By Sam Song, Data Scientist at Kizuna

Mathematics is Everywhere

 About two years ago, Tesla posted a two-minute-long video on YouTube, and it received huge attention with 15 million views (as of Jan 25th, 2020). At a first glance, this short video clip seems like nothing more than a typical car commercial. Within a second, however, you’ll find something interesting: the car is driving itself!

Tesla isn’t the only company implementing ‘Autopilot’ technology; in fact, the autopilot system has already been used by aircrafts for decades. Autopilot is just one of the innumerable advancements that technology brings into our lives. In most cases, people will doubtlessly connect these technologies with computer science or engineering. However, at the heart of all these technologies lies mathematics. 

An autopilot system relies on artificial intelligence, and it is full of math formulas and mathematical algorithms. To collect data, they use many sensors and cameras, but without mathematics, all the other expensive equipment is useless. Just another example of the application of mathematics. Whether you already knew it or not, the truth is that mathematics is the cornerstone of modern technologies.

Why Do You Need Mathematics?

In the world of modern engineering, mathematics is simply essential as nearly everything is expressed in a form of a mathematical equation called Differential Equations. To take a step forward, you will need to solve hundreds of complex equations, which is why mathematical knowledge is so important here. Of course, computers will do all the problem solving and calculations for you—they are much faster and more accurate—so you just need to understand and grasp the concept firmly.

Obviously, most institutions, including schools, businesses, and even governments, will use AI in many ways to provide faster and better services or enhance overall efficiency and productivity. And it is not too much to say that understanding the basic principles of AI, which is mathematics, will work to your advantage. Eventually, the gap and benefits between the ones who know how AI works and those who do not will widen further and quicker, due to the nature of fast-changing technologies.

Likewise, mathematics is an enormously powerful tool that provides AI with the means to implement how it can successfully manage its tasks. Behind most technologies creating an impact, you have Math.

Mathematics and AI

When it comes to artificial intelligence, a few of the most fundamental branches of mathematics are linear algebra, calculus, probability, and statistics. 

• Linear Algebra

Vectors and matrices are the especially important concepts of linear algebra here because most data exist in a form of matrices that consist of rows and columns. And the decision-making and learning process of AI is an endless repeat of calculating a massive volume of matrices. For AI algorithms to properly operate, vectors and matrices must be arranged in accordance with the principle of linear algebra. In a word, linear algebra is a tool that makes AI smarter and able to make more accurate predictions.

• Calculus

Calculus makes everything faster. Technically, AI can work without calculus, but it plays a key role in AI as it accelerates the learning process and data manipulation. Many of the concepts in calculus are needed in the optimization of algorithms. For example, derivatives are used by gradient descent algorithms to determine whether they should increase or decrease the weight, which affects the accuracy. Additionally, training a neural network requires the use of optimization algorithms, which is calculus.

• Probability and Statistics

First, machine learning is statistical learning. Any machine learning process involves an algorithm’s experience from statistical data. When making predictions based on a set of statistical data, probabilities are used to produce better predictions. Rather than giving you the exact answer, AI is more like suggesting solutions or giving a new recommendation that is most likely to satisfy the user, using probabilities and statistics. To increase the accuracy and precision of its decisions, probabilities and statistics are necessary.

What You’ll See

The use of AI and its benefits today are already so immense that, if you look around, in a second you will realize that AI is in every single aspect of our lives. And the application of AI will continue to grow bigger and change the lifestyle of millions of people. Such a trend indicates that you need to know the basics of AI—vectors and matrices, to name a few—to stay abreast of the change.

AI has done a lot, yet there’s plenty of room for improvement. And to improve, AI needs more help from mathematics. Mathematics is not just complicated equations behind the computers but a language for us humans to communicate with machines. The possibility of AI will drastically increase when the three elements intersect: human intelligence, our experience, and mathematics, a surprising tool that provides us with logic, creativity, and insight all at once.