Jan Gullberg

Last updated
Jan Gullberg Jan Gullberg.jpg
Jan Gullberg

Jan Gullberg (1936 – 21 May 1998) was a Swedish surgeon and anaesthesiologist, but became known as a writer on popular science and medical topics. [1] He is best known outside Sweden as the author of Mathematics: From the Birth of Numbers, published by W. W. Norton in 1997 ( ISBN   039304002X).

Sweden constitutional monarchy in Northern Europe

Sweden, formal name: the Kingdom of Sweden, is a Scandinavian Nordic country in Northern Europe. It borders Norway to the west and north and Finland to the east, and is connected to Denmark in the southwest by a bridge-tunnel across the Öresund, a strait at the Swedish-Danish border. At 450,295 square kilometres (173,860 sq mi), Sweden is the largest country in Northern Europe, the third-largest country in the European Union and the fifth largest country in Europe by area. Sweden has a total population of 10.2 million of which 2.5 million have a foreign background. It has a low population density of 22 inhabitants per square kilometre (57/sq mi). The highest concentration is in the southern half of the country.

International Standard Book Number Unique numeric book identifier

The International Standard Book Number (ISBN) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.



Gullberg grew up and was trained as a surgeon in Sweden. He qualified in medicine at the University of Lund in 1964. He practised as a surgeon in Saudi Arabia, Norway and Virginia Mason Hospital, Seattle in the United States, as well as in Sweden. [1] Gullberg saw himself as a doctor rather than a writer. His first book, on science, won the Swedish Medical Society's Jubilee Prize in 1980, and saw him promoted to honorary doctor at the University of Lund the same year. [2]

Virginia Mason Hospital Hospital in Washington, United States

Virginia Mason Hospital is a 336-bed teaching hospital in Seattle, Washington, part of the Virginia Mason Medical Center. The hospital is accredited by the Joint Commission and the Commission on Accreditation of Rehabilitation Facilities (CARF). Founded in 1920, the hospital operates several accredited residency programs that train newly graduated physicians.

He was twice married: first to Anne-Marie Hallin (d. 1983), with whom he had three children; and Ann, [1] with whom he adopted two sons.

He died of a stroke in Nordfjordeid, Norway at the hospital where he was working.

Nordfjordeid Village in Western Norway, Norway

Nordfjordeid is the administrative centre of the municipality of Eid in Sogn og Fjordane county, western Norway. It is located at the end of the Eidsfjorden, an arm off of the main Nordfjorden, west of the large lake Hornindalsvatnet. The village of Stårheim is located about 12 kilometres (7.5 mi) to the west, the village of Mogrenda is about 5 kilometres (3.1 mi) to the east, and the village of Lote is about 7 kilometres (4.3 mi) to the southeast.

Mathematics: From the Birth of Numbers

Gullberg's second (and last) book, Mathematics: From the Birth of Numbers, took ten years to write, consuming all of his spare time. [2] [3] It proved a major success; its first edition of 17,000 copies was virtually sold out within six months. [2]


The book's 1093 pages address the following topics:

  1. Numbers and Language
  2. Systems of Numeration
  3. Types of Numbers
  4. Cornerstones of Mathematics
  5. Combinatorics
  6. Symbolic Logic
  7. Set Theory
  8. Introduction to Sequences and Series
  9. Theory of Equations
  10. Introduction to Functions
  11. Overture to the Geometries
  12. Elementary Geometry
  13. Trigonometry
  14. Hyperbolic Functions
  15. Analytic Geometry
  16. Vector Analysis
  17. Fractals
  18. Matrices and Determinants
  19. Embarking on Calculus
  20. Introduction to Differential Calculus
  21. Introduction to Integral Calculus
  22. Power Series
  23. Indeterminate Limits
  24. Complex Numbers Revisited
  25. Extrema and Critical Points
  26. Arc Length
  27. Centroids
  28. Area
  29. Volume
  30. Motion
  31. Harmonic Analysis
  32. Methods of Approximation
  33. Probability Theory
  34. Differential Equations


Arnold Allen, reviewing Mathematics: From the Birth of Numbers in The American Mathematical Monthly , wrote that although there were many worthy books that could claim the title of people's guide to mathematics, "Gullberg's book is clearly the overall winner. ... It is a wonderful read. I take it with me everywhere I go." [4] Allen says the book has "special charm", making innovative use of the margin and providing "excellent quotes and quips" throughout. [4] His favourite chapter is "Cornerstones of Mathematics" which he believes should appeal both to beginners and "old hands". [4] He professes himself amazed at Gullberg's revelation of an alternative pencil-and-paper method of multiplication from the one we all learned at school, namely the Egyptian method of duplation, and loves the "Russian peasant" multiplication method involving "successive duplation and mediation". [4] He admires the "efficient" Babylonian method of finding square roots, using division and averaging. He learns from Gullberg how to multiply and divide using an abacus. [4]

Abacus Calculating tool

The abacus, also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system. The exact origin of the abacus is still unknown. Today, abacuses are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone, or metal.

