The Vedas, a collection of sacred hymns and texts, contain early mathematical concepts and philosophical ideas that laid the groundwork for later developments in both fields.

The Upanishads explore the concept of Brahman, the ultimate reality, which is infinite and boundless. This idea influenced Indian mathematicians to explore concepts like infinity and the infinite series.

Aryabhata, a renowned mathematician and astronomer, introduced the concept of zero as a placeholder and a number in his work, the Aryabhatiya.

The Fibonacci sequence, a series of numbers where each number is the sum of the two preceding ones, was studied by Indian mathematicians and philosophers as a representation of the patterns and rhythms found in nature.

Adi Shankara, a prominent philosopher of the Advaita Vedanta school, used the phrase 'neti neti' to describe the nature of Brahman, the ultimate reality, which is beyond all conceptualizations and descriptions.

The concept of 'maya' as an illusionary veil over reality influenced Indian mathematicians to explore imaginary numbers and complex numbers, which were seen as a way to represent the hidden dimensions of reality.

Brahmagupta, a renowned mathematician and astronomer, developed the 'chakravala' method, a cyclic algorithm for solving indeterminate equations, which is considered a significant contribution to number theory.

The concept of 'sunya' (void) in Indian mathematics and philosophy goes beyond the idea of emptiness or nothingness. It symbolizes the ultimate reality, the Brahman, which is devoid of all attributes and distinctions.

Jaina philosophers, particularly Mahavira and his followers, developed the theory of 'anekantavada,' which emphasizes the existence of multiple viewpoints and perspectives on reality, acknowledging the complexity and diversity of the world.

The concept of 'dharma' in Indian philosophy emphasizes the importance of righteous action and ethical conduct. This influenced Indian mathematicians to pursue mathematical knowledge not only for intellectual curiosity but also for its practical applications and the betterment of society.

Madhava of Sangamagrama, a renowned mathematician and astronomer, is considered the founder of the 'Kerala school of astronomy and mathematics.' He made significant contributions to calculus, trigonometry, and infinite series.

The 'Lilavati' text, written by Bhaskara II, is a comprehensive treatise on mathematics that covers arithmetic, algebra, geometry, and astronomy. It is considered one of the most important mathematical works in Indian history.

The concept of 'karma' in Indian philosophy emphasizes the relationship between actions and their consequences. This influenced Indian mathematicians to explore mathematics as a tool for understanding the underlying principles of cause and effect, and to develop mathematical models to describe these relationships.

Baudhayana, an ancient Indian mathematician and astronomer, is credited with developing the 'Sulvasutras,' a collection of rules and procedures for constructing altars and performing geometric calculations. These rules laid the foundation for geometry and trigonometry in India.

The 'Bhagavad Gita,' a sacred Hindu text, contains philosophical teachings that have influenced Indian mathematics. It provides a framework for understanding the nature of reality, the relationship between the individual and the universe, and the pursuit of knowledge, including mathematical knowledge.