibilities, especially child-rearing and household duties, left little time for academic pursuits.
Lack of Support: A girl interested in mathematics might be the only one in her class, leading to isolation and discouragement.
Socialization: Women have been traditionally guided toward humanities and caregiving professions rather than STEM fields, affecting their career choices.