# Mathematics in AI

Mathematics is a very fascinating subject. Maths and science both are inspired from nature and its phenomena’s. Many times we are not able to correlate the use of mathematics in real life. But it is foundation of all the advanced technologies. Wired and wireless communication, computers, smartphones etc. all utilize mathematical concepts. Mathematics has been long used to implement logic in softwares.

This brings us to Artificial Intelligence and Machine learning. AI also uses mathematics and lots of it under the hood. It’s the power of mathematics doing all the magical stuff.

Machine Learning uses a lot of algebra, statistics and probability theory to find relationship between different features to predict some value or to classify it. Algorithms like Regression, PCA, SVM etc are taken from statistics. These are very powerful and useful in many operations. Unsupervised algorithms like k nearest neighbours, k means clustering etc can find hidden relationships in data using distance between different data points using mathematical formulas.

Images and videos are stored as numbers ranging from 0 to 255 in memory.  In early days of Computer Vision, filters were developed which were able to detect edges and outlines of shapes in images. These filters consisted of small matrices containing values and were hand crafted by experts. With more advancement in methodologies and technologies, using Deep Learning computers now are capable of learning filters best suited for task using data during training. Convolution operations have refined the Computer Vision tasks. It includes multiplication of filters with different portions of image one by one over the whole image. This in multiple steps is able extract high level features in computers which eventually can be used for different tasks like image classification, segmentation etc. Its fascinating how some numbers and matrix multiplication can be used to perform intelligent decisions on images. As videos consist of multiple frames containing images, all these can be applied to videos as well.

Even in early days of Natural Language Processing, mathematical rules were able to extract meaningful information from text corpora. It included use of vectors, probabilities, word frequencies etc. These models were able to suggest relationships between sentences, predict word based on given phrase, autocorrect and much more. With advancement in technologies, advanced methods were developed which used Deep Learning. Deep Learning uses calculus, along with other branches of mathematics to deliver better results. It uses various functions like Sigmoid, tahH etc to improve results. Deep Learning tires to imitate working of neurons of human brains using maths. Different types of architectural units have been devised which perform some task very well like convolutions which works well on images. All these are fundamentally built using dot products of different values and passing through different activation functions.

Reinforcement learning is another subfield of Machine Learning. It utilizes the principle of rewarding and punishing agents based on their behaviours. This is also implemented using various mathematical concepts.

We have made computers and other computing devices smart using AI, ML and DL. All this has been made possible thanks to mathematics and Big Data. Computers now can see, talk to us, understand natural language, make intelligent decisions on their own etc.