The fourth industrial revolution has become more than just a buzzword, and to say that it is a new reality is an understatement because it is here – permeating every aspect of our lives. It is revolutionising society in various ways; cars are driving themselves, aeroplanes are flying with autopilots instead of human pilots and machines are talking to people as well as each other.

That the fourth industrial revolution (4IR) is a confluence of technologies such as artificial intelligence (AI), blockchain, internet of things and biotechnology has been written about that it is something all-too-familiar now. For starters, artificial intelligence is the use of data and mathematics to create intelligent machines. There are three types of artificial intelligence; machine learning, soft computing and computational intelligence. Machine learning is the use of data and statistics to create intelligent machines. It employs the language of the mathematical sciences to express ideas and concepts that appear intuitively correct but are often difficult to formulate precisely. Machine learning has been successful in applications such as automated diagnosis of diseases, speech recognition and face recognition.

Recently, a new type of machine learning called deep learning has seen so much success that it is now implemented by Facebook to label the identity of a person in a picture. Deep learning is so influential that in 2018, Geoffrey Hinton of Google, Joshua Bengio of Montreal and Yann LeCun of Facebook were awarded the Turing Award, considered equivalent to the Nobel Prize for computer science.

What are the mathematical foundations of machine learning? Firstly, it requires the understanding of vectors; a vector is simply ‘string’ of features or characteristics expressed as numbers, letters, etc. For example, a person, e.g. Sipho, can be described by a vector of several attributes such as height, weight, race, and gender. All these attributes collectively form a vector that provides some useful information about Sipho. Secondly, it requires the understanding of a matrix. A matrix is just a rectangular grid of ‘numbers’. To make the machine learning algorithms learn, optimisation is required. This is a mathematical technique of finding the ‘best’ possible outcome under given circumstances or constraints, for example finding the shortest distance between two points. Algorithms are a set of instructions that make a computer work. The word algorithm is derived from the last name of a Persian Muslim mathematician Muḥammad ibn Mūsā al-Khwārizmī. For example, when we use Google Maps to find the shortest road between Craighall and Soweto, we are using an optimisation method.

The second type of AI is soft computing. An example of soft computing is fuzzy logic, which is a method of reasoning that seeks to mimic human reasoning. Soft computing is important for cases where the quality and quantity of data is limited. Fuzzy logic has been applied in complex problems such as self-driving cars and on decoding the expertise of professionals, e.g. doctors and encoding it into a computer program. What mathematics is used in soft computing? Set theory and discrete mathematics are essential in understanding fuzzy logic. Fuzzy set theory, which does not often feature in the mathematical sciences offerings to engineering, science and mathematics students, is a generalisation of classical set theory and is more appropriate for soft computing.

The third type of AI is computational intelligence. Computational intelligence involves building an intelligent machine using the observation from nature. For example, the behaviour of a population of ants when they move from the nest to the food source, thereby forming the shortest distance between the two locations, has been used to create ant colony optimisation. Ant colony optimisation is used to find the shortest distance between two locations in electronics maps. Other forms of computational intelligence include particle swarm optimisation, which is inspired by the swarming of birds and genetic algorithm, which is inspired by Darwin’s theory of revolution. The theory of evolution explains how species evolve to better adapt to their changing environment. The mathematics required to understand computational intelligence include vectors and matrices. Furthermore, understanding computational intelligence includes understanding biological sciences.

Blockchain is a piece of technology that became famous through its application to create the first cryptocurrency bitcoin. It is electronic money instead of real money such as notes and coin. Blockchain is an electronic ledger where each transaction is witnessed and approved by miners. Once a block has been approved, then it is permanently stored, and it cannot be modified without the collaboration of the miners. The next transaction is verified by different miners, but the code these miners generate after approval is linked to the miners of the previous block. So, the more blocks are added to the chain of the ledger, the more difficult it becomes to modify the latest block because it involves conspiring with all the previous miners. What mathematics do we need to understand blockchain? We need to understand functional analysis.

Students at the EPFL University in Switzerland developed a smart bra this year that screens for breast cancer. This intelligent bra has sensors that sense the state of a woman’s breast. Once it detects some anomaly, it can potentially automatically call a doctor and set up an appointment. The impact of this on the early diagnosis and treatment of breast cancer is extensive. This is what is called the internet of things. The bra is equipped with piezoelectric sensors that measure the vitals of the breast. This measurement is processed using signal processing techniques and fed into an artificial intelligence machine for classification of the health status of the breast. The signal analysis requires mathematical techniques such as the Fourier analysis which was invented by a French mathematician in the 18th century. Fourier analysis breaks down the data into cycles that serve as a signature and in this particular example, the signature of the breast.

The 4IR is revolutionising the world of work through the adoption of robots. On 8 July 2020, in the prestigious journal Nature, Benjamin Burger and collaborator describes a mobile robotic chemist, which automated the researcher rather than the instruments to perform complex and often dangerous experiments. In Japan, because of the coronavirus, robots are used as bartenders, security guards, and messengers. Where are we as South Africa as far as robotics is concerned?

Not very close as there is no single university in South Africa that offers a course that specialises in robotics. However, there is some silver lining such as a school, Curro Mount Richmore, in the North Coast that now offers a course in robotics to learners up to Grade 6. What sort of mathematics do we need to master robotics? We need the mathematics described above such as vectors, matrices, and functional analysis, but furthermore, we need to teach a mathematical topic called topology. Topology is a study of shapes and their relations.

What is the state of mathematics in South Africa? The concerning aspect of mathematics learning in South Africa is that the number of pupils studying mathematics dropped from 270,516 in 2018 to 222,034 in 2019. Furthermore, only 54% of the exam passed it, and this is concerning, particularly given the fact that the pass mark is 30%. We have to fix this; otherwise, we will irreparably damage our path to the 4IR in South Africa. We need to undergo serious curriculum reform across the board in primary, secondary and tertiary levels.

The mathematical sciences curricula at some universities lead to early specialisation, sometimes at the third-year level. It is not uncommon for students to complete their first degrees without having been exposed to foundational topics that underpin the essential pillars of artificial intelligence. No university graduate in engineering, computer science and the mathematical sciences should graduate without a foundational knowledge of areas like linear algebra, probability and statistics, signal processing, optimisation, discrete mathematics and functional analysis.

**Professor Tshilidzi Marwala is the Vice-Chancellor and Principal of the University of Johannesburg. He is the Deputy Chair of the Presidential Commission on the Fourth Industrial Revolution.**

**Professor Loyiso Nongxa is the former Vice-Chancellor and Principal of the University of the Witwatersrand.**