What is the Abel Prize?
The Abel Prize is a prize in mathematics named after the Norwegian
The main goal of the fund is to awardInternational Prize for "outstanding scientific work in the field of mathematics." The prize is also intended to help raise the status of mathematics in society and to stimulate young people's interest in mathematics. Responsibility for the Abel Prize and other uses of funds lies with the Norwegian Academy of Sciences and Letters. The Foundation also supports one or two Abel Symposiums per year on various branches of mathematics, and in 2005 the Foundation created the Bernt Michael Holmbaugh Memorial Prize for promoting excellence in the teaching of mathematics.
John Nash, 2015 laureate, became the firsta person who received both the Abel and Nobel Prizes, and in 2019 the award was for the first time awarded to a woman - Karen Uhlenbeck. Russian mathematician Yakov Sinai received the Abel Prize in 2014, and in 2020 it was received by Grigory Margulis.
When the 100th anniversary of the day approached in 1902Abel's birth, plans for an Abel Prize were promoted by the Norwegian mathematician Sophus Lie, but he died in 1899, and the idea with him. Plans to establish the prize were revived in 1902 by King Oscar II, who organized many prizes during his reign. Including the 1880s prize in celestial mechanics, won by the French mathematician Henri Poincaré. The collapse of the union between Sweden and Norway, and the resulting loss of income, ended efforts to establish an annual mathematics prize. However, Abel's status in Norway remained high, and when plans for the prize were resumed in 2000, which the International Mathematical Union declared as the World Mathematical Year, there was no doubt in whose honor it would be established.
Why is Abel a great mathematician?
“Although Abel shared with many mathematicianscomplete lack of musical talent, it will not sound absurd if I compare his productivity and personality with Mozart,” Felix Klein, a German mathematician and teacher, author of the Erlangen Program, once said.
Niels Henrik Abel (1802-1829) died aged 26years. Mainly self-taught, during his short life, young Abel made pioneering contributions to the study of many subjects of pure mathematics, including algebraic equations, elliptic functions, elliptic integrals, functional equations, and other integral transformations. The first years of Abel's short life were spent on the small island of Finnøy in Rogaland, Norway, determined by the instability of his alcoholic father, who died when the future genius was 16 years old.
The only contemporary portrait of Niels Henrik Abel, painted by Johann Görbitz in 1826. Copyright: Universitetet i Oslo
Abel studied on his own, and in the spring of 1823 he made his scientific debut, publishing an article in the country's first scientific journal, Magazine for Natural Sciences (Magazin for Naturvidenskaberne).
More or less self-taught, at 21, Abelprovided the first complete proof demonstrating that there is no general algebraic solution for the roots of an equation of degree five or any general polynomial equation of degree above four. Today this work is known as Abel's theorem on the unsolvability of equations in radicals. It is worth noting that at that time the problem had not been solved for more than 250 years. In the process of writing his proof, he laid the foundation—independently of Galois, the French mathematician and founder of modern higher algebra—for the branch of mathematics now known as group theory.
At 22, he also wrote a fundamental workover elliptic integrals. She helped lay the groundwork for what would later become the theory of elliptic functions. Then, on April 6, 1829, at the age of 26, Abel died of tuberculosis. He contracted the disease while in Paris. His condition worsened in December of the same year, when he went to meet his bride in Norway practically on his own.
In his entire short life he was never able toobtain a permanent research or teaching position. Living hand in hand on scholarships, temporary teaching positions and various patrons, at the time of his death he was working to pay off the debts of his family in abject poverty. In a most cruel irony, less than two days after his death a letter arrived from August Crelle (from Crelle's Journal), announcing that he had been appointed professor at the University of Berlin.
Who won the Abel Prize this year?
One of the biggest awards in mathematics wasawarded to two people for their "fundamental contributions to theoretical computer science and discrete mathematics." Laszlo Lovas of the Alfred Renyi Institute for Mathematics in Budapest, Hungary, and Avi Wigderson of the Institute for Advanced Study in Princeton, New Jersey, won this year the Abel Prize, sometimes referred to as the Nobel Prize in Mathematics.
Photo: abelprize.no/Hungarian Academy of Sciences / Institute for Advanced Study, Princeton, NJ USA
Avi Wigderson and Laszlo Lovas won for their work in developing complexity theory and graph theory, respectively, and for connecting the two.