The seven bridges of Konigsberg Konigsberg bridges.png
The seven bridges of Königsberg

Allen is delighted by the chapter on combinatorics, with its approach to graph theory and magic squares, complete with 1740 map of the seven bridges of Königsberg (which have to be traversed exactly once). He enjoys Gullberg's account of the Fibonacci, Lucas and Pell sequences; and he finds the two-page account of Fermat's last theorem "at exactly the right level for those who are mathematically disadvantaged, but with some sophistication as well." [4] He loved the chapter on probability. He claims that after he showed colleagues the book, he had to keep it hidden to prevent it from disappearing, and suggests that every high school maths teacher should be given a copy to improve maths teaching across America. He records that he finds its introductory accounts useful for engineers who use maths only occasionally, and suggests how the book could be used for undergraduate students. He concludes by describing the book as "gigantic ... in every sense" (it weighs 4 pounds 13 ounces, is 1100 pages long) and was 10 years in the making, and calls it "a giant leap forward for mathematics and all those who love it!". [4]

The book was positively reviewed in Scientific American , [5] but more reservedly in New Scientist . [6] Kevin Kelly comments that the book is an "oracle" able to provide answers on obscure mathematical concepts; in his view "The book has wit and humor; you’ll need persistence." [7]

Gullberg commented, "At the start no 'real mathematician' would accept my book. And perhaps it was a bit crazy of me to write a book on mathematics, as it would be for a mathematician to write a book on surgery." [2] [8]

Other works

Related Research Articles

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics, from evolutionary biology to computer science, etc.

Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

Discrete mathematics Study of discrete mathematical structures

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.

George Pólya Hungarian mathematician

George Pólya was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education. He has been described as one of The Martians.

History of mathematics aspect of history

The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, together with Ancient Egypt and Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy and to formulate calendars and record time.

Mathematics Field of study concerning quantity, patterns and change

Mathematics includes the study of such topics as quantity, structure, space, and change. It has no generally accepted definition.

Magma is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structure magma. It runs on Unix-like operating systems, as well as Windows.

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

This article itemizes the various lists of mathematics topics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing.

Serge Lang mathematician

Serge Lang was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He received the Frank Nelson Cole Prize in 1960 and was a member of the Bourbaki group. As an activist, he campaigned successfully against the nomination of the political scientist Samuel P. Huntington to the National Academies of Science, and later descended into AIDS denialism, claiming that HIV had not been proven to cause AIDS and protesting Yale's research into HIV/AIDS.

Harold Davenport English Mathematician

Harold Davenport FRS was an English mathematician, known for his extensive work in number theory.

Mathematics encompasses a growing variety and depth of subjects over history, and comprehension requires a system to categorize and organize the many subjects into more general areas of mathematics. A number of different classification schemes have arisen, and though they share some similarities, there are differences due in part to the different purposes they serve. In addition, as mathematics continues to be developed, these classification schemes must change as well to account for newly created areas or newly discovered links between different areas. Classification is made more difficult by some subjects, often the most active, which straddle the boundary between different areas.

Hjalmar Gullberg Swedish writer, poet and translator of Greek drama into Swedish

Hjalmar Gullberg was a Swedish writer, poet and translator of Greek drama into Swedish.

In mathematics, ancient Egyptian multiplication, one of two multiplication methods used by scribes, was a systematic method for multiplying two numbers that does not require the multiplication table, only the ability to multiply and divide by 2, and to add. It decomposes one of the multiplicands into a sum of powers of two and creates a table of doublings of the second multiplicand. This method may be called mediation and duplation, where mediation means halving one number and duplation means doubling the other number. It is still used in some areas.

Pierre de Fermat French mathematician and lawyer

Pierre de Fermat was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' Arithmetica.

Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

In mathematics, a multiplicative calculus is a system with two multiplicative operators, called a "multiplicative derivative" and a "multiplicative integral", which are inversely related in a manner analogous to the inverse relationship between the derivative and integral in the classical calculus of Newton and Leibniz. The multiplicative calculi provide alternatives to the classical calculus, which has an additive derivative and an additive integral.

Jiří Matoušek (mathematician) Czech mathematician (b.1963)

Jiří (Jirka) Matoušek was a Czech mathematician working in computational geometry and algebraic topology. He was a professor at Charles University in Prague and the author of several textbooks and research monographs.

Mathematics is a field of study that investigates topics including number, space, structure, and change. For more on the relationship between mathematics and science, refer to the article on science.

This is a glossary of terms that are or have been considered areas of study in mathematics.


  1. 1 2 3 "Jan Gullberg, 62, Swedish Science Writer". New York Times. 1998-06-18. Retrieved 2010-01-18.
  2. 1 2 3 4 Örn, Peter (1997). "Kirurgen Jan Gullberg skrev matematikens historia" [The surgeon Jan Gullberg wrote the history of mathematics](PDF). Läkartidningen (in Swedish). 94 (45): 4023–4025.
  3. Isdahl, Hans (2006). "Skoleelever, matematikk og den hellige gral" [School pupils, mathematics and the holy grail](PDF) (in Norwegian). Archived from the original (PDF) on 2015-01-12.
  4. 1 2 3 4 5 6 7 Allen, Arnold (January 1999). "Reviews: Mathematics: From the Birth of Numbers. By Jan Gullberg". The American Mathematical Monthly. 106 (1): 77–85. doi:10.2307/2589607. JSTOR   2589607.
  5. Donald J. Albers (September 1998). "Reviews". Scientific American . Retrieved 2010-01-18.
  6. Keith Devlin (1997-06-14). "Those were the days". New Scientist . Retrieved 2010-01-18.
  7. Kelly, Kevin. "Mathematics: From the Birth of Numbers" . Retrieved 29 December 2014.
  8. In the Swedish: "Till en början ville ingen »riktig matematiker» ta i min bok. Och kanske är det lika tokigt av mig att skriva en bok om matematik, som det skulle vara för en matematiker att skriva en bok om kirurgi"