Long before the Renaissance started in Europe, Indians were ruling the world of Mathematics! From simple numbers to algebra, from the value of π to the values of complex trigonometric functions, Indian Mathematicians were all over the place! They weren’t just mathematicians, they were astronomers, philosophers, linguists, and visionaries who saw patterns in the stars and order in the chaos.

From Aryabhata, who gave zero its voice, to Bhaskara II, who played with calculus centuries ahead of Europe, and Madhava, who reached toward infinity through series expansions, India’s mathematical minds deserve a front-row seat in the story of human genius!

ARYABHATA (476-550 CE)

Born in Kusumapura (modern-day Patna), at just 23 years of age, Aryabhata had written the Aryabhatiya, a book comprising Sanskrit verses that covered everything from arithmetic and algebra to planetary motion and eclipses.

1. He introduced Zero to the world, or maybe, the world to Zero, though he didn’t treat it as a number, but just as ‘nothing’ and didn’t use the symbol ‘0’ for it.
2. He approximated π to 3.1416, close to its actual value and hinted that it was irrational, a fact that was proven over a thousand years later.
3. He proposed that the Earth rotates on its axis and revolves around the Sun based on the movement of stars.
4. He developed methods for solving Diophantine equations using what’s now called the Kuttaka or Pulveriser method.

VARAHAMIHIRA (505-587 CE)

Born around 505 CE in Ujjain, Madhya Pradesh, Varāhamihira was a polymath whose brilliance earned him a place among the legendary Navaratnas (Nine Gems) in the court of King Yashodharman Vikramaditya.

1. He introduced trigonometric identities like:
   sin2x + cos2x=1
   sin x= cos(π/2-x)
   where x is in degrees
2. He gave the Pascal’s Triangle for calculating binomial coefficients, long before Pascal himself was born!
3. He gave numerous arrangements of numbers and patterns, giving magic squares and combinatorics.

BRAHMAGUPTA (598-668 CE)

Born in 598 CE in Bhillamala (modern-day Bhinmal, Rajasthan), Brahmagupta wrote the Brāhmasphuṭasiddhānta (628 CE), which became a cornerstone of Indian mathematics and astronomy.

1. He gave Zero the symbol ‘0’ and was the first to treat it as a number, not just ‘nothing.’
2. He described positive numbers as ‘fortunes’ and negative ones as ‘debts,’ and gave rules for how they interact; centuries before Europe caught on.
3. He gave methods to solve indeterminate equations, which are now known as Pell’s equations.
4. He gave a formula for the area of a cyclic quadrilateral (a four-sided figure with all corners on a circle), now known as Brahmagupta’s formula.
5. He even described gravity as a force of attraction—using the Sanskrit term gurutvākarṣaṇam, long before Newton.

BHASKARA I (600-680 CE)

Bhaskara I was a famous Indian Mathematician and Astronomer who flourished in the 7th century, born in 600 C.E. at Valabhi near modern Bhavnagar in Saurashtra, Gujarat. He is considered to be one of the three jewels of Indian Astronomy and Mathematics, along with Brahmagupta and Madhava Samgramagrama in this elite list, whose works were popular in South India.

1. He was the first to write numbers in the Hindu decimal system. Mathematicians who existed before him used to write numbers in words.
2. He gave an approximate value of sine.
3. He gave the sine formula:
   sin x = 4x(180 − x)/(40,500 − x(180 − x))
   Where x is in degrees
4. He was the first mathematician to discuss quadrilaterals whose four sides are not equal, with none of the opposite sides parallel.

MAHAVIRA (9th century CE)

Flourishing around 850 CE in Karnataka, Mahavira, also known as Mahaviracharya, was a Jain scholar whose contributions to mathematics were both profound and poetic. His book, the Gaṇita-sāra-saṅgraha (“Compendium of the Essence of Mathematics”), is one of the earliest Indian texts entirely devoted to mathematics, rather than astronomy or astrology.

1. He tackled linear and quadratic equations, permutations and combinations, and even complex series, centuries before Europe even knew about their existence.
2. He viewed Mathematics separately from Astrology.
3. He devised formulas for the area and perimeter of ellipses and even of ‘conch-like’ figures made of unequal semicircles.
4. He correctly stated that the square root of negative numbers doesn’t exist.

BHASKARA II (1114-1185 CE)

Born in 1114 CE in Vijjadavida (likely in present-day Maharashtra), Bhaskara II, also called Bhaskaracharya (‘Bhaskara the Teacher), wrote his magnum opus, the Siddhānta Śiromaṇi, a four-part masterpiece that covered arithmetic, algebra, astronomy, and spherical geometry.

1. In the section Golādhyāya, Bhaskara described concepts similar to differential calculus, including the idea of instantaneous motion and the derivative of sine. He even used a rudimentary form of what we now call Rolle’s Theorem.
2. Bhaskara attempted to define division by zero, suggesting that a number divided by zero yields infinity.
3. His book Līlāvatī, named after his daughter, is filled with charming math problems wrapped in poetic riddles.

MADHAVA (1340-1425 CE)

Born around 1340 CE in Sangamagrama (believed to be modern-day Irinjalakuda in Kerala), Madhava was a visionary who dared to do what few before him had attempted: tame infinity!

1. He was the first to develop infinite series expansions for trigonometric functions like sine, cosine and arctangent.
2. He further calculated the value of π up to 13 decimal places!
3. Besides writing the infinite series, he also understood their limits and even estimated error terms, long before all this was even discovered in Europe!
4. He formed methods to calculate the Moon’s position every 36 minutes, way back in the 14th century itself!

CONCLUSION

From tracing the curves of the cosmos to sketching the first outlines of infinity, India’s ancient and medieval mathematicians weren’t just solving equations; they were rewriting humanity’s understanding of the universe. So, the next time someone mentions Newton or Pascal, pause and remember Aryabhata, Bhaskara, Madhava, and the rest of the Math League you’ve just met. Because history isn't always written by the first, but by the loudest. And it's time these quiet giants.

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