Maths, the language of numbers and the science of patterns, reason, space and structure, has been developed and intrigued mankind for several centuries. It was part of the most ancients of civilisations: may it be Sumerian, Egyptian, Indian, Greek or Chinese. And over the past two millennia, it has been applied to several fields that have enriched our lives: engineering, medicine, finance, social sciences, actuarial science, sports, etc. Thus, it has become a foundation stone for our modern day civilisation. It has been studied (and it's fun to study) in its pure form too: to solve mathematical problems in its own domain.
The primary application of Maths has been in engineering. Engineers use mathematical knowledge and tools to create buildings, bridges, computer software, automobiles, aircrafts and several other machines. So, from the device that you are reading this text on, to the vehicle that you use to travel everywhere, or from the electrical appliances that make your lives efficient, to the apartment that you are living in - Maths has been used everywhere. Lately, you would have surely heard about Artificial Intelligence! - the foundational bases for that too, are the Mathematical Concepts of Linear Algebra, Calculus and Optimisation!
Our Mother Nature also has mathematical patterns hidden in it. You can find the Fibonacci series in the spirals of a pine cone, pineapple or sunflower seeds, you can see Ellipses in our planetary orbits, you can see Fractals in leaves of ferns and tree branches, and you can see Hexagonal Tessellations in a beehive. Maybe there are more ways in which Maths is hidden in nature, that you would find on your own!