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How does a calculator recognize so many math equations?

Asked by: Trenton Scull
School: Maine-Endwell Middle School
Grade: 6
Teacher: Kevin Wagstaff
Hobbies/Interests: Playing video games, rollerskating and racing my dogs
Career Interest: Video game designer

Answer from Hiroki Sayama

Director, Collective Dynamics of Complex Systems Research Group, Binghamton University

Research area: Complex systems, artificial life, mathematical biology, computer and information sciences
PhD school: University of Tokyo
Interests/hobbies: Traveling, walking and swimming
Family: Wife, Mari; two sons (Takehiro - 15) and (Yukihiro - 10)
Web page address:  

A great question Trenton. There are so many intelligent machines around us these days ---  computers, calculators, smart phones, videogame consoles and sometimes your TV or even the air conditioner in your room! These machines seem to understand inputs given to them, perform some complex information processing and then give us back sophisticated outputs. Does this mean they are really smart?

My answer is rather simple. It is not those machines that are truly smart, but the people who have designed and programmed them. Those people are called computer programmers and engineers. The intelligent machines that surround us usually have small computational units inside them, in which various kinds of instructions are stored and executed. These instructions are developed by humans, i.e., computer programmers and engineers, so if they are smart (I hope they are!), so are the machines they have made. As simple as that.

In order for your calculator to recognize so many math equations, the programmers and engineers who developed it needed to come up with a way to translate each equation into a machine-readable format (called "data structure") and also a step-by-step instruction of how to compute and solve that equation (called "algorithm"). This had to be done for each and every equation the calculator should be able to handle. Imagine the amount of effort the programmers and engineers had put into your calculator.

Computer programming and engineering is now playing an extremely important role in our modern society. It develops and supports the technological backbones of our world, including the Internet, media, financial transaction systems, healthcare systems, you name it. It is expected that the world will need increasingly more computer programmers in the near future, although there is currently a significant shortage for them. We need more smart people who can make the machines around us smarter.

This past week, December 9-15, 2013, was Computer Science Education Week ( dedicated to inspiring students to take an interest in computer science. Even President Obama recently called on everyone to learn computer programming (! Programming is fun to learn, and soon you will find that it will allow you to do a lot of fascinating things you never imagined you could before. I am sure you will appreciate your experience of learning programming later on in your life, because that was how I ended up being a researcher. :)

So, start learning computer programming today!

Last Updated: 3/1/17