Āryabhaṭa was an Indian mathematician and astronomer, and the author of the Maha-Siddhanta. The numeral II is given to him to distinguish him from the earlier and more influential Āryabhaṭa I.
Āryabhaṭa was an Indian mathematician and astronomer, and the author of the Maha-Siddhanta,written in Sanskrit, the work that deals with topics related to mathematical astronomy. He constructed tables of sines accurate up to about 5 figures
Born: 920 AD
Died: 1000 AD, India
Books: Maha-Siddhanta

Essentially nothing is known of the life of Aryabhata II. Historians have argued about his date and have come up with many different theories. Manuscripts of his work are found in Maharastra, Gujarat, and Bengal.Another important point noted is that Āryabhaṭa II tried to remove some discrepancies involving the criticism of Brahmagupta on Āryabhaṭa I. Thus Dikshita assigns him a date around śātavāhana śaka 875, which corresponds to 953. This corroborates the opinions of other historians as well. The most famous work by Aryabhata II is the Mahasiddhanta( Aryasidhanta) which consists of eighteen chapters. The treatise is written in Sanskrit verse and the first twelve chapters form a treatise on mathematical astronomy covering the usual topics that Indian mathematicians worked on during this period. The topics included in these twelve chapters are: the longitudes of the planets, eclipses of the sun and moon, the projection of eclipses, the lunar crescent, the rising and setting of the planets, conjunctions of the planets with each other and with the stars.

The remaining six chapters of the Mahasiddhanta form a separate part entitled On the sphere. It discusses topics such as geometry, geography and algebra with applications to the longitudes of the planets.

In Mahasiddhanta Aryabhata II gives in about twenty verses detailed rules to solve the indeterminate equation: by = ax + c. The rules apply in a number of different cases such as when c is positive, when c is negative, when the number of the quotients of the mutual divisions is even, when this number of quotients is odd, etc. Aryabhata II gives the correct formula for the area of a triangle, a square, a rectangle, and an isosceles trapezium.i.e., “The area of a triangle, a square, a rectangle, and an isosceles trapezium is equal to one-half of the product of the altitude and the sum of the base and face.”

Aryabhata II constructed a sine table to correct up to five decimal places when measured in decimal parts of the radius, Indian mathematicians were very interested in giving accurate sine tables since they were used to calculate the planetary positions as accurately as possible.

Aryabhata II covered the positions of the planets and their conjunctions with each other and the stars, eclipses of the sun and moon, and the phases and rising and setting of the moon and planets.

His work The Mahdsiddhdnta consists of eighteen chapters, as follows:

1. On the mean longitudes of the planets.

2. On the mean longitudes of the planets according to the (otherwise unknown) Pardsarasiddhanta.

3. On the true longitudes of the planets.

4. On the three problems relating to diurnal motion.

5. On lunar eclipses.

6. On solar eclipses.

7. On the projection of eclipses and on the lunar crescent.

8-9. On the heliacal risings and settings of the planets.

10. On the conjunctions of the planets.

11. On the conjunctions of the planets with the stars.

12. On the patas of the sun and moon.

Chapters 13-18 form a separate section entitled

Goladhyaya (“On the Sphere”).

13. Questions on arithmetic, geography, and the mean longitudes of the planets.

14-15. On arithmetic and geometry.

16. On geography.

17. Shortcuts to finding the mean longitudes of the planets.

18. On algebra.

The Mahdsiddhdnta was edited, with his own Sanskrit commentary, by MM. Sudhakara Dvivedin, in Benares Sanskrit Series 148-150 (Benares, 1910).

ARYABHATTA I’S 10 MAJOR CONTRIBUTIONS AND ACHIEVEMENTS
#1 HE WROTE THE HUGELY INFLUENTIAL ARYABHATIYA
#2 ARYABHATTA WAS THE FIRST KNOWN PERSON TO SOLVE DIOPHANTINE EQUATIONS
#3 HE MADE MAJOR CONTRIBUTIONS TO TRIGONOMETRY AND ALGEBRA
#4 HE MOST PROBABLY UNDERSTOOD THE CONCEPT OF ZERO AND THE PLACE VALUE SYSTEM
#5 HE CALCULATED THE CLOSEST APPROXIMATE VALUE OF PI TILL THAT TIME
#6 HE MADE INCREDIBLY ACCURATE CALCULATIONS OF THE LENGTH OF THE DAY AND THE YEAR
#7 HE WAS FIRST TO EXPLAIN THAT MOON AND PLANETS SHINE DUE TO REFLECTED SUNLIGHT
#8 HE EXPLAINED HOW MOVEMENT OF CELESTIAL BODIES WAS DUE TO ROTATION OF THE EARTH
#9 HE AUTHORED ANOTHER INFLUENTIAL TEXT TITLED ARYA-SIDDHANTA
#10 ARYABHATTA IS A TOWERING FIGURE IN WORLD MATHEMATICS AND ASTRONOMY