“Mathematics is the language with which God has written the universe.” -Galileo Galilei

The future we have seen in science fiction movies is here. From virtual reality to functional gadgets, AI has invaded our lives in ways that no one has ever seen or expected before. AI tools and chatbots have been on the verge of a breakthrough in the promptly-evolving tech realm.

AI is not magic; it’s just mathematics. The ideas behind thinking machines and the possibility to mimic human behavior are done with the help of mathematical concepts.

Artificial Intelligence and Mathematics are the two branches of the same tree. If you want to thrive in your AI career, then you need to study mathematics; merely being a fan of science fiction won’t be enough. If you’re going to build an Artificial Intelligence career and dominate hiring in the space, be friends with mathematics, and it will rock your world.

Being a mathematician, and a fan of Artificial Intelligence, here I am sharing the magical connection of AI and mathematics.

Let’s dive deeper into the fascinating realm.

How is AI connected with mathematics?

Artificial intelligence problems constitute on two general categories, Search Problems, and Representation Problems. Following them are interconnected models and tools like Rules, frames, Logics, and Nets. All of them are very mathematical topics.

The primary purpose of Artificial intelligence is to create an acceptable model for human understanding. And these models can be prepared with the ideas and strategies from various branches of Mathematics.

Consider self-driving cars; their goal is to recognize objects and people in videos images. There are mathematics behind these cars in the form of minimization procedures and back-propagation. Mathematics helps to solve challenging deep abstract problems by using traditional methods and techniques known for hundreds of years.

What kind of math is used in Artificial Intelligence?

Behind all of the significant advances, there is mathematics. The concepts of Linear Algebra, Calculus, game theory, Probability, statistics, advanced logistic regressions, and Gradient Descent are all major data science underpinnings.

Math helps in understanding logical reasoning and attention to detail. It enhances your abilities to think under pressure and increase your mental endurance. Mathematical concepts give the real solution of hypothetical or virtual problems. It is about structure, developing principles that remain true even if you make any alteration in the components.

The three main branches of mathematics that constitute a thriving career in AI are Linear algebra, calculus, and Probability.

Linear algebra

Linear Algebra is the field of applied mathematics which is something AI experts can’t live without. You will never become a good AI specialist without mastering this field. As Skyler Speakman said,

“Linear Algebra is the mathematics of the 21st century.”

Linear Algebra helps in generating new ideas, that’s why it is a must-learn thing for AI scientists and researchers. They can abstract data and models with the concepts of scalars, vectors, Tensors, matrices, sets and sequences, Topology, Game Theory, Graph theory, functions, linear transformations, eigenvalues and eigenvectors.

Vectors

In linear programming, vectors are used to deal with inequalities and systems of equations for notational conveniences. Artificial Intelligence scientists use different techniques of vectors to solve problems of regression, clustering, speech recognition, and machine translation. The concepts are also used to store the internal representations of AI models like linear classifiers and deep learning networks.

Matrix theory

In science fiction movies, you usually see that by performing some computational structure similar to the neural system, a neural network has been produced by generating the connections between neurons to match the way of reasoning of a human brain. The concept of Matrix is used in the study of neural networks.

A Non-Linear hypothesis can be done in neural network by forming artificial neurons in three layers:

1. Input layer

2. Hidden layers

3. Output layer

AI Scientists classify the neural networks from their quantity of hidden layers and the way they connect.

Real Neuron

Artificial Neuron

The neural network can be formed by those artificial neurons and it took about 20 years to discover this.

Eigenvalues and eigenvectors

The science of search engine ranking is based on mathematical science. Page Rank, which is the very groundwork of Google as a company is based on the mathematical perspective. Page Rank is the algorithm, originally formulated by Larry Page and Sergey Brin in their research paper “The Anatomy of a Large-Scale Hyper-textual Web Search Engine.” The application of the basic concept of principal eigenvalues and eigenvectors, known for hundreds of years, is used behind this tremendous breakthrough.

Robot crawlers first retrieve the webpages, and then index and catalog them by assigning Page Rank Values. The credibility of each page depends on the number of links to that page.

The rank r (P) of a given page P is assumed as,

Where,

Bp = all pages pointing to P

|Q| = number of outlinks from Q.

P is the matrix with the terms,

To find the convergence and convergence rates, the matrix P is adjusted. When the row Google matrix P reaches the sum to 1, then it is called a row stochastic matrix. The Page Rank iteration represents the evolution of a Markov Chain in which the web directed graph is represented as a transition probability matrix P.

It shows the probability of a random surfer at each of the three pages at any point in time.

First, a binary Adjacency matrix is created to signify the link structure, then it is transformed into a probability matrix by normalizing it.

To compute the Page Rank, it is essential to solving an eigenvector problem for the linear system,

The eigenvalues of Stochastic matrix P can be assumed as 1> λ1 ≥ λ2 ≥ … ≥ λn,

and V1, V2, V3, ……, Vn be the corresponding eigenvectors.

After the process of convergence, the dominant eigenvalue of matrix P should be λ=1 to satisfy,

With,

which is the steady state distribution of the Markov Model.

The process of PageRank convergence is shown in this graph,

This is how Google automatically characterizes the Page Rank value of each site.

Calculus

Differential calculus, Multivariate calculus, Integral calculus, Error minimization and optimization via gradient descent, Limits, Advanced logistic regressions are all the concepts used in mathematical modeling. A well-designed mathematical model is used in Biomedical sciences to simulate complex biological processes of human health and diseases with high fidelity.

In-Silico modeling, which is the application of AI approaches in Bio-medicine is a fully automated model that does not require human samples, crude animal tests, clinical trials or laboratory equipment. A differential mathematical equation is used in the model to test new mechanistic hypotheses and evaluate novel therapeutic targets. It is the most inexpensive and convenient way to study human physiology, drug responses, and diseases way more accurately by manipulating mathematical model parameters.

In Silico clinical trials for pediatric orphan diseases

Probability

There are a lot of abstract problems in the Artificial intelligence world. You may experience uncertainty and stochasticity in many forms. Probability theory offers tools to deal with uncertainty. To analyze the frequency of happening of an event, the concepts of probability are used, as it is defined as the chance of occurrence of an event.

Let’s consider a Robot. A robot can only move forward for a certain number of seconds, but not a certain distance. To make the robot go forward, scientists use mathematics in its programming. Discrete random variables, continuous random variables, Bayes Formula, and normalization are some concepts of probability that are used in Robotics navigation and locomotion along with other concepts of linear algebra. Mathematics and Robotics are broad areas, which I will discuss next time in detail.

The Final Verdict

Whether you want to pursue a career as a machine learning engineer, data scientist, or a robotic scientist, you need to excel in mathematics. Mathematics can enhance analytical thinking skills which are vital in Artificial intelligence. AI scientists believe that what people think about AI is that, it is all magic, but it isn’t magic, it’s the mathematics that creates magic behind all the inventions. So, to lead in today’s AI-driven world, you need to have a great flair in math.