In this post: the creator together with his axioms, a story about beans, and a model playing flappy bird. Find yourself a reason to learn Machine Learning here!
Mathematics and its way to reality
Mathematics begins from axioms
Every branch of mathematics has its creator. From the very beginning of the mathematics universe, the creator proposed the thoughts that he or she thought to be true which are called the axioms. With these axioms, the supreme god has created their mathematics world’s rule. Based on these basic rules, inhabitants of this branch started to use logical reasoning and created theorems that follows the god’s axioms. Finally, a world of mathematics has shaped up.
One day, a dweller of this existing world suddenly felt upset with the god’s unbreakable axioms. He started to wonder and then came up with his own system of axioms. The new axioms imply theorems that would be considered false in the former world; furthermore, some theorems believed to be true in the former world are now not true anymore according to the logic of new axioms. There, a new world of mathematics has been formed with its god is the dissatisfied inhabitant, marking the expansion of mathematics universe.
Since then, the mathematics universe has gradually been expanding with more and more worlds created, each with its own god and the omnipresent rules: the axioms.
The tool named mathematics
How can we make use of our systems of axioms and their corresponding theorems? This is the issue we had always been concerning about studying mathematics. Because the theorems are only true in their respective context, we cannot apply them directly to problems in our life. How could this distant subject be integrated into everyday life? Is there a way for us to make mathematics a tool?
Machine Learning: the bridge between mathematics and reality
Once upon a time, in a kingdom far far away, there was a girl named Tam who is hated by her cruel stepmother. In order to prevent Tam from going to a ball held by the Prince, the stepmother mixed green beans and black beans together and then made Tam seperate the two types of bean from each other. How can a normal human like Tam could accomplish the task in time to get to the ball? It seems to be an impossible mission without magic, doesn’t it? However, there is a type of magic that can solve the problem easily: machines. Machines can do any task without getting tired; they can work continually and efficiently. But how can they be teached to distinguish the two types of beans? That is when machine learning appeared.
Human use color cognition to differentiate the two. So do machine. We firstly need to give machine inputs about the bean and then machine will try to find a function to specify the type of bean the input one was. The input for each bean will be two numbers which are the indexes of “blackness” and “greenness” of that bean. Then, Tam will give some examples to the machine about the some of the beans’ types by pick up several ones and say if it is a black bean or a green bean. Based on the examples, our machine figured out an interesting rule: if a bean’s index of “blackness” is greater than its index of “greenness”, it will a black bean and vice versa. Let’s sketch the examples on a graph:
After recognizing the pattern, all the machine has to do now is return “green” labels for those beans which lie above the 
The story above shown an example for the classification problem, a well-known Machine Learning task. Another practical example for the classification problem that you may find in your everyday life is the spam email filter. Just like the beans, every email has its own features, and the spam ones are the ones that show some special characteristics in their features. Computers can learn these characteristics from some training examples and use them to decide whether a new email is a spam or not. The aspects of Mathematics used in Machine Learning are actually practical and interesting rather than distant or boring as they’re usually thought of.
Machine learning: limit breaker
Although humans’ ability are limited in certain boundaries, we always want to surpass the limits and improve ourselves. I have never scored 50 points or more in the flappy bird game. Tam can hardly separate the beans in time and make it to the ball on her own. At those time, Artificial Intelligence (AI) will become our helpful assistant supporting us in creating new frontier out of our reach. In real life, AI has created new frontiers. May 1997, Deepblue, chess-playing machine developed by IBM, beat the contemporary world champion Kasparov in a 6-game match. Recently, AlphaGo, Google Deepmind’s Go playing program, beat Lee Sedol, worldwide second-best player in the world at the time, 3-0 in a five-game match. These examples show that machines have the potential to overcome human’s limitation and and advance further in the future.
This is a program that plays flappy bird trained by Minh at MaSSP 2018. Source code of the program can be found here.
Machine to Learn 