You’re sitting in a classroom. You look around and see your friends writing something down. It seems they are taking the exam, and they know all the answers (even Johnny who, how to say it… wasn’t the brilliant one). You realize that your exam is in front of you, and it’s Maths. You start reading it but you don’t understand a thing. That’s terrible, your heart speeds up, you’re sweating and then… you wake up.

Uff, it was only a dream. You get back to sleep, but one thing bothers you. This paper from a dream, there was something about… how is it called… derivatives? You remember you learned it by heart at school, but never truly understood it. It’s time to face this ghost from the past.

Don’t be afraid, it’s there for a while

The idea of the derivative is not new. There is a little bit of controversy about the inventor of derivatives. The battle is between Sir Isaac Newton and Gottfried Wilhelm Leibniz.

Apparently, these two great minds discovered it independently, not being aware of their colleagues’ work. What’s interesting they came to similar conclusions having completely different ideas and approaches to the problems they were trying to solve[1].

Newton thought in the context of physics and motion, while Leibniz thought in terms of formula that could describe a change in the metaphysical meaning. However, people worked on similar theorems before the 17th century, when Newton & Leibniz lived. Arab and Persian mathematicians from the 11th and 12th centuries are supposed to discover basic ideas behind derivatives[2].

And it’s useful!

If you have ever been wondering if you’ll use any of the things you learned at school in real life, the answer is yes, derivatives are such a thing. Nowadays they are an important part of algorithms in many innovative areas, like Artificial Intelligence. In Machine Learning which is one of the AI domains, derivatives help computer programs to learn.

Generally speaking, such algorithms optimize objective functions (very often derivatives are needed for this purpose) so programs can find optimal parameters to solve different tasks (e.g. recognizing people on photos). Let’s get the key idea behind derivatives.

#derivatives #math #data-science #learning #mathematics #deep learning