Question: How old was the man for whom Āryabhaṭa numeration is named when he wrote Āryabhaṭīya?

full_context: Document 1: Yahya Ibn al-Batriq: Abu Yahya Ibn al-Batriq (working 796 - 806) was a Syrian scholar who pioneered the translation of ancient Greek texts into Arabic, a major early figure in the transmission of the Classics at the close of Late Antiquity. He translated for Al-Mansur the major medical works of Galen and Hippocrates, and also translated Ptolemy's "Tetrabiblos".
Document 2: Sangita: Sangita (Devanagari: संगीत , IAST: saṃgīta ), also spelled Samgita or Sangeeta, refers to "music and associated performance arts" in the Indian traditions. According to Guy Beck, the root "saṃ-" implies "combining, coming together, convergent wholesome blending, unison" in the context of musical arts. "Sangita" connotes any form of singing with music, harmonious recitation or chorus singing in particular. In some medieval era literary genre such as the Puranas and poetic texts such as "Kathasaritsagar", a related term "Sangita-shastra" and "Sangita-vidya" mean the "art, science or knowledge of singing and dancing with music". According to Alison Arnold and Bruno Nettl, the modern term music fails to capture the historic sense of "Sanskrit "sangita" and Greek "mousike"". In the Indian tradition, the term "sangita" includes melodious singing, rhythmic dancing, instrumental music, classical, provincial, ritual chanting and incidental forms of music-related performance arts.
Document 3: Ibn Yunus: Abu al-Hasan 'Ali ibn 'Abd al-Rahman ibn Ahmad ibn Yunus al-Sadafi al-Misri (Arabic: ابن يونس) (c. 950-1009) was an important Egyptian Muslim astronomer and mathematician, whose works are noted for being ahead of their time, having been based on meticulous calculations and attention to detail.
Document 4: Disquisitiones Arithmeticae: The Disquisitiones Arithmeticae (Latin for "Arithmetical Investigations") is a textbook of number theory written in Latin by Carl Friedrich Gauss in 1798 when Gauss was 21 and first published in 1801 when he was 24. It is notable for having a revolutionary impact on the field of number theory as it not only turned the field truly rigorous and systematic but also paved the path for modern number theory. In this book, Gauss brought together and reconciled results in number theory obtained by mathematicians such as Fermat, Euler, Lagrange and Legendre and added many profound and original results of his own.
Document 5: Abu Ja'far ibn Habash: Abu Ja'far ibn Habash was a Persian astronomer. He was most likely a son of Habash al-Hasib. Since his father died after 864 AD at the age of 100, it can be concluded that he was active in 3rd century AH (9th century AD). According to Ibn Nadim and Al-qifti, he wrote a book on astrolabe, named "al-ostorlab al-mosatah".
Document 6: Aryabhata: Aryabhata (IAST: Āryabhaṭa ) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the "Āryabhaṭīya" (499 CE, when he was 23 years old) and the "Arya-siddhanta".
Document 7: Arabic Numeral Series: The Arabic Numeral Series, sometimes referred to as the Arabics, is a series of 19 short 16mm films completed by the American experimental filmmaker Stan Brakhage in 1981 and 1982. The "Arabic Numeral Series" gets its name from the fact that none of the films included in it have titles, instead opening with an arabic numeral. Brakhage produced another cycle, the "Roman Numeral Series", whose films all have Roman numerals instead of titles, around the same time. All of the "Arabics" are silent and are intended to be projected at 18 frames per second.
Document 8: Āryabhaṭa numeration: The Āryabhaṭa numeration is a system of numerals based on Sanskrit phonemes. It was introduced in the early 6th century in India by Āryabhaṭa, in the first chapter titled "Gītika Padam" of his "Aryabhatiya". It attributes a numerical value to each syllable of the form consonant+vowel possible in Sanskrit phonology, from "ka " = 1 up to "hau " = 10.
Document 9: Amoghavarsha: Amoghavarsha I (also known as Amoghavarsha Nrupathunga I ) (800–878 CE) was a Rashtrakuta emperor, the greatest ruler of the Rashtrakuta dynasty, and one of the great emperors of India. His reign of 64 years is one of the longest precisely dated monarchical reigns on record. Many Kannada and Sanskrit scholars prospered during his rule, including the great Indian mathematician Mahaviracharya who wrote "Ganita-sara-samgraha", Jinasena, Virasena, Shakatayan and Sri Vijaya (a Kannada language theorist). Amoghavarsha I was an accomplished poet and scholar. He wrote (or co-authored) the "Kavirajamarga", the earliest extant literary work in Kannada, and "Prashnottara Ratnamalika", a religious work in Sanskrit. During his rule he held such titles as "Nrupathunga", "Atishadhavala", "Veeranarayana", "Rattamarthanda" and "Srivallabha". He moved the Rashtrakuta regal capital from Mayurkhandi in the Bidar district to Manyakheta in the Gulbarga district in the modern Karnataka state. He is said to have built the regal city to "match that of Lord Indra". The capital city was planned to include elaborately designed buildings for the royalty using the finest of workmanship. The Arab traveler Sulaiman described Amoghavarsha as one of the four great kings of the world. Sulaiman also wrote that Amoghavarsha respected Muslims and that he allowed the construction of mosques in his cities. For his religious temperament, his interest in the fine arts and literature and his peace-loving nature, historian Panchamukhi has compared him to the legendary emperor Ashoka and given him the honorific "Ashoka of the South". Amoghavarsha seems to have entertained the highest admiration for the language, literature and culture of the Kannada people as testified to in the text Kavirajamarga.
