Alexander Kronrod
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Aleksandr Semyonovich Kronrod (; October 22, 1921 – October 6, 1986) was a Soviet
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and
computer scientist A computer scientist is a scientist who specializes in the academic study of computer science. Computer scientists typically work on the theoretical side of computation. Although computer scientists can also focus their work and research on ...
, best known for the
Gauss–Kronrod quadrature formula The Gauss–Kronrod quadrature formula is an adaptive method for numerical integration. It is a variant of Gaussian quadrature, in which the evaluation points are chosen so that an accurate approximation can be computed by re-using the information ...
which he published in 1964. Earlier, he worked on computational solutions of problems emerging in theoretical
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
. He is also known for his contributions to
economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...
, specifically for proposing corrections and calculating price formation for the
USSR The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...
. Later, Kronrod gave his fortune and life to
medicine Medicine is the science and Praxis (process), practice of caring for patients, managing the Medical diagnosis, diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care, palliation of their injury or disease, ...
to care for terminal
cancer Cancer is a group of diseases involving Cell growth#Disorders, abnormal cell growth with the potential to Invasion (cancer), invade or Metastasis, spread to other parts of the body. These contrast with benign tumors, which do not spread. Po ...
patients. Kronrod is remembered for his captivating personality and was admired as a student, teacher and leader. He is the author of several well known books, including ''"Nodes and weights of quadrature formulas. Sixteen-place tables"'' and ''"Conversations on Programming"''. A biographer wrote Kronrod gave ideas "away left and right, quite honestly being convinced that the authorship belongs to the one who implements them."


