**Alexander Kronrod** was a Russian mathematician and computer scientist who worked on applications of mathematical methods to physical problems. He is also known for his contributions to economics and medicine.

- Alexander won one of the prizes at the fourth Moscow Mathematical Olympiad in 1938 while still a member of Shklyarskii's group.
- Let us note at this point that our biography is based largely on translations of various Russian biographies of Alexander Kronrod made by University of St Andrews student Yulia Yashneva.
- Kronrod entered the Faculty of Mechanics and Mathematics of Moscow State University in 1938 and became an outgoing student, whose abilities were immediately recognised by a large number of academic staff.
- During his first year at the university Kronrod managed to solve an open question and publish his first independent work.
- Aleksandr Osipovich Gelfond, head of Mathematical Analysis Department, suggested a problem to his student group of which Kronrod was a member, regarding the possible structure of the set of points of discontinuity of a function which is differentiable at each point where it is continuous.
- Alexander Kronrod published his first article about this problem in 1939 in the journal Izvestiya Akademii Nauk.
- Graduate level students, including Kronrod were sent to a military academy and helped with building trenches around Moscow during first days of war against Germany.
- Kronrod did not just provide an answer to the question but also categorised such permutations.
- Kronrod still needed to complete the final year of his university course and resumed his studies in 1944 in the Faculty of Mechanics and Mathematics of Moscow State University.
- At this time Luzin was a legendary figure with an exceptional reputation as a teacher so Kronrod was proud to attend the course and the seminar.
- Kronrod and Adelson-Velskii became Luzin's final two students, and Kronrod, having no other advisors unlike Adelson-Velskii, was always proud of his status as "Luzin's last student'.
- Luzin gave Kronrod a signed copy of the French edition of his famous book The integral and trigonometric series which Kronrod loved to show to every one.
- Luzin suggested a problem for both Kronrod and Adelson-Velskii to work on.
- Kronrod went further and explored linear variation and monotonicity of functions of two or more variables.
- Development of the theory of functions of two variables, for which he used 'Kronrod's tree', can be seen as one of his most significant achievements.
- The importance of this idea can easily be seen since Vladimir Igorevich Arnold used Kronrod's tree to solve Hilbert's 13th problem in his Candidate's thesis in 1961.
- Kronrod, however, showed that the question had a positive answer, but he did not publish the solution.
- Even when studying at Moscow State University Kronrod has worked in the computing department of the Kurchatov Atomic Energy Institute.
- Kronrod was involved in building the first Russian computer 'Relay Computer RVM-1' with the engineer Nikolal Ivanovic Bessonov.
- We note that a significant fact about Kronrod's personality was his modesty since he said that Bessonov was the sole inventor.
- Unlike many mathematicians and scientists, Kronrod loved being an organiser so this position suited him.
- Apart from being involved in research work, Kronrod also organised his own student group in 1946-1953.
- In 1950-1955 Kronrod was mostly working on numerical solutions for physical problems and collaborating with his close friends Isaak Ya Pomeranchuk and Lev Landau.
- Kronrod was awarded the Stalin Prize and an Order of the Red Banner for his work at the Institute.
- Kronrod made a significant contribution to Artificial Intelligence, a new area in computing at that time.
- Kronrod created a team of mathematicians and physicists to develop Artificial Intelligence.
- Whenever the team struggled with recursion issues, Kronrod always helped to address them.
- The program of the Kronrod's team won with a score of 3:1.
- Kronrod is believed to be one of the first scientists to work in the area of Artificial Intelligence.
- There was strict control in Kronrod's department.
- Kronrod claimed that from his experience women worked better and provided more accurate results.
- In 1963, under the leadership of Kronrod, Bessonov rewrote the command system and doubled the power of the machine.
- Kronrod's department resembled an industrial factory with strict discipline and regular achievement of excellent results.
- Even though Soviet computers were less powerful than Western ones, Kronrod's team still managed to excel due to his programming skills.
- Towards the end of the 1950s Kronrod became interested in economics, especially in issues regarding pricing.
- A commission to consider pricing issues was created in the Ministry of Finance, which Kronrod was involved in during 1961-1962.
- After a while, Kronrod's student V D Belkin led the project.
- In the 1960s Kronrod discovered a new area of interest for him: differential diagnostics for some illnesses with the use of computers.
- At the Gertsen Research Institute for cancer research P E Kunin, who was a physicist and a student of Kronrod, set up a laboratory for differential diagnostics for lung cancer and central pneumonia.
- When working there Kronrod achieved some significant results.
- During that time Kronrod also organized mathematical classes in middle schools and developed teaching methods.
- This led to Kronrod receiving a reprimand from the Communist Party, and he was dismissed from the Moscow Institute for Theoretical and Experimental Physics in 1968.
- The reprimand was really used as an excuse for his dismissal, for the physicists thought that Kronrod was taking up precious computer time "playing games." Later that year he became the head of the mathematical laboratory at the Central Scientific Research Institute of Patent Information.
- After failing to find common ground with the newly appointed director, Kronrod left the Institute.
- Kronrod was very sociable and had friends from completely different circles.
- Kronrod organized the production of similar medicine milil to help cancer patients.
- Kronrod, however, never used animal testing but instead carried out all the experiments on himself.
- Therefore, the case was dismissed and Kronrod's card index file returned.
- Soon after that Kronrod suffered a stroke.
- Alexander Kronrod was a very talented scientist and a good teacher.

Born 22 October 1921, Moscow, Russia. Died 6 October 1986, Moscow, Russia.

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Origin Russia

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive