The Bedrock of Artificial Intelligence

Author:   Sahil Singh
BSc Mathematics (Hons.)

---

Famous American Mathematics and Science writer Martin Gardner once said, “Mathematics is not only real, but it is the only reality.” It is indeed true. Mathematics in itself is an extremely vast subject and to add to that, it is the basis of a number of other fields. One such field is Artificial Intelligence.

Introduction

We have all heard how mathematics is all around us, but what we might not realise is that Artificial Intelligence is all around us too. In the midst of the conversations about the marvelous (and sometimes dangerous) future which AI holds for us, with its autonomous cars, AI robots, huge potential in healthcare, education and so on, we fail to acknowledge its contribution in our current day to day lives.

Google’s AI-Powered Predictions for Google Maps analyses the movement of traffic at any given time by collecting anonymous location data from mobile devices; ride sharing apps like Ola and Uber use the help of AI in determination of price, minimization of wait time and detours; commercial flights use AI autopilots, reducing human involvement time to 7 minutes, that too only for take-off and landing; in email, the spam filter and the smart categorization of email; plagiarism checker; in banking/personal finance, AI is used to determine and prevent fraudulent transactions, and also in credit decisions; in social networking, Facebook uses AI to recognize faces and suggest tags, Instagram uses machine learning to identify contextual meaning of emojis, even the Snapchat filters are possible because of AI; online shopping sites use our search to automatically recommend relevant items etc

The list is indeed long, and it also includes our current favorites of AI applications, which is Smart Personal Assistants. Be it Google Assistant, Siri, Alexa or Cortana, these assistants have played a huge role in making our lives more convenient, all by using voice-to-text technology. They are still going strong in cementing the pathway between humans and “smart” homes. And this is just the beginning.

One of the biggest reasons Artificial Intelligence has been able to achieve so much, and still has the potential to achieve so much more, is mathematics. Professor Angel Garrido, Faculty of Science, UNED, Madrid wrote, “Mathematics and Artificial Intelligence are two branches of the same tree.” To put it simply, Artificial Intelligence is mainly a blend of mathematics and programming.

Having a mathematical degree is not an absolute necessity in order to make neural networks for AI, but the people who write the algorithms, do the research and investigate the boundaries of AI capabilities cannot go far without learning the mathematics involved. This is why mathematics is essential for AI and machine learning, because it guides us in how we can solve very difficult deep abstract problems and it does that by using methods and techniques already known. Artificial intelligence is described as a technology which enables a machine to simulate human behavior and machine learning is a division of AI which allows a machine to automatically learn from past data without having to be explicitly programmed to do so.

Mathematics Branches Essential for Artificial Intelligence

The topics of mathematics that are used in AI include Calculus, Linear Algebra, Probability & Statistics.


• Linear Algebra: Used in Machine Learning to define the parameters and structure of different machine learning algorithms. This helps understand how neural networks are put together and how they are operating.
  
  
  Important topics are:
  
  
  • Singular value decomposition
  • Special Matrices and Vectors Eigenvalues and
  • Matrix Norms
  • Principal component analysis
  • Scalars, Vectors, Matrices, Tensors



• Calculus: Used to augment the sophistication part of machine learning. This is what makes AI learn from examples, update the parameters of different models from time to time and make the performance better altogether.
  
  
  Important topics are:
  
  
  • Derivatives (Scalar Derivative-Chain rule), Partial and Directional Derivative
  • Integrals
  • Differential Operators
  • Gradients
  • Convex Optimization
  • Gradient algorithms- local/global maxima and minima, SGD, NAG, MAG, Adams



• Probability Theory: Used for making assumptions about the underlying data when we are designing these deep learning or AI algorithms. It is essential to understand the key probability distributions.
  
  
  Important topics are:
  
  
  • Random Variables
  • Distributions (Binomial, Bernoulli, Poisson, Exponential, Gaussian)
  • Variance and Expectation
  • Elements of Probability
  • Bayes’ Theorem, MAP, MLE
  • Special Random Variables

Conclusion

The foundation of artificial intelligence, like more or less everything related to computers, is based on mathematical concepts. If we discuss about deep learning (a subpart of AI), a lot of it is based on mathematics taught at the undergraduate level, such as the concepts of matrices, calculus and so on.

Different research papers in the pertinent areas and careful examination into any effective algorithms in Artificial Intelligence can make it clear that the pillar of it is pure mathematics. In ANN (Artificial Neural Network), which is an algorithm in AI, the principal working of it is designed using differential calculus, and it holds true for other learning algorithms. The core plan is almost always a result of a set of equations. Therefore, for research on finding new algorithms, some might even feel mathematics is more relevant than even computer science in the field of Artificial Intelligence.