Florentin Smarandache

from Wikipedia, the free encyclopedia

Florentin Smarandache (born December 10, 1954 in Bălceşti , Vâlcea County ) is a Romanian - American artist and author. The scientific nature of his writings on mathematics and philosophy is controversial.


Smarandache left Romania, the country of his birth, in 1988 and emigrated to the United States in 1990. In 1997 he received his doctorate in mathematics from the State University of Chișinău , Moldova . He worked from 1997 to 2003 as an assistant professor and since 2003 as an associate professor of mathematics at the University of New Mexico , Gallup , a two-year college .

Florentin Smarandache


Smarandache has published poetry , a novel , dramas and poetry in Romanian , French and English . His works often refer to paradoxes . He invented what he called “Neutrosophy” to treat logical problems and calls his position “Paradoxism”. Smarandache published mathematical, philosophical and artistic writings and published his own texts and those of his followers in anthologies.


Smarandache calls his artistic position "Outer-Art". He explained it in the 1990s: it was about creating the least artistic things and calling them works of art.

Since the 1980s, Florentin Smarandache has called his artistic and political view a paradox. He is about an anti-totalitarian protest, about a literary, artistic, humanities and scientific avant-garde that is based on the excessive use of antitheses, antinomies, contradictions, parables, probabilities and paradoxes. This is expressed in slogans such as:

  • Everything has a meaning and a non-meaning, in harmony with one another.
  • The sense has a nonsense, and vice versa: the nonsense has a sense.
  • Everything is possible, including the impossible!


Smarandache has constructed logical problems on various occasions. The so-called “Smarandachean Paradox” is a variant of the well-known Sorites Paradox.

Smarandache proposes an extension of the fuzzy and dialectical logic that he calls "neutrophic logic". A fact can be evaluated according to probabilities with regard to truth, falsehood and indeterminacy. The uncertainty equals 0 if and only if falsehood or truth are evaluated with 1. If the three values ​​with regard to a fact add up to 1, this is called “fully determined” true. Larger values ​​are called "overdetermined", smaller values ​​"underdetermined". This should be useful for evaluating aggregates of information: if expert opinions contradict one another, the case should be evaluated as “overdetermined”, and insufficient information should correspond to an evaluation as “underdetermined”. The Dezert Smarandache theory, a modification of the evidence theory by Dempster and Shafer , which he presented together with J. Dezert, is based on this . A proposed application is also the graph display of cognitive evaluations by means of so-called fuzzy cognitive maps, with the indeterminacy being added here as an additional relation. In its previous publications, however, Smarandache only refers to Fuzzy Cognitive Maps applications actually implemented by third parties. These are then also expanded later. Independent applications have not yet been published.

Number theory and statistics

In mathematics, he wrote on number theory and statistics . He described problems that he presented as new and still unsolved. Among other things, he gave some constants, some special solutions to general functions, new names. He also defined numerous series and gave new names to some common series of numbers. An example is the series 1, 11, 112, 1123, 11235, ... where the n th value is obtained by connecting the digit extensions of the first n Fibonacci numbers . One already u. a. The function presented by E. Lucas in 1883 was published again by Smarandache in 1980 as the Smarandache function . Many other proposals are similarly dependent on known third party publications.

See also: Smarandache-Wellin number


Smarandache proposed different types of geometries, which he called "Smarandache geometries". These are not or only partially Euclidean. You have at least one axiom that behaves in at least two different ways within the same area (permissible and impermissible, or impermissible in different ways).

An example is the modification of the fifth axiom of Euclid as it is made in numerous known geometries. In Euclidean and parabolic geometry, a straight line has exactly one parallel through a given point. In Lobachevskian or hyperbolic geometry, a line has at least two parallels through a given point. In Riemannian or elliptical geometry, a straight line has no parallel through a given point. On the other hand, in “Smarandache's geometry” there are straight lines that have no parallels through a given point and other straight lines that have one or more parallels through a given point. The fifth postulate is of course violated in many ways. Smarandache is far more radical than the well-known non-Euclidean geometries, since it wants to allow violations of all Euclidean axioms and any combination of Euclidean axioms or their negations. Howard Iseri constructed a model of a two-dimensional geometry within the framework of these proposals, in which the Euclidean postulate is replaced by various definitions within the same geometric space.


