Alexander Bogomolny (January 4, 1948 July 7, 2018) was a
Soviet
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 ...
-born
Israeli-American
Israeli Americans () are Americans who are of full or partial Israeli descent.
The Israeli-American community, while predominantly Jewish, also includes various ethnic and religious minorities reflective of Israel's diverse demographics. This c ...
mathematician. He was
Professor Emeritus
''Emeritus/Emerita'' () is an honorary title granted to someone who retirement, retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus".
...
of Mathematics at the
University of Iowa
The University of Iowa (U of I, UIowa, or 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 organized int ...
, and formerly research fellow at the
Moscow Institute of Electronics and Mathematics, senior instructor at
Hebrew University
The Hebrew University of Jerusalem (HUJI; ) is an Israeli public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. It is the second-ol ...
and software consultant at
Ben Gurion University. He wrote extensively about
arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms.
...
,
probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
,
algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
,
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
,
trigonometry
Trigonometry () is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The fiel ...
and mathematical games.
He was known for his contribution to
heuristics
A heuristic or heuristic technique (''problem solving'', '' mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a pragmatic method that is not fully optimized, perfected, or rationalized, but is nevertheless ...
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 method, scholarly research into the transfer of mathematical know ...
, 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
A university () is an educational institution, institution of tertiary edu ...
(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 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 ...
school No. 444, for gifted children, then entered
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 ...
, where he graduated with a master's degree in
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
in 1971.
[ From 1971 to 1974 he was a junior research fellow at the Moscow Institute of Electronic Machine Building (MIEM). He emigrated to Israel and became a senior programmer at Lake Kinneret Research Laboratory in Tiberias, Israel (19741977) and a software consultant at Ben Gurion University in Negev, ]Be’er Sheva
Beersheba ( / ; ), officially Be'er-Sheva, is the largest city in the Negev desert of southern Israel. Often referred to as the "Capital of the Negev", it is the centre of the fourth-most populous metropolitan area in Israel, the List of cities ...
, Israel (19761977). From 1976 to 1983 he was a senior instructor and researcher at Hebrew University
The Hebrew University of Jerusalem (HUJI; ) is an Israeli public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. It is the second-ol ...
in Jerusalem
Jerusalem is a city in the Southern Levant, on a plateau in the Judaean Mountains between the Mediterranean Sea, Mediterranean and the Dead Sea. It is one of the List of oldest continuously inhabited cities, oldest cities in the world, and ...
. He received his Ph.D. 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 (Ohio State or OSU) is a public university, public Land-grant university, land-grant research university in Columbus, Ohio, United States. A member of the University System of Ohio, it was founded in 1870. It is one ...
, where he taught mathematics.[
From 1982 to 1987 he was professor of mathematics at the ]University of Iowa
The University of Iowa (U of I, UIowa, or 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 organized int ...
.[ 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) is a free, advertisement-funded educational website
A website (also written as a web site) is any web page whose content is identified by a common domain name and is published on at least one web server. Websites are typically dedicated to a particular topic or purpose, such as news, educatio ...
which Bogomolny maintained from 1996 to 2018. It is devoted to popular exposition of various topics in mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
. 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 (; 20/21 July 356 BC – 10/11 June 323 BC), most commonly known as Alexander the Great, was a king of the Ancient Greece, ancient Greek kingdom of Macedonia (ancient kingdom), Macedon. He succeeded his father Philip ...
's solution to the Gordian knot
The cutting of the Gordian Knot is an Ancient Greek legend associated with Alexander the Great in Gordium in Phrygia, regarding a complex knot that tied an oxcart. Reputedly, whoever could untie it would be destined to rule all of Asia. In 33 ...
.
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 scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Pri ...
'' Web Award in 2003, the ''Encyclopædia Britannica
The is a general knowledge, general-knowledge English-language encyclopaedia. It has been published by Encyclopædia Britannica, Inc. since 1768, although the company has changed ownership seven times. The 2010 version of the 15th edition, ...
''s Internet Guide Award, and ''Science
Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...
''s NetWatch award.
The site contains 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, Napoleon's theorem, logarithmic spiral
A logarithmic spiral, equiangular spiral, or growth spiral is a self-similarity, 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" ("ewi ...
s, the "Futurama Theorem" from the episode " The Prisoner of Benda", the Pitot theorem
The Pitot theorem in geometry states that in a tangential quadrilateral the two pairs of opposite sides have the same total length. It is named after French engineer Henri Pitot.
Statement and converse
A tangential quadrilateral is usually defin ...
, and the monkey and the coconuts problem. One page includes 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 ...
.
Bogomolny 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 applet, small applications written in the Java (programming language), Java programming language, or another programming language that Compiled language, compiles to Java bytecode, and delivered to users in the form of Ja ...
s, but most were later replaced by GeoGebra applications, also used for material added later. CTK wiki (powered by PmWiki) 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. His 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 tertiary education. The name traces back to Plato's school of philosophy, founded approximately 386 BC at Akademia, a sanctuary of Athena, the go ...
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 audiological condition. In this context it is written ...
in his later 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
The Kaddish (, 'holy' or 'sanctification'), also transliterated as Qaddish, 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 lit ...
in honor of his father, originally on The Times of Israel
''The Times of Israel'' (ToI) is an Israeli multi-language online newspaper that was launched in 2012 and has since become the largest English-language Jewish and Israeli news source by audience size. It was co-founded by Israeli journalist Dav ...
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
Mathematics websites
Science bloggers
Moscow State University alumni
University of Iowa faculty
21st-century American mathematicians
Einstein Institute of Mathematics alumni
Scientists from Moscow
21st-century science writers