The origin of the number system in India is deeply rooted in ancient mathematical traditions. The Indian numeral system, often referred to as the Hindu-Arabic numeral system, is believed to have originated in India around the 3rd century AD. This system is characterized by the use of ten digits (0-9) and the place-value principle, which is a fundamental concept in modern mathematics.

The development of the Indian numeral system is attributed to several factors. Firstly, the ancient Indian mathematicians, such as Brahmagupta and Aryabhata, made significant contributions to the field of mathematics. Brahmagupta, in the 7th century AD, is credited with introducing the concept of zero and the use of negative numbers. Aryabhata, in the 5th century AD, is known for his work on algebra and trigonometry, which laid the groundwork for the numeral system.

Historical evidence suggests that the Indian numeral system was introduced to the Islamic world through Persian mathematicians in the 8th century AD. From there, it spread to Europe, where it was further developed and refined. The system's adoption in Europe was a turning point in the history of mathematics, as it greatly facilitated calculations and the development of various scientific disciplines.

The Indian numeral system's influence can be seen in various historical documents and mathematical texts. For instance, the "Brahma Sutras," a collection of mathematical texts from the 3rd century AD, contain references to the use of zero and place-value notation. Additionally, the "Lilavati," a 12th-century mathematical treatise by Bhaskara II, provides detailed explanations of the numeral system and its applications.

The Indian numeral system's impact on mathematics is undeniable. Its simplicity and efficiency have made it the most widely used numeral system in the world today. The system's adoption has significantly contributed to the advancement of mathematics, science, and technology. For example, the use of zero as a placeholder and the concept of place-value have greatly simplified arithmetic operations and calculations.

In conclusion, the origin of the number system in India is a testament to the ancient civilization's contributions to mathematics. The Indian numeral system, with its ten digits and place-value principle, has had a profound impact on the development of mathematics and science worldwide. The system's introduction and subsequent spread have revolutionized the way we perform calculations and understand numbers, making it a cornerstone of modern mathematics.