Education

Kronrod was born on October 22, 1921 in
Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...
. Growing up, he studied math with D. O. Shklyarsky in school and in 1938 entered the Department of Mechanics and Mathematics at
Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...
. He did his first independent mathematical work as a freshman with Professor
Alexander Gelfond Alexander Osipovich Gelfond (; 24October 19067November 1968) was a Soviet mathematician. Gelfond's theorem, also known as the Gelfond–Schneider theorem, is named after him. Biography Alexander Gelfond was born in Saint Petersburg, Russian ...
. Kronrod was honored as a student with the first prize of the
Moscow Mathematical Society The Moscow Mathematical Society (MMS) is a society of Moscow mathematicians aimed at the development of mathematics in Russia. It was created in 1864, and Victor Vassiliev is the current president. History The first meeting of the society w ...
and was the only person to win the prize twice. During
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
he was rejected for military service because at the time students of higher classes were given deferments. Instead, they helped to build trenches around Moscow, and when he returned, Kronrod reapplied and was accepted. He served twice, and was injured twice. He was awarded several medals, including the
Order of the Red Star The Order of the Red Star () was a military decoration of the Soviet Union. It was established by decree of the Presidium of the Supreme Soviet of the USSR of 6 April 1930 but its statute was only defined in decree of the Presidium of the ...
. The second injury in 1943 hospitalised him for a year and he was discharged from the army in 1944. This injury made him an invalid of sorts for life. Kronrod was married and his son was born in 1943. During next four years he continued his studies at the University, simultaneously working, from 1945, in the computational branch of the nuclear energy research and development
Kurchatov Institute The Kurchatov Institute (, National Research Centre "Kurchatov Institute") is Russia's leading research and development institution in the field of nuclear power, nuclear energy. It is named after Igor Kurchatov and is located at 1 Kurchatov Sq ...
. There he chose to leave pure mathematics and pursue computational mathematics. In his last undergraduate year, Kronrod studied with
Nikolai Luzin Nikolai Nikolayevich Luzin (also spelled Lusin; rus, Никола́й Никола́евич Лу́зин, p=nʲɪkɐˈlaj nʲɪkɐˈlajɪvʲɪtɕ ˈluzʲɪn, a=Ru-Nikilai Nikilayevich Luzin.ogg; 9 December 1883 – 28 February 1950) was a Sov ...
the teacher of many of the Soviet Union's finest scientists. Kronrod and
Georgy Adelson-Velsky Georgy Maximovich Adelson-Velsky (; name is sometimes transliterated as Georgii Adelson-Velskii) (8 January 1922 – 26 April 2014) was a Soviet mathematician and computer scientist. Born in Samara, Adelson-Velsky was originally educated as ...
were colleagues and Luzin's last students. He graduated with a thesis on the
permutations In mathematics, a permutation of a Set (mathematics), set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example ...
of
conditionally convergent In mathematics, a series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely. Definition More precisely, a series of real numbers \sum_^\infty a_n is said to converge conditionally if \lim_\,\s ...
series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used i ...
. He then went on to advanced study and teaching. Like his teacher Luzin, Kronrod led a series of supplementary seminars for younger mathematics students. Unusually for the time, instead of students merely reporting on the content of courses, Kronrod made his students undertake training exercises, even proving basic theorems themselves. The preparation required for this reduced the numbers of participants, but those who remained, including
Robert Minlos Robert Adol'fovich Minlos (; 28 February 1931 – 9 January 2018) was a Soviet and Russian mathematician who has made important contributions to probability theory and mathematical physics. His theorem on the extension of cylindrical measures to ...
and
Anatoli Vitushkin Anatoli Georgievich Vitushkin () (June 25, 1931 – May 9, 2004) was a Soviet mathematician noted for his work on analytic capacity and other parts of mathematical analysis. Early life Anatoli Georgievich Vitushkin was born on 25 June 1931 in Mo ...
, derived great benefit. Vitushkin described him as "witty and friendly". At his own request, Kronrod was called simply "Sasha" by his students. He was considered to be a prophet in his field. The Kronod circle met between 1946 and 1953. Kronrod's position was formally at the Institute of Physics, which meant that his students had to register with other advisers, accounting for the decline of the circle into a series of friendly meetings. When he defended thesis in 1949, on the theory of functions of two variables, his committee including
Mstislav Keldysh Mstislav Vsevolodovich Keldysh (; – 24 June 1978) was a Soviet mathematician who worked as an engineer in the Soviet space program. He was the academician of the Academy of Sciences of the Soviet Union (1946), President of the Academy of Sc ...
,
Andrey Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet ...
and Dmitrii Menshov bypassed the
Candidate of Sciences A Candidate of Sciences is a Doctor of Philosophy, PhD-equivalent academic research degree in all the post-Soviet countries with the exception of Ukraine, and until the 1990s it was also awarded in Central and Eastern European countries. It is ...
degree and directly awarded him a
Doctor of Sciences A Doctor of Sciences, abbreviated д-р наук or д. н.; ; ; ; is a higher doctoral degree in the Russian Empire, Soviet Union and many Commonwealth of Independent States countries. One of the prerequisites of receiving a Doctor of Sciences ...
degree in the physical-mathematical sciences. Kronrod taught at the Moscow Pedagogical Institute.
Evgenii Landis Evgenii Mikhailovich Landis (, ''Yevgeny Mikhaylovich Landis''; 6 October 1921 – 12 December 1997) was a Soviet mathematician who worked mainly on partial differential equations. Life Landis was born in Kharkiv, Ukrainian SSR, Soviet Union. H ...
was a student, early collaborator and one of his biographers. During the 1960s he worked on mathematics education in high schools by organizing courses and teaching methods.


