Isabella Grigoryevna Bashmakova (russian: Изабелла Григорьевна Башмакова, 1921–2005) was a Russian

historian of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...

. In 2001, she was a recipient of the Alexander Koyré́ Medal of the International Academy of the History of Science.

Education and career

Bashmakova was born on January 3, 1921, in

Rostov-on-Don Rostov-on-Don ( rus, Ростов-на-Дону, r=Rostov-na-Donu, p=rɐˈstof nə dɐˈnu) is a port city and the administrative centre of Rostov Oblast and the Southern Federal District of Russia. It lies in the southeastern part of the East Eu ...

, to a family of Armenian descent. Her father, Grigory Georgiyevich Bashmakov, was a lawyer. Her family moved to

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

in 1932. She began studies in the Faculty of Mechanics and Mathematics at

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

in 1938, but was evacuated from Moscow during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

, during which she served as a nurse in

Samarkand fa, سمرقند , native_name_lang = , settlement_type = City , image_skyline = , image_caption = Clockwise from the top:Registan square, Shah-i-Zinda necropolis, Bibi-Khanym Mosque, view inside Shah-i-Zinda, ...

... She completed a Ph.D. in 1948, under the supervision of

Sofya Yanovskaya Sofya Aleksandrovna Yanovskaya (also Janovskaja; russian: Софи́я Алекса́ндровна Яно́вская; 31 January 1896 – 24 October 1966) was a Soviet mathematician and historian, specializing in the history of mathematics, math ...

. She continued at Moscow State as an assistant professor, and in 1949 was promoted to associate professor. In 1950 her husband, mathematician Andrei I. Lapin, was arrested for his opposition to

Lysenkoism Lysenkoism (russian: Лысенковщина, Lysenkovshchina, ; uk, лисенківщина, lysenkivščyna, ) was a political campaign led by Soviet biologist Trofim Lysenko against genetics and science-based agriculture in the mid-20th cen ...

, but in part due to Bashmakova's efforts he was freed again in 1952.. Bashmakova completed her D.Sc. in 1961 and became a full professor in 1968. She retired and become a

professor emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

in 1999, and died on July 17, 2005 while vacationing in

Zvenigorod Zvenigorod (russian: Звени́город) is an old town in Moscow Oblast, Russia. Population: History The town's name is based either on a personal name (cf. Zvenislav, Zvenimir) or on a hydronym (cf. the Zvinech, Zvinyaka, Zveniga Rivers) ...

Contributions

Bashmakova's dissertation concerned the history of definitions of

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

s and

rational number In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ration ...

s, from

Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...

and Eudoxus to

Zolotarev Zolotaryov or Zolotarev; feminine: Zolotaryova or Zolotareva (russian: Золотарёв, Золотарёва) is a Russian-language occupational surname derived from the occupation of золотарь, or goldsmith. It may be transliterate in Ge ...

Dedekind Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and the axiomatic foundations of arithmetic. His ...

, and Kronecker. Her later research contributions include a comparison of the tools used by

Diophantus Diophantus of Alexandria ( grc, Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 200 and 214; died around the age of 84, probably sometime between AD 284 and 298) was an Alexandrian mathematician, who was the aut ...

to solve

Diophantine equation In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ...

, versus more modern methods; following a line of thought suggested by

Jacobi Jacobi may refer to: * People with the surname Jacobi (surname), Jacobi Mathematics: * Jacobi sum, a type of character sum * Jacobi method, a method for determining the solutions of a diagonally dominant system of linear equations * Jacobi eigenva ...

, she suggested that Diophantus' methods were more sophisticated than previously thought, but that their sophistication had been hidden by the emphasis on specific cases in Diophantus's writings. She used

complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...

s to reinterpret the geometric transformations studied by

François Viète François Viète, Seigneur de la Bigotière ( la, Franciscus Vieta; 1540 – 23 February 1603), commonly know by his mononym, Vieta, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to i ...

. She has also studied the history of

algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane c ...

s, and translated the works of

Fermat Pierre de Fermat (; between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he i ...

into Russian.

Books

Bashmakova's books include: *''Диофант и диофантовы уравнения'', Nauka, 1972; ''Diophant und diophantische Gleichungen'', Birkhäuser, 1974; ''

Diophantus and Diophantine Equations ''Diophantus and Diophantine Equations'' is a book in the history of mathematics, on the history of Diophantine equations and their solution by Diophantus of Alexandria. It was originally written in Russian by Isabella Bashmakova, and published by ...

'', Mathematical Association of America, 1997. *''Становление алгебры: Из истории математических идей'' 'The development of algebra: From the history of mathematical ideas'' Znanie, 1979. *''История диофантова анализа: От Диофанта до Ферма'' [''History of Diophantine analysis: From Diophantus to Fermat'', Nauka, 1984. *''The beginnings and evolution of algebra'' (with Galina Smirnova, Mathematical Association of America, 2000)

Recognition

In 1986, the International Congress of Mathematicians initially published a list of speakers that included no women. After protests, the executive committee of the congress invited six women to speak at the congress. Bashmakova was one of those six; she was unable to travel to the congress, but her paper appears in its proceedings. The

International Academy of the History of Science The International Academy of the History of Science (french: Académie Internationale d'Histoire des Sciences) is a membership organization for historians of science. The academy was founded on 17 August 1928 at the Congress of Historical Science by ...

elected her as a corresponding member in 1966, and a full member in 1971. She was awarded honorary diplomas in 1971, 1976, and 1980. In 2001, she was awarded the Alexander Koyré́ Medal of the International Academy of the History of Science. In 2011, a conference of the Russian Academy of Sciences was dedicated in her honor..

References

{{DEFAULTSORT:Bashmakova, Izabella Grigoryevna 1921 births 2005 deaths Scientists from Rostov-on-Don Russian mathematicians Russian women mathematicians Women mathematicians Historians of mathematics Moscow State University alumni Academic staff of Moscow State University Russian people of Armenian descent 20th-century women scientists Soviet mathematicians Soviet historians