Articles
BY OUR STUDENT CONTRIBUTORS
Malhar Rajpal A few weeks ago, two extremely renowned mathematicians, Avi Wigderson and László Lovász, won the prestigious Abel Prize. Becoming an Abel Prize laureate is not an easy feat, since it is only awarded to the most accomplished mathematicians in a given year. Known colloquially as the Nobel Prize pf mathematics, it has a substantial cash prize of 7.5 million Norwegian Kroner. In this article, I will talk about one of the 2021 Abel Prize winners, László Lovász and his work.
On March 9, 1948, Lovász was born in Budapest, Hungary. He was an extremely talented mathematician from an early age and managed to win three gold medals and a silver medal at the renowned International Mathematical Olympiad, the most competitive and largest high school math competition in the world, where countries send teams of their six best mathematicians to compete. Winning a medal is not an easy feat with only around the top 8% of already brilliant participants receiving a gold medal. Achieving four medals, thus, is quite an amazing achievement and truly showed Lovász’s outstanding mathematical ability at a young age. As a prodigious mathematician, he had the opportunity to meet and learn about game theory from Paul Erdös in his youth. After studying mathematics at the undergraduate and postgraduate level at Hungary's top universities, Lovász became increasingly prominent as a researcher in the field of mathematics and computer science. He worked under the supervision of Tibor Gallai through his doctoral research in the 1970s. He also worked closely with Erdös to develop methods to complement Erdös’ graph theory techniques. One of his largest accomplishments was developing the Lovász local lemma in graph theory which states that as long as a certain number of events are ‘mostly’ independent from each other, and aren’t individually very likely, then there will be a probability that none of them occurs. Of course, there are several intricacies to this lemma that are beyond the scope of this article but it was a vital development because it led to breakthroughs in creating existential proofs for rare graphs and is used in the probabilistic method. Relating to graph theory, he also contributed to the formulation of the Erdös-Faber-Lovász conjecture in 1972 which stated that ‘If k complete graphs, each having exactly k vertices, have the property that every pair of complete graphs has at most one shared vertex, then the union of the graphs can be properly colored with k colors’. This conjecture remains unsolved, however, in 2021, a proof of the conjecture was made for all sufficiently large values of k by a team of five researchers. He also proved Kneser’s conjecture in 1978, where Martin Kneser conjectured in 1955 that the chromatic number (the minimum number of colours needed to colour the nodes of a graph such that no two nodes that share an edge have the same colour) of the Kneser graph K(n, k), for n >= 2k is exactly n-2k+2. Lovász proved it by using topological methods which was significant because it made developments to the huge field of topological combinatorics. Further, in 1982, Lovász worked with Arjen Lenstra and Hendrik Lenstra to create the LLL algorithm which is a polynomial time reduction algorithm. This algorithm was a huge breakthrough for Lovász since it led to massive developments in cryptography and polynomial factorisation, the basis of RSA cryptography. This is, by no means, an exhaustive list of Lovász’s numerous accomplishments, and Lovász has made a considerable impact in the fields of mathematics and computer science over the last five decades. He has been rewarded with several prestigious awards and has worked in numerous outstanding institutions including Yale University, Microsoft Research Center, and the Hungarian Academy of Sciences. His Abel Prize for significant contributions to theoretical computer science and discrete mathematics is therefore fully deserved.
0 Comments
Leave a Reply. |
Our AuthorsWe are high school and college students from around the world who are passionate about maths, and want to share that passion with others. Categories
All
|