Abel Prize 2021 Awarded For Enriching Link Between Mathematics and Computer Science

This year’s Abel Prize has been awarded to two researchers -- László Lovász belonging to the Alfred Renyi Institute of Mathematics in Budapest, Hungary, and Avi Wigderson belonging to the Institute for Advanced Study in Princeton,US.

The Abel Prize has been awarded to them “for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics”—reads a statement of the Abel Prize website. The award is named after the Norwegian mathematician Niels Henrik Abel.

Abel Prize is one of the most prestigious honours in the field of mathematics and is often equated to the Nobel Prize in Mathematics. This award is given by the Abel committee appointed by the Norwegian Academy of Science and Letters. Since its inception in 2002, this prize has been awarded annually to outstanding mathematicians.

Lovász and Wigderson helped developing the field of computational complexity and, in fact, were among the pioneers in the field. The field of computational complexity mainly studies the speed and efficiency of computer algorithms.

Fundamentally, algorithms are sets of instructions to be followed in order to complete a task. The task could include solving an equation or determining the shortest route between two places or grouping of words in alphabetical order and so on. Any computer programme designed to solve such problems have an algorithm, that is, a list of instructions with the help of which such a problem can be solved.

In our day-to-day lives we often deal with computer apps designed to solve such problems. But, some apps are better in solving the problems in comparison to others. This implies that the algorithms in such apps or computer programmes are better than the others, meaning that they use fewer steps consistently in reaching the solution.

To use a better app and quickly find solutions to our problems may seem to be very usual and normal, but working it out computationally is not an easy task. Here, a whole field of research emerged and it exists in the overlap of mathematics and computer science.

Widgerson and Lovász cemented the link between mathematics and computer science and enhanced the field of computational complexity. Widgerson, who is known for seeing links among different disciplines, was quoted to have commented: “There are no more important problems anywhere in science. Any process is an algorithm – neurons in the brain or planets in the solar system or crises in the financial markets, all of these have some fixed rules. What can be applied to computers can be applied to basically everything.”

Lovász is a mathematician and worked across many disciplines of mathematics. He applied graph theory, a branch of mathematics to the study of computational complexity. “In addition to his work on the foundational underpinning of computer science, Lovász has also devised powerful algorithms with wide-ranging applications, such as the LLL algorithm, which has had remarkable applications in areas including number theory, cryptography and mobile computing”—reads the Abel prize website.

Computational complexity, has now become an established field for both mathematics and computer science. This field is also important from the perspective of cyber security as it provides the theoretical basis internet security.

The field of computational complexity was in infancy in 1970s, but a new generation of mathematicians of that period realised that mathematics would be a new area of application in computer science. Lovász and Wiggerson have been consistently working in this field since then and played an important role in its development.