Vedic mathematics is an ancient system of mathematics from India that allows for highly efficient calculations. It uses a unique set of techniques based on simple principles to solve arithmetic, algebraic, geometric, and trigonometric problems mentally and rapidly without the use of calculators or paper and pencil. Some key techniques include using vertical and crosswise operations to perform additions and multiplications, finding squares by adding one more than the previous number, and using tricks to easily multiply or divide by numbers like 9, 11, and 12. Vedic mathematics is becoming increasingly popular due to allowing calculations up to 15 times faster than traditional methods while reducing memorization requirements and scratch work.