Mathematics Through Ages: From Antiquity to Modernity

Introduction

Mathematics through ages has been a profound exploration of patterns, logic, and abstraction. From ancient civilizations’ basic arithmetic to modern calculus and beyond, each era has built upon previous discoveries, shaping our understanding of the fundamental principles underlying the universe.

Development of Science

• Harappan town planning reflects advanced knowledge of measurement and geometry in ancient India. 
• The earliest book on mathematics was Sulvasutra, written by Baudhayana in the 6th century BC. 
  • Sulbasutra mentions ‘Pi’ and some concepts very similar to the Pythagoras theorem.
  • It is a manual providing rules for the construction of Vedic altars, preparation of the site where Vedic sacrifices were to be carried out, etc.
  • In the 2nd century BC, Apastamba introduced practical geometry.
• Aryabhatta made significant contributions to mathematics, including the discovery of algebra and the formulae for the area of a triangle, which led to the development of trigonometry.
• Varahamihira’s Brihatsamhita (6th century AD) was a pioneering work in both astronomy and mathematics. 
  • Varahamihira’s observation that the moon orbits the earth and the earth orbits the sun gained recognition and influenced later discoveries.
• The technique of algebra and the concept of zero originated in India. 
  • Brahmagupta’s Brahmasputa Siddhantika (7th century AD) mentioned zero for the first time as a number.
• Ganit Sara Sangraha (9th century AD) by Mahaviracharya is a textbook on arithmetic.
• Bhaskaracharya was one of the leading mathematicians in the 12th century AD. 
  • His book, Siddhanta Shiromani, deals with four sections: Lilavati (dealing with arithmetics), Beejganita (dealing with algebra), Goladhyaya (about spheres) and Grahaganita (mathematics of planets).

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• In the medieval period, mathematical masterpieces like Ganita Kaumudi and Bijaganita Vatamsa were created by Narayan Pandit.
• Nilakantha Somasutvan wrote Tantrasamgraha, which contains the rules of trigonometric functions. 
• Nilakanatha Jyotirvida compiled Tajik, dealing with a large number of Persian technical terms. 
• Akbar mandated the inclusion of mathematics in the educational curriculum.
• Mathematicians like Bahauddin-Amili, Nasiruddin Tusi, Arraq, and Al-Kashi made significant contributions to the field.
• Nasiruddin Tusi, the founder and director of the Maragha observatory, was widely recognized as an authority in mathematics.

Conclusion

• The journey of mathematics through ages is a testament to human intellect and creativity. 
  • From the invention of numerals and geometry in antiquity to contemporary breakthroughs in algebra and cryptography, mathematics remains an indispensable tool for understanding the world and advancing scientific knowledge.