When Avi Wigderson and Laszlo Lovas began theira career in the 1970s, theoretical computer science and pure mathematics were almost entirely separate disciplines. Today they are so close that it is difficult to find the line between them. For their great fundamental contributions to both fields and for their unifying work, Lovas and Wigderson are today honored with the Abel Prize, an award given by the Norwegian Academy of Sciences and Literature and considered one of the highest awards in mathematics.
2021 Abel Prize Winner Avi Wigderson (Photo: Dan Komoda / Institute for Advanced Study, Princeton, NJ, USA)
“In many ways, their work complements each other.friend. Avi is a computer scientist and Lovas is a math major, but many of the problems they work on are related,” said Russell Impagliazzo, a computer scientist at the University of California, San Diego, who collaborated with both researchers, Quanta Magazine reported.
With their work, scientists have given impetus to the field of computational complexity - the study of the speed and efficiency of algorithms.
What is the essence of the laureates' work?
According to the official statement, these scientists have played a key role in the development of computer algorithms, cryptography and optimization of computations over the past decades.
In the seventies of the last century, there wasa surge of interest in discrete mathematics, which studies, for example, logical statements or graphs. It became clear to scientists that it can be applied in computer science. With the help of graph theory, computational complexity is expressed - the amount of resources required for an algorithm to obtain a result.
Algorithms are lists of instructions, essentiallythe recipe to follow to complete the task. This could include solving an equation, sorting a list of words alphabetically, or finding the fastest route between two places. Some algorithms are better than others - they require fewer steps to complete a task, but this does not mean that they are easier to solve. Hence the need for a whole field of research to sort out this, which is at the intersection of mathematics and computer science.
2021 Abel Prize Laureate Laszlo Lovas (Source: Hungarian Academy of Sciences / Laszlo Mudra)
Wigderson worked on every major openproblems in the field of computational complexity. “There are no more important problems in science,” he emphasizes. — Any process is an algorithm. Neurons in the brain or the planets of the solar system or crises in financial markets - all of this has certain fixed rules. What can be applied to computers can be applied to almost everything,” reports New Scientist.
Around the concept of computational complexity is builtmodern cryptography, since information is considered encrypted, the decoding algorithm of which is impracticable without a key in a reasonable time. Graphs are also used to create artificial neural networks.
According to the jury of the Norwegian Abel PrizeAcademy of Sciences and Literature, Laszlo Lovas and Avi Wigderson achieved the greatest results in discrete mathematics. Thus, the latter's contribution to the acceleration and optimization of algorithms is greater than that of any other scientist. In his works, Wigderson considered almost all topical problems of complexity theory, becoming a co-author of more than a hundred researchers.
The two researchers will share a prize fund of NOK 7.5 million (over RUB 65 million).
Read more
Oxygen will definitely disappear: what will happen to the Earth without the main source of life
Solar energy made liquid fuel in China
Physicists have created an analogue of a black hole and confirmed Hawking's theory. Where it leads?
Erlangen Program - Performance by a 23-year-oldGerman mathematician Felix Klein at the University of Erlangen, where he proposed a general algebraic approach to various geometric theories and outlined a promising path for their development.
Elliptic function - in complex analysisa two-way periodic function defined on the complex plane. Elliptic functions can be viewed as analogs of trigonometric functions. Historically, elliptic functions were discovered as the inverse functions of elliptic integrals.
Functional equation - an equation expressingthe relationship between the value of a function at one point with its values at other points. Many properties of functions can be determined by examining the functional equations that these functions satisfy.
Integral transformations - one of the most powerful tools for solving differential equations, both ordinary and, especially, in partial derivatives, is the method of integral transformations.
The first proof of the Abel-Ruffini theorem was published in 1799 by Ruffini. There were several inaccuracies in the evidence. In 1824, the complete proof was published by Abel.
Their proofs were based on the ideas of Lagrange,associated with permutations of the roots of the equation. Later, these ideas were developed in Galois theory, it allowed to formulate a modern presentation of proofs and served as a starting point in the development of abstract algebra.
Group theory is a branch of general algebra that studiesalgebraic structures called groups and their properties. The group is a central concept in general algebra, since many important algebraic structures, such as rings, fields, vector spaces, are groups with an extended set of operations and axioms.
An elliptic integral is some f over the field of real or complex numbers.
Elliptic function - in complex analysisa two-way periodic function defined on the complex plane. Elliptic functions can be viewed as analogs of trigonometric functions (having only one period). Historically, elliptic functions were discovered as the inverse functions of elliptic integrals.