0/9~ Brahmagupta is rightly titled by Bhāskara II as Gaṇakacakracūḍāmaṇi ~ Jewel among the circle of mathematicians. Just as we saw Āryabhaṭa, here is a glimpse of Brahmagupta’s genius contributions in History of Math, deprived from our current education! #IndicSciences

1/9 Brahmagupta (b.598CE) composed 2 great works Brāhmasphuṭa-siddhānta (628CE) & Khaṇḍakhādyaka (665CE). Khaṇḍakhādyaka is also a pun meaning “portions relishable”. It shows how learners were enthusiastically invited to relish math, a consistent trend through Indic works!

2/9 Then popular Brāhmasphuṭa-siddhānta has 24 chapters and a total 1008 verses making us wonder how are we not reading these now. First 10 chapters cover various astronomical phenomena & the remaining chapters detail interesting math methods!

3/9 Astronomical topics covered are mean longitudes, true longitudes of the planets, problems in diurnal rotation, lunar, solar eclipses, risings and settings, moon's crescent, moon's shadow, conjunctions of planets with each other and with the fixed stars.

4/9 He then covers 20 logistics: Addition, Subtraction, Multiplication, Division, Square, Square root, Cube, Cube root, 6 rules of reduction of fractions, rule of 3,5,7,9 & 11, barter and 8 determinations: Mixture, Progression, Plane figure, Excavation, Stack, Saw, Mound & Shadow

5/9 The amazing Chapter 18 Kuṭṭakādhyāya of Brāhmasphuṭasiddhānta gives some path-breaking findings in Math: Dharṇaśūnya~ all operations with +ve -ve & zero numbers, dealing with surds, finding square root of non-square numbers...

6/9 Ekavarṇasamı̄karaṇam~ equations with 1 unknown, Anekavarṇasamı̄karaṇam~ many unknowns, Bhāvita~ equations with products of unknowns and Varga-prakṛti and Bhāvanā principles for solving what is now known as Diophantine quadratic equations

7/9 Brahmagupta’s expressions for diagonals of a cyclic quadrilateral is held as the “most remarkable in Hindu Geometry and solitary in its excellence” by some historians of mathematics. The formula is said to be rediscovered in Europe by W. Snell in his Van Ceulen’s work 1619 CE