Rewritten Article:

The ancient Vedic mathematical sciences held a prominent position in the development of Indian culture, considering mathematics as the mother of all sciences. It played a crucial role in comprehending astronomical phenomena, devising calendars, and determining the timing of festivals, rituals, and events. The fundamental principles of counting, including the concept of zero, were based on Sanskrit figures. Algebra also emerged from these mathematical advancements [1]. During ancient times, mathematics was primarily employed in practical applications. Mathematical methods were utilized to solve problems in architecture and construction, such as the public works of Harappa, as well as in astronomy and astrology, as evidenced by the works of Jain mathematicians. Mathematical techniques were also employed in the construction of Vedic altars, as exemplified by the Shula Sutras of Baudhayana and his successors. Evidence suggests that mathematics began to be studied for its own sake during the fifth or sixth century BCE.

In ancient India, the division between different professions was not as distinct as it is today. Consequently, most mathematicians were considered priest-mathematicians or rishis who also focused on mathematics, among other areas of knowledge.

The Vedic perspective on mathematics emphasized that understanding the material reality could be achieved through the cultivation of transcendental knowledge. According to this worldview, knowing the absolute truth also leads to the understanding of relative truths. Thus, science was regarded as a smaller circle encompassed by the larger circle of spirituality.

Mathematics served as a bridge between comprehending the material world and spiritual concepts. Vedic mathematicians strongly believed that every discipline should have a purpose and viewed the ultimate goal of life as achieving self-realization and self-perfection. As a result, mathematics was often presented in a unique format. Most mathematical concepts were conveyed through the Sutra method, where a list of laws was provided, and each law derived its data and authority from a preceding law. These lists were condensed into short poems, similar to the indexing method known as hashing used in computer science today. Practices that contributed directly or indirectly to this ultimate goal were pursued with utmost rigor.

To illustrate the integration of secular and spiritual aspects in Vedic India, Bharati Krishna Tirtha Maharaja demonstrated that mathematical formulas and laws were often taught within the context of mantras (sacred chants). This allowed individuals to learn mathematical rules while imbibing spiritual teachings. Thus, mathematics had its roots in Vedic literature dating back to the Vedas themselves. Some of the earliest known mathematical treatises, which focused on concepts like zero, algebraic techniques, square roots, and cube roots, were written between 1000 BCE and 1000 CE.

Numbers were represented in Sanskrit using the Devanagari script instead of numerical notations, especially for larger numbers. This facilitated the recording of arguments and conclusions, making it easier for students of mathematics. Textbooks, including technical and abstruse ones, were often written in verse or sutra, allowing for easier memorization by students, including children. This practice extended beyond mathematics and encompassed theological, philosophical, medical, astronomical, and other treatises, as well as massive dictionaries written in Sanskrit verse. The use of verse, sutra, and codes lightened the burden and facilitated the work by presenting scientific and mathematical material in an easily comprehensible form.

The technique of algebra and the concept of zero are generally believed to have originated in India. In the 5th century CE, a mathematical system that simplified astronomical calculations was developed in India. Initially, its application was limited to astronomy due to its association with astronomers. Algebra, known as "Bijaganitam" in India, was considered the "other mathematics" (Bija meaning "another" or "second," and Ganitam meaning mathematics) distinct