Introduction

Why do I have to learn mathematics? - This is a question I am asked daily.

Well, you don’t have to. But you should!

On the surface, advanced mathematics doesn’t impact software engineering and machine learning in a production setting. You don’t have to calculate gradients, solve linear equations, or find eigenvalues by hand. Basic and advanced algorithms are abstracted away into libraries and APIs, performing all the hard work for you.

Nowadays, implementing a state-of-the-art deep neural network is almost equivalent to instantiating an object in PyTorch, loading the pre-trained weights, and letting the data blaze through the model. Just like all technological advances, this is a double-edged sword. On the one hand, frameworks that accelerate prototyping and development enable machine learning in practice. Without them, we wouldn’t have seen the explosion in deep learning that we witnessed in the last decade.

On the other hand, high-level abstractions are barriers between us and the underlying technology. User-level knowledge is only sufficient when one is treading on familiar paths. (Or until something breaks.)

If you are not convinced, let’s do a thought experiment! Imagine moving to a new country without speaking the language and knowing the way of life. However, you have a smartphone and a reliable internet connection.

How do you start exploring?

With Google Maps and a credit card, you can do many awesome things there: explore the city, eat in excellent restaurants, and have a good time. You can do the groceries every day without speaking a word: just put the stuff in your basket and swipe your card at the cashier.

After a few months, you’ll also start to pick up some language – simple things like saying greetings or introducing yourself. You are off to a good start!

There are built-in solutions for everyday tasks that just work – food ordering services, public transportation, etc. However, at some point, they will break down. For instance, you need to call the delivery person who dropped off your package at the wrong door. You need to call help if your rental car breaks down.

You may also want to do more. Get a job, or perhaps even start your own business. For that, you need to communicate with others effectively.

Learning the language when you plan to live somewhere for a few months is unnecessary. However, if you want to stay there for the rest of your life, it is one of the best investments you can make.

Now, replace the country with machine learning and the language with mathematics.

The fact is that algorithms are written in the language of mathematics. To get proficient with algorithms, you have to speak it.