Alexander Bogomolny (January 4, 1948 July 7, 2018) was a

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

-born

Israeli-American , native_name_lang = , image = , caption = , population = 110,000–150,000 , popplace = New York metropolitan area, Los Angeles metropolitan area, Miami metropolitan area, and other large metropolitan are ...

mathematician. He was

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 ...

of Mathematics at the

University of Iowa The University of Iowa (UI, U of I, UIowa, or simply Iowa) is a public university, public research university in Iowa City, Iowa, United States. Founded in 1847, it is the oldest and largest university in the state. The University of Iowa is org ...

, and formerly research fellow at the

Moscow Institute of Electronics and Mathematics Moscow Institute of Electronics and Mathematics, MIEM (russian: Московский институт электроники и математики НИУ ВШЭ, МИЭМ; also occasionally referred to as ''Moscow Institute of Electronic Enginee ...

, senior instructor at

Hebrew University The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weiz ...

and software consultant at

Ben Gurion University Ben-Gurion University of the Negev (BGU) ( he, אוניברסיטת בן-גוריון בנגב, ''Universitat Ben-Guriyon baNegev'') is a public research university in Beersheba, Israel. Ben-Gurion University of the Negev has five campuses: the ...

. He wrote extensively about

arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. T ...

and mathematical games. He was known for his contribution to

heuristics A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, ...

and

mathematics education In contemporary education, mathematics education, known in Europe as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into the transfer of mathematical knowledge. Although rese ...

, creating and maintaining the mathematically themed educational website ''Cut-the-Knot'' for the

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...

(MAA) Online. He was a pioneer in mathematical education on the internet, having started ''Cut-the-Knot'' in October 1996.Interview with Alexander Bogomolny
MathTango, March 2, 2014

Education and academic career

Bogomolny attended

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 ...

school No. 444, for gifted children, then entered

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 ...

, where he graduated with a master's degree in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

in 1971. From 1971 to 1974 he was a junior research fellow at the

Moscow Institute of Electronic Machine Building Moscow Institute of Electronics and Mathematics, MIEM (russian: Московский институт электроники и математики НИУ ВШЭ, МИЭМ; also occasionally referred to as ''Moscow Institute of Electronic Enginee ...

(MIEM). He emigrated to Israel and became a senior programmer at Lake Kinneret Research Laboratory in

Tiberias, Israel Tiberias ( ; he, טְבֶרְיָה, ; ar, طبريا, Ṭabariyyā) is an Israeli city on the western shore of the Sea of Galilee. A major Jewish center during Late Antiquity, it has been considered since the 16th century one of Judaism's Fou ...

(19741977) and a software consultant at

in Negev,

Be’er Sheva Beersheba or Beer Sheva, officially Be'er-Sheva ( he, בְּאֵר שֶׁבַע, ''Bəʾēr Ševaʿ'', ; ar, بئر السبع, Biʾr as-Sabʿ, Well of the Oath or Well of the Seven), is the largest city in the Negev desert of southern Israel. ...

, Israel (19761977). From 1976 to 1983 he was a senior instructor and researcher at

Jerusalem Jerusalem (; he, יְרוּשָׁלַיִם ; ar, القُدس ) (combining the Biblical and common usage Arabic names); grc, Ἱερουσαλήμ/Ἰεροσόλυμα, Hierousalḗm/Hierosóluma; hy, Երուսաղեմ, Erusałēm. i ...

. He received his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

in mathematics at Hebrew University in 1981. His dissertation is titled, ''A New Numerical Solution for the Stamp Problem'' and his thesis advisor was Gregory I. Eskin. From 1981 to 1982 he was also a visiting professor at

Ohio State University The Ohio State University, commonly called Ohio State or OSU, is a public land-grant research university in Columbus, Ohio. A member of the University System of Ohio, it has been ranked by major institutional rankings among the best publ ...

, where he taught mathematics. From 1982 to 1987 he was professor of mathematics at the

. From August 1987 to August 1991 he was vice president of software development at CompuDoc, Inc.Linked in: Alexander Bogomolny
software developer at CTK Software Development

Cut-the-Knot

Cut-the-Knot (CTK) was a free, advertisement-funded educational

website A website (also written as a web site) is a collection of web pages and related content that is identified by a common domain name and published on at least one web server. Examples of notable websites are Google Search, Google, Facebook, Amaz ...

which Bogomolny maintained from 1996 to 2018. It was devoted to popular exposition of various topics in

. The site was designed for teachers, children and parents, and anyone else curious about mathematics, with an eye to educating, encouraging interest, and provoking curiosity. Its name is a reference to the legend of

Alexander the Great Alexander III of Macedon ( grc, wikt:Ἀλέξανδρος, Ἀλέξανδρος, Alexandros; 20/21 July 356 BC – 10/11 June 323 BC), commonly known as Alexander the Great, was a king of the Ancient Greece, ancient Greek kingdom of Maced ...

