Indian Mathematics: A Historical Journey
Indian mathematics flourished in the Indian subcontinent from around 1200 BCE until the 18th century. During the classical period (400 CE to 1200 CE), notable scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava made significant contributions. Here are some key points:
1. Decimal Number System:
- The decimal number system we use today was first documented in Indian mathematics.
- Indian mathematicians explored the concept of zero as a number and worked with negative numbers, arithmetic, and algebra.
- Trigonometry also advanced significantly in India, with modern definitions for sine and cosine originating there.
2. Mathematical Works:
- Ancient and medieval Indian mathematical texts were composed in Sanskrit.
- These works typically included concise sutras (rules or problems) in verse form, aiding memorization.
- Prose commentaries followed, providing detailed explanations and justifications for solutions.
3. Transmission and Manuscripts:
- Initially, mathematical knowledge was transmitted orally until around 500 BCE.
- Later, both oral and manuscript-based transmission methods were used.
- The oldest surviving mathematical document from the Indian subcontinent is the Bakhshali Manuscript (7th century CE), discovered in present-day Pakistan.
4. Kerala School and Trigonometric Series:
- In the 15th century CE, mathematicians from the Kerala school developed series expansions for trigonometric functions (sine, cosine, and arc tangent).
- Remarkably, their work predated the invention of calculus in Europe by two centuries.
- Although they didn't formulate a systematic theory of differentiation and integration, their contributions remain influential.
These mathematical ideas traveled beyond India, shaping the foundations of various mathematical disciplines worldwide.
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Greek Mathematics: A Journey of Learning
The term "mathēmatikē" (meaning "mathematics" in Greek) originates from the Ancient Greek word "μάθημα" (máthēma), which translates to "something learned." While it could refer to any branch of knowledge, certain mathēmata (such as arithmetic, geometry, astronomy, and harmonics) held special significance since antiquity.
The early origins of Greek mathematics remain somewhat mysterious. Advanced civilizations like the Minoan and Mycenaean cultures thrived in Greece and Europe during the 2nd millennium BCE. Despite their engineering prowess and written language, they left no mathematical records.
Although direct evidence is lacking, it is believed that neighboring Babylonian and Egyptian civilizations influenced Greek mathematics. Unlike the flourishing literary scene between 800 and 600 BCE, information about early Greek mathematics primarily comes from later authors, starting around the mid-4th century BCE.
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