According to Smarandache, there is "unmatter" alongside matter and antimatter and there is no limit to the speed of light. These views contradict all established scientific theories and numerous experimental findings without being empirically proven themselves.

Criticism of his writings

Smarandache's works have numerous supporters and opponents.

While it is common in mathematics, logic and theoretical philosophy for research contributions to be reviewed by independent experts and published in established locations (such as renowned specialist journals and book series from established scientific publishers, etc.), Smarandache has not yet submitted any publications that fall into this category fall. The independent academic mathematical or physical specialist literature does not refer to him in any other way. Exceptions can only be found in publications by his own followers. The internet portal arxiv.org, a central publication archive established in the relevant specialist disciplines, does not treat its contributions as serious publications. Smarandache himself speaks of a “mafia in science” that has conspired against him.

Many recognized experts consider his writings scientifically worthless. The physics lecturer Randall J. Scalise gives some examples that Smarandache's theses must be nonsensical if modern physics is valid.

His opponents criticize his geometric proposals just as sharply.

Critics often see Smarandache as a self-promoter and often refer to its presence on the Internet.


Many of his more than 75 books have appeared both in print and on the Internet. A selection of these are:

Publications on mathematics and logic

  • F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (third edition), Am. Res. Press, 143 p., 2003.
  • F. Smarandache, editor, Proceedings of the First International Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics, editor, University of New Mexico, Gallup Campus, Xiquan, Phoenix, 147 p., 2002.

Performing arts and literature

  • Florentin Smarandache: OUTER-ART, Abaddaba, Romania, ISBN 973-8102-00-6 (contains graphics as "non-art")
  • F. Smarandache, Le sens du non-sens (The Sense of the Non-Sense), non-poems, Ed. Artistiques, Fès, Morocco, 1983.
  • F. Smarandache, A Trilogy in pARadOXisM: Avant-garde political dramas, ZayuPress, Hampton, VA, USA, 2005.


About his literary and artistic work

  • I. Soare, Un scriitor al paradoxurilor: Florentin Smarandache, Editura Almarom, Rm. Vâlcea, 114 p., 1994.
  • Titu Popescu, Estetica Paradoxismului, Editura Tempus, Bucharest, 143 p., 1995.

Publications by followers relating to his writings on mathematics and physics

  • C. Dumitrescu, V. Seleacu, Proceedings of the First International Conference on Smarandache Type Notions in Number Theory, University of Craiova, Romania, 1997.
  • K. Atanassov, On Some of the Smarandache's Problems, Vol. I by Krassimir Atanassov, Lupton, 1999.
  • L. Stephen Young, G-Dimensional Theory & The Smarandache Quantum Paradoxes: Comparative Logic and Modern Quantum Theory, Rehoboth, 2001.
  • Linfan Mao, Automorphism Groups of Maps, Surfaces and Smarandache Geometries (partially post-doctoral research for the Chinese Academy of Sciences, Beijing), Am. Res. Press, 115 p., 2005.

Web links


  1. See Wolframs MathWorld
  2. WB Vasantha Kandasamy, Florentin Smarandache: Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps (PDF; 5.4 MB) , 2003, ISBN 1-931233-76-4
  3. Bart Kosko, Fuzzy Cognitive Maps , International Journal of Man-Machine Studies, 24 (1986) 65–75 (first presentation of FCMs)
  4. See Wolframs Mathworld
  5. For numerous other examples cf. Wolframs Mathworld .
  6. Lucas, E .: Question No. 288 , in: Mathesis 3 (1883), 232.
  7. Eric Weissstein
  8. See his complaints: Archive link ( Memento of the original from June 7, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , Archive link ( Memento of the original from October 7, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , Archive link ( Memento of the original from October 7, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. . @1@ 2Template: Webachiv / IABot / www.archivefreedom.org @1@ 2Template: Webachiv / IABot / www.archivefreedom.org @1@ 2Template: Webachiv / IABot / archivefreedom.org
  9. See his contribution to the discussion .
  10. For an ironic representation, also on other aspects of his work, cf. everything2
  11. Jon Dorbolo: The Philosopher's Web , in: Journal of Library Administration 30 / 3–4 (2000), 351–378, for example, describes the "Smarandache Notion Journal", a collection of publications available on the Internet, as "Vanity Publication" by Smarandache .
  12. See PlanetMath