Mathematics
What parts of math do you use most? Least?
In my profession I use Calculus most often, if you include the extensions to calculus called Vector Calculus and Differential Equations. These math tools describe a huge range of physical systems around us very well: for example the radio waves that carry cell-phone conversations and wireless data, which is what I work on at my present job. Other examples are: sound waves, vibrating strings in musical instruments or vocal cords, mechanical vibrations (important to people designing skyscrapers, car engines or anything that withstands forces or moves), electrical circuits, chemical reactions, ocean currents, how animal populations change, etc. Calculus is even used in economics! As for least used, I'll mention a math area I am familiar with but don't use called Number Theory. It involves, in part, thinking about infinities. Sometimes the things you don't use are really the coolest. A cool area of research in Number Theory is a math function called Riemann's Zeta Function. This function oscillates and goes through zero an infinite number of times. For reasons no one understands, the distribution of prime numbers is somehow connected to the zeroes of Riemann's Zeta Function. It's interesting because lots of people want to understand prime numbers (even the government, which uses them for secret cryptographic codes). But there's more. Chaos Theory (weather patterns, for instance, or the flow of air over a wing or fast-moving car) also seems connected to the same zeroes, but there's hardly a clue how! So physical behavior around us is connected in fundamental ways to pure math. Maybe one day you'll be the one to figure out the connection between chaos and math! I recommend that people study math even if they don't think they'll use it in daily life-- it can lead them to beautiful deep thoughts about meaning in nature.