Mathematics for AI/ML/DL, OR/MS/IE, and Data Science

- Overview

Mathematics is an important aspect of machine learning. While some people may absolutely love math, others may not. However, one must have at least some mathematical knowledge and understand the concepts of probability, statistics, and calculus to successfully solve machine learning tasks. You can't do anything without math. Everything around you is math. Everything around you is digital. 

The relationship between AI and mathematics can be summarized as:

• A person in AI who doesn't know math is like a politician who doesn't know how to persuade. Both have an unavoidable field of work!
• A popular suggestion for learning math for AI is this: learn linear algebra, probability, multivariate calculus, optimization, and a few other topics.

- The Mathematics Involved in AI/ML/DL, Neural Networks, and Data Science

Driven by data, machine learning (ML) models are the mathematical engines of artificial intelligence, algorithmic expressions that can discover patterns and make predictions faster than humans. For the most transformative technological AI journey of our time, the engine you need is a machine learning model. For example, an ML model for computer vision might be able to identify cars and pedestrians in live video. A translatable word and sentence for natural language processing. 

However, math can be daunting, especially for someone from a non-technical background. Apply this complexity to machine learning and you're in a very bad place. We can easily build models and perform various machine learning tasks using widely available libraries in Python and R. So it's easy to avoid the math part of the field.

The main branches of mathematics involved in artificial intelligence are: Calculus, linear algebra, probability, and statistics. 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.    

[The 17 equations that changed the world]

- Mathematics is the Mother of All Sciences

Mathematics (from Greek μάθημα máthēma “knowledge, study, learning”) is the study of quantity, structure, space, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. 

Since the pioneering work of Giuseppe Peano (1858-1932), David Hilbert (1862-1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning often provides insight or predictions. 

Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.

- The Goals

The foundations of mathematics as a whole does not aim to contain the foundations of every mathematical topic. Generally, the foundations of a field of study refers to a more-or-less systematic analysis of its most basic or fundamental concepts, its conceptual unity and its natural ordering or hierarchy of concepts, which may help to connect it with the rest of human knowledge. The development, emergence, and clarification of the foundations can come late in the history of a field, and might not be viewed by everyone as its most interesting part. 

Mathematics always played a special role in scientific thought, serving since ancient times as a model of truth and rigor for rational inquiry, and giving tools or even a foundation for other sciences (especially physics). Mathematics' many developments towards higher abstractions in the 19th century brought new challenges and paradoxes, urging for a deeper and more systematic examination of the nature and criteria of mathematical truth, as well as a unification of the diverse branches of mathematics into a coherent whole.