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🔗 Biography 🔗 Philosophy 🔗 Politics 🔗 Philosophy/Social and political philosophy 🔗 Biography/science and academia 🔗 Philosophy/Philosophers 🔗 India 🔗 Philosophy/Ancient philosophy 🔗 India/Bihar 🔗 Philosophy/Eastern philosophy 🔗 Hinduism 🔗 India/Indian history workgroup 🔗 India/Patna

Chanakya (IAST: Cāṇakya, pronunciation ) was an ancient Indian teacher, philosopher, economist, jurist and royal advisor. He is traditionally identified as Kauṭilya or Vishnugupta, who authored the ancient Indian political treatise, the Arthashastra, a text dated to roughly between the 3rd century BCE and the 3rd century CE. As such, he is considered the pioneer of the field of political science and economics in India, and his work is thought of as an important precursor to classical economics. His works were lost near the end of the Gupta Empire in the 6th century CE and not rediscovered until the early 20th century.

Chanakya assisted the first Mauryan emperor Chandragupta in his rise to power. He is widely credited for having played an important role in the establishment of the Maurya Empire. Chanakya served as the chief advisor to both emperors Chandragupta and his son Bindusara.

🔗 Biography 🔗 Mathematics 🔗 Biography/science and academia 🔗 History of Science 🔗 India 🔗 India/Indian history workgroup 🔗 India/Tamil Nadu

Srinivasa Ramanujan FRS (; listen ; 22 December 1887 – 26 April 1920) was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation: "He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered". Seeking mathematicians who could better understand his work, in 1913 he began a postal partnership with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognizing Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Ramanujan had produced groundbreaking new theorems, including some that Hardy said had "defeated him and his colleagues completely", in addition to rediscovering recently proven but highly advanced results.

During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations). Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Nearly all his claims have now been proven correct. The Ramanujan Journal, a scientific journal, was established to publish work in all areas of mathematics influenced by Ramanujan, and his notebooks—containing summaries of his published and unpublished results—have been analyzed and studied for decades since his death as a source of new mathematical ideas. As late as 2011 and again in 2012, researchers continued to discover that mere comments in his writings about "simple properties" and "similar outputs" for certain findings were themselves profound and subtle number theory results that remained unsuspected until nearly a century after his death. He became one of the youngest Fellows of the Royal Society and only the second Indian member, and the first Indian to be elected a Fellow of Trinity College, Cambridge. Of his original letters, Hardy stated that a single look was enough to show they could only have been written by a mathematician of the highest calibre, comparing Ramanujan to mathematical geniuses such as Euler and Jacobi.

In 1919, ill health—now believed to have been hepatic amoebiasis (a complication from episodes of dysentery many years previously)—compelled Ramanujan's return to India, where he died in 1920 at the age of 32. His last letters to Hardy, written in January 1920, show that he was still continuing to produce new mathematical ideas and theorems. His "lost notebook", containing discoveries from the last year of his life, caused great excitement among mathematicians when it was rediscovered in 1976.

A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess. "An equation for me has no meaning," he once said, "unless it expresses a thought of God."

🔗 Mathematics 🔗 Books 🔗 India 🔗 Pakistan 🔗 India/Indian history workgroup

The Bakhshali manuscript is an ancient Indian mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan, historical Gandhara). It is perhaps "the oldest extant manuscript in Indian mathematics". For some portions a carbon-date was proposed of AD 224–383 while for other portions a carbon-date as late as AD 885–993 in a recent study, but the dating has been criticised by specialists on methodological grounds (Plofker et al. 2017 and Houben 2018 §3). The manuscript contains the earliest known Indian use of a zero symbol. It is written in a form of literary Sanskrit influenced by contemporary dialects.

🔗 Religion 🔗 Classical Greece and Rome 🔗 Greece 🔗 India 🔗 Pakistan 🔗 Buddhism 🔗 India/Indian history workgroup 🔗 Pakistan/Pakistani history

Greco-Buddhism, or Graeco-Buddhism, is the cultural syncretism between Hellenistic culture and Buddhism, which developed between the 4th century BC and the 5th century AD in Gandhara, in present-day north-western Pakistan and parts of north-east Afghanistan.

It was a cultural consequence of a long chain of interactions begun by Greek forays into the Indian subcontinent from the time of Alexander the Great. A few years after Alexander's death, the Easternmost fringes of the empire of his general Seleucus were lost in a war with the Mauryan Empire, under the reign of Chandragupta Maurya. The Mauryan Emperor Ashoka would convert to Buddhism and spread the religious philosophy throughout his domain, as recorded in the Edicts of Ashoka. This spread to the Greco-Bactrian kingdom, which itself seceded from the Seleucid empire. Within its borders, the Greek fondness for statuary produced the first statues of the Buddha, leading ultimately to the modern tradition.

Following the collapse of the Mauryan Empire, Greco-Buddhism continued to flourish under the Greco-Bactrian Kingdom, Indo-Greek Kingdoms, and Kushan Empire. Mahayana Buddhism was spread from the Gangetic plains in India into Gandhara and then Central Asia during the Mauryan Era, where it became the most prevalent branch of Buddhism in Central Asia. Mahayana Buddhism was later transmitted through the Silk Road into the Han Dynasty during the Kushan era under the reign of Emperor Kanishka. Buddhist tradition details the monk, Majjhantika of Varanasi, was made responsible for spreading Buddhism in the region by Emperor Ashoka.