कागजों में पुल और सड़कों की बहार है,
India’s contributions to mathematics span centuries, influencing global mathematical thought and practice. In the ancient period, the Sulba Sutras (~800 BCE) detailed geometric constructions, including the approximation of the square root of 2 and Pythagorean triples. Pingala (~200 BCE) introduced binary numbers and rules for permutations and combinations. The Jain texts (~500 BCE) explored concepts of infinity, while the place value system was fully developed between the 2nd century BCE and the 5th century CE.
During the classical period, Aryabhata (5th century CE) made pioneering contributions, including the approximation of π, advancements in trigonometry, and methods for solving quadratic equations. Brahmagupta (7th century CE) formalized the decimal system and introduced zero as a number, alongside rules for its operations. The Sulba Sutras and other texts also documented the rule of three, magic squares, and foundational mathematical astronomy. Mahavira (9th century CE) worked on algebraic solutions for cubic equations, while Halayudha (~10th century CE) expanded on Pascal’s triangle and binomial coefficients.
In the medieval period, Bhaskara II (12th century CE) advanced spherical trigonometry, logarithmic tables, and the Chakravala method for solving quadratic equations. The Kerala School of Mathematics, led by Madhava (14th century CE), developed infinite geometric series, approximations for π, and early concepts of calculus, including Taylor series-like expansions and tangent series. Nilakantha Somayaji (15th century CE) refined trigonometric calculations and planetary models. Jyesthadeva (16th century CE) documented these findings in Yuktibhasha, providing insights into the Newton-Gauss interpolation formula.
In modern times, Srinivasa Ramanujan (early 20th century CE) made groundbreaking discoveries in number theory, including infinite series, partitions, mock theta functions, and modular forms. Harish-Chandra contributed to Lie groups and representation theory, while Alladi Ramakrishnan, M.S. Narasimhan, and others advanced matrix analysis and topology. The AKS Primality Test by Manindra Agrawal, along with innovations in cryptography and coding theory, showcases India’s continued leadership in mathematics in the 21st century. This enduring legacy is a testament to India's rich mathematical heritage and its global influence across millennia.
Read more here - Mathematical Discoveries of India
🧮📜 Mathematical Discoveries of India 🇮🇳
— Bihar (@bihar) January 1, 2025
🪷 Ancient Period
Geometric Constructions and Proofs - Sulba Sutras - ~800 BCE
Pythagorean Triples - Sulba Sutras - ~800 BCE
Approximation of the Square Root of 2 - Sulba Sutras - ~800 BCE
Binary Numbers - Pingala (Chandaḥśāstra) -…
मुज़फ्फरपुर, जो बिहार राज्य में स्थित है, का एक समृद्ध और विविध इतिहास है, जो इसकी सांस्कृतिक, राजनीतिक और आर्थिक महत्ता को दर्शाता है। यहाँ इसका एक ऐतिहासिक अवलोकन दिया गया है:
मुज़फ्फरपुर की सांस्कृतिक विरासत मैथिली और बिहारी परंपराओं से समृद्ध है। छठ पूजा और दुर्गा पूजा जैसे त्योहार बड़े उत्साह के साथ मनाए जाते हैं। यहाँ का खानपान, लोक संगीत और नृत्य इसकी अनूठी पहचान को दर्शाते हैं।
आज का मुज़फ्फरपुर एक आधुनिक शहर है जिसमें ऐतिहासिक आकर्षण और वर्तमान आकांक्षाओं का मेल है। यह बिहार की अर्थव्यवस्था और सांस्कृतिक ताने-बाने में योगदान करते हुए एक कृषि और औद्योगिक केंद्र बना हुआ है। इसकी लीची की खेती, मंदिर और शैक्षणिक संस्थान इसके प्रमुख स्थल हैं।
Bihari Languages: From the Era of Ashoka to Modern Bihar
The
linguistic heritage of Bihar is as rich and diverse as its cultural and
historical legacy. The languages spoken in this region have evolved over
centuries, shaped by the region's rulers, cultural exchanges, and
socio-political transformations. This essay delves into the journey of Bihari
languages, tracing their roots to the time of Emperor Ashoka and their
development into the modern linguistic landscape of Bihar.
Ancient Linguistic Roots in Bihar
Bihar’s
association with language and literature dates back to ancient times, playing a
pivotal role in the cultural and intellectual history of India.
Medieval Period and Linguistic Evolution
The
medieval era witnessed the gradual transformation of Prakrit into Apabhramsha,
a precursor to the modern languages of Bihar. This period saw the
diversification of regional dialects and the emergence of early forms of
today’s Bihari languages.
Colonial Era and the Modernization of Bihari
Languages
The
British colonial period (18th–20th centuries) brought significant changes to
the linguistic landscape of Bihar.
Modern Bihar and Its Languages
Today,
Bihar is home to a diverse linguistic landscape, with its people speaking a
variety of languages and dialects.
Revival and Cultural Pride
Efforts
are underway to revive and promote the rich linguistic heritage of Bihar:
Legacy of Bihari Languages
From the
time of Ashoka, when Magadhi Prakrit was used to communicate a message of peace
and morality, to the present day, Bihari languages have been a testament to the
region’s vibrant cultural identity. They represent the voices of millions,
embodying their history, traditions, and aspirations.
As Bihar
continues to modernize, the preservation and celebration of its linguistic
diversity will remain crucial in honoring its past and enriching its future.
Conclusion
Bihari
languages have journeyed through the corridors of history, adapting and
thriving amidst changing times. They stand as a bridge between ancient wisdom
and modern expression, connecting the legacy of Ashoka's edicts to the dynamic
cultural fabric of contemporary Bihar. By embracing and promoting this
linguistic heritage, Bihar not only preserves its identity but also contributes
to the rich mosaic of India’s linguistic diversity.