's solution to the

Gordian knot The Gordian Knot is an Ancient Greek legend of Phrygian Gordium associated with Alexander the Great who is said to have cut the knot in 333 BC. It is often used as a metaphor for an intractable problem (untying an impossibly tangled knot) sol ...

. CTK won more than 20 awards from scientific and educational publications, including a ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...

'' Web Award in 2003, the ''

Encyclopædia Britannica The (Latin for "British Encyclopædia") is a general knowledge English-language encyclopaedia. It is published by Encyclopædia Britannica, Inc.; the company has existed since the 18th century, although it has changed ownership various time ...

''s Internet Guide Award, and ''

Science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...

''s NetWatch award. The site contained extensive analysis of many of the classic problems in

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

including the

Apollonian gasket In mathematics, an Apollonian gasket or Apollonian net is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three. It is named after Greek mat ...

Napoleon's theorem In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral tr ...

logarithmic spiral A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie"). Mor ...

s, the "Futurama Theorem" from the episode "

The Prisoner of Benda "The Prisoner of Benda" is the 10th episode of the sixth season of the animated sitcom '' Futurama''. It aired on Comedy Central on August 19, 2010. In the episode, Professor Farnsworth and Amy build a machine that allows them to switch minds s ...

", the

Pitot theorem In geometry, the Pitot theorem, named after the French engineer Henri Pitot, states that in a tangential quadrilateral (i.e. one in which a circle can be inscribed) the two sums of lengths of opposite sides are the same. Both sums of lengths equa ...

, and the monkey and the coconuts problem. Once CTK published 122 proofs of the

Pythagorean theorem In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite t ...

. He wrote a manifesto for CTK in which he said that "Judging Mathematics by its pragmatic value is like judging symphony by the weight of its score." He described the site as "a resource that would help learn, if not math itself, then, at least, ways to appreciate its beauty," and he wondered why it is acceptable among otherwise well-educated people "to confess a dislike and misunderstanding of Mathematics as a whole." Many mathematical ideas were originally illustrated by

Java applet Java applets were small applications written in the Java programming language, or another programming language that compiles to Java bytecode, and delivered to users in the form of Java bytecode. The user launched the Java applet from a ...

s, but most of them got later replaced by

GeoGebra GeoGebra (a portmanteau of ''geometry'' and ''algebra'') is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is av ...

applications, which were also used for material added later. CTK wiki (powered by

PmWiki PmWiki is wiki softwareWikiMatrix / PmWiki Features - Compare Them All
Wiki ...

) extends the main site with additional mathematical content, especially that with more complicated formulae than available on the main site.

Book

* ''Cut the Knot: Probability Riddles.'' Champaign, IL: Wolfram Media, 2020. Published after Bogomolny's death, with a foreword by his friend

Nassim Nicholas Taleb Nassim Nicholas Taleb (; alternatively ''Nessim ''or'' Nissim''; born 12 September 1960) is a Lebanese-American essayist, mathematical statistician, former option trader, risk analyst, and aphorist whose work concerns problems of randomness, ...

, this book of probability riddles is curated to challenge the mind and expand mathematical and logical thinking skills. First housed on cut-the-knot.org, these puzzles and their solutions represent the efforts of great minds around the world. Bogomolny presented these selected riddles by topical progression.

Personal life

Bogomolny had to leave

academia An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary education, secondary or tertiary education, tertiary higher education, higher learning (and generally also research or honorary membershi ...

because he had an uncorrectable hearing problem and was practically

deaf Deafness has varying definitions in cultural and medical contexts. In medical contexts, the meaning of deafness is hearing loss that precludes a person from understanding spoken language, an Audiology, audiological condition. In this context it ...

in latter years.Obituary of Alexander Bogomolny
By Gary Ernest Davis in Crikey Math, July 13, 2018

Tribute

Bogomolny's older son David chronicled his yearlong recitation of

kaddish Kaddish or Qaddish or Qadish ( arc, קדיש "holy") is a hymn praising God that is recited during Jewish prayer services. The central theme of the Kaddish is the magnification and sanctification of God's name. In the liturgy, different version ...

in honor of his father, originally on

The Times of Israel ''The Times of Israel'' is an Israeli multi-language online newspaper that was launched in 2012. It was co-founded by Israeli journalist David Horovitz, who is also the founding editor, and American billionaire investor Seth Klarman.

blogs, in a series titled, "The skeptic's kaddish for the atheist", consisting of traditional Jewish sources, religious text analysis, modern interpretations and expressions of kaddish, philosophy, theology, eschatology, creative writing, and the personal reflections; memories; and experiences of a son in mourning.

References

External links

*
Math of all types: The problems of Alexander Bogomolny

Cut-the-Knot official website
{{DEFAULTSORT:Bogomolny 1948 births 2018 deaths Mathematics popularizers Recreational mathematicians 20th-century American mathematicians Soviet mathematicians Israeli emigrants to the United States Israeli people of Russian-Jewish descent Israeli American Mathematics websites Science blogs Moscow State University alumni University of Iowa faculty 21st-century American mathematicians Einstein Institute of Mathematics alumni Scientists from Moscow