Computer science

Kronod played an important role in building the first major Russian computer, ''Relay Computer RVM-1'', though he liked to say his colleague N.I. Bessonov was the sole inventor. At the Moscow
Institute for Theoretical and Experimental Physics The Institute for Theoretical and Experimental Physics (ITEP; Russian Институт теоретической и экспериментальной физики) is a multi-disciplinary research center located in Moscow, Russia. ITEP carries ou ...
(ITEF or ITEP) during 1950–1955 Kronod collaborated with physicists, among them
Isaak Pomeranchuk Isaak Yakovlevich Pomeranchuk (; 20 May 1913 – 14 December 1966) was a Soviet physicist of Polish origin in the former Soviet nuclear weapons program. His career in physics spent mostly studying the particle physics (including thermonuclear ...
and
Lev Landau Lev Davidovich Landau (; 22 January 1908 – 1 April 1968) was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. He was considered as one of the last scientists who were universally well-versed and ma ...
. For providing theoretical physics with numerical solutions he received the Stalin Prize and an
Order of the Red Banner of Labour The Order of the Red Banner of Labour () was an order of the Soviet Union established to honour great deeds and services to the Soviet state and society in the fields of production, science, culture, literature, the arts, education, sports ...
. In 1955, he first used an electronic computer at the
Krzhizhanovsky Krzhizhanovsky (feminine: Krzhizhanovskaya) is a Russian surname derived from Polish Krzyżanowski. Notable persons with that name include: * Gleb Krzhizhanovsky (1872–1959), Soviet economist * Sigizmund Krzhizhanovsky (1887–1950), Russian shor ...
laboratory of the Institute of Energy of the
Academy of Sciences of the Soviet Union The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991. It united the country's leading scientists and was subordinated directly to the Council of Ministers of the Soviet Union (un ...
, later called the Institute for Electronic Control Machines. He directed the mathematics division of ITEP. They could surpass the results achieved outside the USSR by far faster machines, in the case of
CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...
in
Geneva Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...
, five hundred times faster. Requests for computation were analyzed and sometimes solved by other means. The equipment was maintained and there were almost no hardware malfunctions. A policy said finished programs had to be re-examined if they ran for more than ten minutes. Kronrod rewarded accuracy. He held what today are controversial views on the role of gender in computing. He employed women in ITEP's coding and card punching groups, believing that female computing staff members are more accurate than males. He also believed that in order to think, the male scientists qualified to use the computers needed to be free from operating them. The women did the input and quality assurance side by side with the men and for each month without an error received a 20% raise in salary. He applied computing resources to the USSR
planned economy A planned economy is a type of economic system where investment, production and the allocation of capital goods takes place according to economy-wide economic plans and production plans. A planned economy may use centralized, decentralized, ...
and to
cancer research Cancer research is research into cancer to identify causes and develop strategies for prevention, diagnosis, treatment, and cure. Cancer research ranges from epidemiology, molecular bioscience to the performance of clinical trials to evaluate ...
. He served with
Leonid Kantorovich Leonid Vitalyevich Kantorovich (, ; 19 January 19127 April 1986) was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources. He is regarded as the founder of linear programm ...
and others on a cabinet ministry commission and oversaw the computation of the country's material expenditures to correct price formation. Kronrod's student, the economist V. D. Belkin, further developed this work. At the Gertsen cancer research institute during the 1960s, with his student P. E. Kunin he studied the differential diagnostics of
lung cancer Lung cancer, also known as lung carcinoma, is a malignant tumor that begins in the lung. Lung cancer is caused by genetic damage to the DNA of cells in the airways, often caused by cigarette smoking or inhaling damaging chemicals. Damaged ...
and
pneumonia Pneumonia is an Inflammation, inflammatory condition of the lung primarily affecting the small air sacs known as Pulmonary alveolus, alveoli. Symptoms typically include some combination of Cough#Classification, productive or dry cough, ches ...
to help doctors determine when surgery is needed.


Artificial intelligence

Kronrod had a profound interest in
artificial intelligence Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...
known in the USSR at the time as heuristic programming. He is well known for saying, "chess is the ''
Drosophila ''Drosophila'' (), from Ancient Greek δρόσος (''drósos''), meaning "dew", and φίλος (''phílos''), meaning "loving", is a genus of fly, belonging to the family Drosophilidae, whose members are often called "small fruit flies" or p ...
'' of artificial intelligence." This quote graces the top of the
American Association for Artificial Intelligence The Association for the Advancement of Artificial Intelligence (AAAI) is an international scientific society devoted to promote research in, and responsible use of, artificial intelligence. AAAI also aims to increase public understanding of artif ...
"Games & Puzzles" chess home page. In 1965, ITEP challenged and in 1966–1967 defeated the American chess program
Kotok-McCarthy Kotok-McCarthy, also known as A Chess Playing Program for the IBM 7090 Computer' was the first computer program to play chess convincingly. It is also remembered because it played in and lost the first chess match between two computer programs. ...
. The developers included Adelson-Velsky who used
Alexander Brudno Alexander L'vovich Brudno () (10 January 1918 – 1 December 2009)
was a Russians, Russ ...
's adversarial
search algorithm In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the Feasible region, search space of a problem do ...
and a "general recursive search scheme" by Kronrod. They were advised by Russian chess master A.R. Bitman and world champion
Mikhail Botvinnik Mikhail Moiseyevich Botvinnik (; ;  – May 5, 1995) was a Soviet and Russian chess grandmaster who held five world titles in three different reigns. The sixth World Chess Champion, he also worked as an electrical engineer and computer sci ...
in what was the first test of Shannon brute force vs. selective search. Kronrod's participation came at great cost. The physics users at ITEP complained, thinking that the lab was being used for game playing, when the division was writing the
Crazy Eights Crazy Eights is a Card game#Shedding games, shedding-type card game for two to seven players and the best known American member of the Eights Group which also includes Pig (card game), Pig and Spoons (card game), Spoons. The object of the game i ...
card game and
chess Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arran ...
trying to teach a machine to think.