Document 10: Wagon numbering system in India: A new wagon numbering system was adopted in Indian Railways in "2003". Wagons are allocated 11 digit numbers making it easy for identification and computerization of the wagon information. The first two digits indicate "Type of Wagon", the third and fourth digits indicate "Owning Railway", the fifth and sixth digits indicate "Year of Manufacture", the seventh through tenth digits indicate "Individual Wagon Number", and the last digit is a "Check digit".
Document 11: Siddhaṃ script: Siddhaṃ , also known in its later evolved form as Siddhamātṛkā, is the name of a script used for writing Sanskrit from c. 550 – c. 1200. It is descended from the Brahmi script via the Gupta script and later evolved into the Assamese alphabet, the Bengali alphabet, and the Tibetan alphabet. There is some confusion over the spelling: "Siddhāṃ " and "Siddhaṃ " are both common, though "Siddhaṃ " is preferred as "correct". The script is a refinement of the script used during the Gupta Empire.
Document 12: List of Janya ragas: Janya ragas are Carnatic music ragas derived from the fundamental set of 72 ragas called "Melakarta" ragas, by the permutation and combination of the various ascending and descending notes. The process of deriving janya ragas from the parent "melakartas" is complex and leads to an open mathematical possibility of around thirty thousand ragas. Though limited by the necessity of the existence of individual "swaroopas" (unique identities) for the "janya" ragas, a list is never comprehensive or exhaustive. Thus the list below is open to additions or corrections. Moreover, some musicians experiment and use new scales, leading to new "janya" ragas. The 72 "Melakarta" ragas are numbered according to the ancient Indian system for numerical notation — the "Katapayadi system".
Document 13: Neelakantha (Hindu astrologer): Neelakantha, the 16th century author of Tajika Neelakanthi and Prasna Tantra, and the son of Anantadeva, hailed from Kashmir; his brother, Ramchandra, wrote "Muhurta Chintamani", the famous treatise on Electional Astrology. Neelakantha was the court astrologer of the Moghul Emperor, Jalaluddin Akbar. According to Deepak Kapoor, Neelakantha was born in the year 1556 The Tajika system of prognostication depends on the Varshaphala, Neelakantha wrote his famous book on Varshaphala, Tajika Neelakanthi, in the year 1587. However, B V Raman in the introduction to Prasna Tantra states that in the last part of his Varshatantra (of Tajika Neelakanthi), Neelakantha records that he composed this book on the eighth day of the bright half of Aswija of Saka year 1509 which means 1567 AD. There is also evidence that he hailed from Vidarbha and that he was 43 or 44 years old when he wrote this book.
Document 14: Vatteluttu alphabet: The Vaṭṭeḻuttu alphabet, also spelled Vattezhutthu (literally "rounded script", Tamil: வட்டெழுத்து , "vaṭṭeḻuttu ", ] ; Malayalam: വട്ടെഴുത്ത് "vaṭṭeḻuttŭ ") is an abugida writing system originating from the ancient Tamil people of South India. Developed from Tamil-Brahmi, Vatteluttu is one of the three main alphabet systems developed by Tamil people to write the Proto-Tamil language, alongside the ancient Grantha or Pallava alphabet and the Tamil script. The syllabic alphabet is attested from the 6th century CE to the 14th century in present-day Tamil Nadu and Kerala states of India. It was later supplanted by modern Tamil script and Malayalam script. Vaṭṭeḻuttu replaced Tamil-Brahmi for writing Tamil after the 2nd century CE. This rounded form of writing was also used in Kerala to write in Tamil as well as in proto-Malayalam and Malayalam language. Currently, Malayalam uses the Malayalam script. Inhabitants of Kuccaveli, located north of Trincomalee, used the Vaṭṭeḻuttu script between the 5th and 8th centuries, attested to on rock inscriptions found there. Inscriptional records in Tamil date from 300 BCE to 1800. Grantha was an alphabet in which extra letters were created specifically for Sanskrit words. It was also a modified form of Tamil script to write Sanskrit granthas or books. In Tamil, many of the letters which are found in Sanskrit do not exist.
Document 15: Kaktovik Inupiaq numerals: Inuit, like other Eskimo languages (and Celtic and Mayan languages as well), uses a vigesimal counting system. Inuit counting has sub-bases at 5, 10, and 15. Arabic numerals, consisting of 10 distinct digits (0-9) are not adequate to represent a base-20 system. Students from Kaktovik, Alaska, came up with the Kaktovik Inupiaq numerals, which has since gained wide use among Alaskan Iñupiaq, and is slowly gaining ground in other countries where dialects of the Inuit language are spoken.
ground_truth: 23