Kautilya's Arthashastra, written around the 4th century BCE, contains a detailed section on agriculture, including crop rotation, irrigation, and soil management.

Mathematics was used in ancient Indian agriculture for a variety of purposes, including calculating the area of fields, predicting weather patterns, and determining the best time for planting and harvesting.

Brahmagupta's formula, developed by the Indian mathematician Brahmagupta in the 7th century CE, was used to calculate the area of irregular fields.

Time series analysis was used in ancient India to predict weather patterns by analyzing historical data on temperature, rainfall, and other meteorological variables.

Logistic regression was used in ancient India to determine the best time for planting and harvesting crops by analyzing historical data on crop yields, weather conditions, and other factors.

Ancient Indian farmers used mathematics to calculate the flow rate of water, determine the optimal size of irrigation canals, and schedule irrigation cycles.

Manning's equation, developed by the Irish engineer Robert Manning in the 19th century, was used to calculate the flow rate of water in irrigation canals.

Linear programming was used to determine the optimal size of irrigation canals by minimizing the cost of construction and operation.

Ancient Indian farmers used mathematics to calculate the water requirements of crops, determine the optimal frequency of irrigation, and schedule irrigation cycles based on weather forecasts.

Crop water use models, soil water balance models, and evapotranspiration models were used to calculate the water requirements of crops.

Dynamic programming was used to determine the optimal frequency of irrigation by minimizing the total cost of irrigation and crop production.

Ancient Indian farmers used mathematics to adjust irrigation schedules based on predicted rainfall, schedule irrigation cycles to avoid frost damage, and schedule irrigation cycles to minimize water losses due to evaporation.

Ancient Indian mathematicians made significant contributions to the field of agriculture, including the development of mathematical models for calculating the area of irregular fields, mathematical techniques for predicting weather patterns, mathematical models for determining the best time for planting and harvesting crops, and mathematical techniques for managing irrigation systems.

The integration of mathematics and agriculture in ancient India contributed to the development of sustainable farming practices by enabling farmers to make informed decisions about crop selection, planting and harvesting times, and irrigation schedules, optimizing the use of water and other resources, and developing new and more efficient farming techniques.

Modern agriculture faces a number of challenges that could be addressed using mathematical techniques, including optimizing crop yields while minimizing environmental impact, predicting and mitigating the effects of climate change on agriculture, and developing new and more efficient irrigation systems.