Andrew Michael Odlyzko (Andrzej Odłyżko) (born 23 July 1949) is a Polish-

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

mathematician and a former head of the

University of Minnesota The University of Minnesota, formally the University of Minnesota, Twin Cities, (UMN Twin Cities, the U of M, or Minnesota) is a public land-grant research university in the Twin Cities of Minneapolis and Saint Paul, Minnesota, United States. ...

's Digital Technology Center and of the Minnesota Supercomputing Institute. He began his career in 1975 at

Bell Telephone Laboratories Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...

, where he stayed for 26 years before joining the

in 2001.

Work in mathematics

Odlyzko received his B.S. and M.S. in mathematics from the California Institute of Technology and his Ph.D. from the Massachusetts Institute of Technology in 1975. In the field of mathematics he has published extensively on

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Diri ...

computational number theory In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithm ...

cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adv ...

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

s and

computational complexity In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) ...

combinatorics 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 a ...

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an 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 1, where, roughly speaking, ...

, and

error-correcting code In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea i ...

s. In the early 1970s, he was a co-author (with D. Kahaner and

Gian-Carlo Rota Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, proba ...

) of one of the founding papers of the modern

umbral calculus In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain "shadowy" techniques used to "prove" them. These techniques were introduced by John Blis ...

. In 1985 he and Herman te Riele disproved the

Mertens conjecture In mathematics, the Mertens conjecture is the statement that the Mertens function M(n) is bounded by \pm\sqrt. Although now disproven, it had been shown to imply the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes, in an 1 ...

. In mathematics, he is probably known best for his work on the

Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > ...

, which led to the invention of improved algorithms, including the Odlyzko–Schönhage algorithm, and large-scale computations, which stimulated extensive research on connections between the zeta function and

random matrix In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathemat ...

theory. As a direct collaborator of

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...

, he has

Erdős number The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual ...

Work on electronic communication

More recently, he has worked on

communication network A telecommunications network is a group of nodes interconnected by telecommunications links that are used to exchange messages between the nodes. The links may use a variety of technologies based on the methodologies of circuit switching, mess ...

electronic publishing Electronic publishing (also referred to as publishing, digital publishing, or online publishing) includes the digital publication of e-books, digital magazines, and the development of digital libraries and catalogues. It also includes the edit ...

economics of security The economics of information security addresses the economic aspects of privacy and computer security. Economics of information security includes models of the strictly rational “homo economicus” as well as behavioral economics. Economics of ...

and

electronic commerce E-commerce (electronic commerce) is the activity of electronically buying or selling of products on online services or over the Internet. E-commerce draws on technologies such as mobile commerce, electronic funds transfer, supply chain manage ...

. In 1998, he and Kerry Coffman were the first to show that one of the great inspirations for the Internet bubble, the myth of "Internet traffic doubling every 100 days," was false. In the paper "Content is Not King", published in ''

First Monday ''First Monday'' is an American legal drama television series which aired on CBS during the midseason replacement from January 15 to May 3, 2002. The series centered on the U.S. Supreme Court. Like another 2002 series, '' The Court'', it was i ...

'' in January 2001, he argues that # the

entertainment industry Entertainment is a form of activity that holds the attention and interest of an audience or gives pleasure and delight. It can be an idea or a task, but is more likely to be one of the activities or events that have developed over thousan ...

is a small industry compared with other industries, notably the

telecommunications industry The telecommunications industries within the sector of information and communication technology is made up of all telecommunications/telephone companies and internet service providers and plays a crucial role in the evolution of mobile communicati ...

; # people are more interested in

communication Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inqui ...

than

entertainment Entertainment is a form of activity that holds the attention and interest of an audience or gives pleasure and delight. It can be an idea or a task, but is more likely to be one of the activities or events that have developed over thousa ...

; # and therefore that entertainment "content" is not the

killer app In marketing terminology, a killer application (commonly shortened to killer app) is any computer program or software that is so necessary or desirable that it proves the core value of some larger technology, such as computer hardware, a video game ...

for the

Internet The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a '' network of networks'' that consists of private, p ...

. In 2012, he became a fellow of the International Association for Cryptologic Research and in 2013 of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meeting ...

Network value

In the paper "Metcalfe's Law is Wrong","Metcalfe's Law is Wrong"
Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly, July 2006 IEEE Spectrum. Andrew Odlyzko argues that the incremental value of adding one person to a network of ''n'' people is approximately the ''n''th

harmonic number In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: H_n= 1+\frac+\frac+\cdots+\frac =\sum_^n \frac. Starting from , the sequence of harmonic numbers begins: 1, \frac, \frac, \frac, \frac, \do ...

, so the total value of the network is approximately ''n'' * log(''n)''. Since this curves upward (unlike

Sarnoff's law David Sarnoff (February 27, 1891 – December 12, 1971) was an American businessman and pioneer of American radio and television. Throughout most of his career, he led the Radio Corporation of America (RCA) in various capacities from shortly afte ...

), it implies that Metcalfe's conclusion – that there is a

critical mass In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (specifically, its nuclear fi ...

in networks, leading to a

network effect In economics, a network effect (also called network externality or demand-side economies of scale) is the phenomenon by which the value or utility a user derives from a good or service depends on the number of users of compatible products. Net ...

– is qualitatively correct. But since this linearithmic function does not grow as rapidly as

Metcalfe's law Metcalfe's law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system (''n''2). First formulated in this form by George Gilder in 1993, and attributed to Robert Metcalf ...

, it implies that many of the quantitative expectations based on Metcalfe's law were excessively optimistic. For example, by Metcalfe, if a hypothetical network of 100,000 members has a value of $1M, doubling its membership would increase its value 4X (200,000²/100,000²). However Odlyzko predicts its value would only slightly more than double: 2e5*log(2e5)/(1e5*log(1e5). Empirical tests, in part stimulated by this criticism, strongly support Metcalfe's law.

Financial History

In recent years, Odlyzko has published multiple papers on the financial history of bubbles, particularly the South Sea and English railway episodes of the eighteenth and nineteenth centuries, respectively.

References

External links

Andrew Odlyzko: Home Page

Digital Technology Center
at the

* Andrew Odlyzko
Tragic loss or good riddance? The impending demise of traditional scholarly journals
* Andrew Odlyzko
Content is Not King
''First Monday'', Vol. 6, No. 2 (5 February 2001).

at

MathWorld ''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Di ...