End of a career

When the Communist Party reprimanded him in 1968 for cosigning a letter with many mathematicians in defense of the mathematician and logician
Alexander Esenin-Volpin Alexander Sergeyevich Esenin-Volpin (also written Ésénine-Volpine and Yessenin-Volpin in his French and English publications; rus, Алекса́ндр Серге́евич Есе́нин-Во́льпин, p=ɐlʲɪˈksandr sʲɪrˈɡʲejɪvʲ ...
, a son of the poet
Sergei Yesenin Sergei Alexandrovich Yesenin (, ; 1895 – 28 December 1925), sometimes spelled as Esenin, was a Russian lyric poet. He is one of the most popular and well-known Russian poets of the 20th century. One of his narratives was "lyrical evocations ...
, the physicists were able to oust him from ITEP. He was also fired from his professorship. He then directed the mathematics laboratory at the Central Scientific Research Institute of Patent Information (CNIIPI) where he proposed
patent A patent is a type of intellectual property that gives its owner the legal right to exclude others from making, using, or selling an invention for a limited period of time in exchange for publishing an sufficiency of disclosure, enabling discl ...
reform to stimulate inventions. After gaining support he lost this position to an unsympathetic director. His last position was heading a Central Geophysical Expedition laboratory that processed drilling data where he made calculations for gas and
oil exploration Hydrocarbon exploration (or oil and gas exploration) is the search by petroleum geologists and geophysicists for hydrocarbon deposits, particularly petroleum and natural gas, in the Earth's crust using petroleum geology. Exploration methods V ...
, but he was not challenged by this work. He re-examined his goals and soon changed course.


Medicine

Kronrod decided that his best work was to help others and most importantly the terminally ill. He spent his fortune developing ''milil'' from a sour milk extract for cancer patients, to fill a shortage of ''anabol'', an expensive drug developed in small quantities by his acquaintance Bogdanov in Bulgaria. He was promised but never acquired an
animal testing Animal testing, also known as animal experimentation, animal research, and ''in vivo'' testing, is the use of animals, as model organisms, in experiments that seek answers to scientific and medical questions. This approach can be contrasted ...
laboratory so he tested the medicine on himself. Kronrod had no medical degree but he was well-informed in medicine and administered his treatments with the assistance of physicians. ''Milil'' was a last resort for seriously ill patients and was administered by physicians; in one case in a hospital ward A.A. Vishnevskiy reserved for treatments by Kronrod's method. Kronrod himself never gave the drug to patients and through physicians gave it away free. The drug was unapproved and a criminal case was brought against him. He regained his research records when a relative of the plaintiff required ''milil'' for treatment and the case was dismissed.


Strokes and death

He slowly recovered when a stroke took his speech and ability to read and write but was forced to resign at the Central Geophysical Expedition and stop all work on math. He saved his own life by asking to be soaked in a tub of very hot water for several hours after a second stroke. He died on 6 October 1986 of a third stroke.


Notes


References

* (also availabl
in Russian


External links

* {{DEFAULTSORT:Kronrod, Alexander Kronrod, Aleksandr Kronrod, Aleksandr 20th-century Russian mathematicians Mathematicians from Moscow Institute for Theoretical and Experimental Physics alumni Moscow State University alumni Recipients of the Stalin Prize Recipients of the Order of the Red Banner of Labour Recipients of the Order of the Red Star Computer chess people Kronrod, Aleksandr Jewish scientists Russian computer scientists Kronrod, Aleksandr Kronrod, Aleksandr Burials at Donskoye Cemetery Russian scientists