Science and Literature: Imagination, Medicine nad Space

Posted in Art and Mathematics, Books with tags , on September 24, 2021 by tefcros

I am happy to announce the publication as an e-book of “Science and Literature: Imagination, Medicine and Space” a collection of articles presented during the 3rd International Conderence on Science and Literature, held in Paris during the summer of 2018. Many thanks to the organisers and the editors of the volume, Kostas Tambakis and George Vlahakis.

The volume can be downloaded here:

Included (p. 67) is my paper: Gödel’s theorem as a source of inspiration for literary production

Murder in the Great Church

Posted in Art and Mathematics, Books, Fiction, math crime fiction with tags , , , , , , , , , , on March 2, 2020 by tefcros

My new novel, Murder in the Great Church, was recently published by Polis Editions.  The setting is 6th century Constantinople, under the reign of Justinian and Theodora (the cover photo pictures Sarah Bernhardt impersonating Theodora in a play by Victorien Sardou).

On the opening day of  Hagia Sophia, the new church commissioned by Justinian, Ioannis, the principal assistant of the architect is murdered. The main suspect is Theano, a young mathematician, former student in Plato’s Academy and close friend of the victim. Eutocius of Ascalone, editor of the works of Archimedes and Apollonius undertakes the research for the culprit. 10 Φονικό στη μεγάλη εκκλησία

On your nameday I’ll be there

Posted in Art and Mathematics, Books, Fiction, math crime fiction with tags , , , , on March 2, 2020 by tefcros

My short story “On your nameday I’ll be there” was included in HELLAS NOIR, an anthology of Greek crime fiction edited by Kostas Kalfopoulos and published in Germany under the title An Deinem Namenstag werde ich da seinHellas-Noir

The Mathematical Encounters of Maurits Cornelis Escher.

Posted in Art and Mathematics, Books, Fiction with tags , , , , , on March 31, 2019 by tefcros

Although I am absolute innocent of training or knowledge in the exact sciences, I often seem to have more in common with mathematicians then with my fellow artists.

At the website Mac Tutor History of Mathematics of St. Andrews University, today’s most accurate and complete source of mathematical biographies, one can find Escher among such names as Archimedes, Fermat, Eüler and Gauss. Is it merely an extravagant nod towards an artist who, while not a mathematician himself, honored the Science of Mathematics like no other? True enough, Escher was not a Mathematician in the usual sense: he did not study Mathematics, did not teach it, did not publish any research or educational essay on it, whatsoever. However, numerous mathematical textbooks contain his work, not merely as a decorative, but also as an instructive means. Also numerous are those who argue that his work has contributed actively, albeit in a non-conventional manner, to the progress of Mathematics.

At high school in Arnhem, I was extremely poor at arithmetic and algebra because I had, and still have, great difficulty with the abstractions of numbers and letters. When, later, in stereometry, an appeal was made to my imagination, it went a bit better, but in school I never excelled in that subject. But our path through life can take strange turns.

We can be fairly sure that, while spending whole days studying the Arabian decorative motifs, at the Alhambra Palace in Spain (during two journeys in 1922 and 1936), he never suspected he was conducting primary mathematical research. The regular paving motifs, i.e. the ways in which a flat surface could be covered by a periodical repetition of the same shape, without breaks or overlaps, was one of the outlets for Moorish artists, whose creativity was stifled under the Q’ran’s prohibition of any and all human or animal representations.

Escher described this paving technique, what we call today the “regular division of a plane” as “the richest source of inspiration” he ever had. In fact, not having any religious restrictions, he himself had no difficulty at all in applying the basic plane transformations (parallel transposition, revolution, reflection, rolling reflection) in images of people, horses, fish and birds. That is to say, the very man who claimed not to understand mathematical abstraction, managed to tell structure apart from content  and reproduce the first, while altering the second.

Thus, when in 1937 his brother, Bered, gave him Georg Polya’s article on plane symmetry groups, to read, Escher, though failing to perceive the abstract concept of group, had no difficulty in understanding the basic classification of regular plane divisions into 17 categories, nor grasping, in practice (that is to say, without the mathematical formalism), the structure of the 17 groups of symmetry. It was Escher’s first mathematical encounter, resulting in a particularly productive period (from 1937 to 1941), during which he created 43 colored sketches, approaching the different groups of symmetry in a very methodical way and adopting his own “mathematical” symbolism. Over the next years, he created woodblock paintings, experimenting with all 17 groups of plane symmetry, discovering in practice, along the way, what Mathematics had already predicted. It is at this point he finds his work different from that of Mathematicians:

In mathematical quarters, the regular division of the plane has been considered theoretically. … [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it.

Despite their different goals, it seems that Mathematicians and artists have one thing in common: the tendency to generalize. There were two possible paths towards generalization: first, one could research the regular division of three-dimensional space and second, one could turn to the non-regular division of a plane, that is to say, using paving methods that subject the “tiles” to transformations other than symmetries, which alter the “tiles” themselves, such as enlargement or reduction.

His second mathematical encounter, with English-Canadian geometer, Donald Coxeter, also played an important role in moving him towards this new direction. They met in 1954, at the International Congress of Mathematicians in Amsterdam, and remained close friends until Escher’s death, in 1972. Through his discussions with Coxeter, Escher came in contact with hyperbolic geometry and the way one can use it to create a picture of infinity.

It is very likely that Coxeter “engineered” the amazing meeting (in the way of ideas) between Escher and the great French Mathematician, Henri Poincaré .

Poincaré  and Escher never met physically, of course, since the first died in 1912, when the second was but 14 years old. In fact, we have absolutely no indication that Escher ever read any of his work. However, it seems that, at some point in their respective lives, each, for different reasons and from an altogether different starting point, had the same inspiration, expressed in their own separate way and medium: Poincaré  using a, now famous, thought experiment and Escher with a series of woodblock paintings, “Circle Limits”, I, II, III, IV. All we have to do is read Poincaré’s text from his book “Science et Hypothèse” and then compare it to the corresponding woodblock paintings:

Let us think of a world enclosed inside a sphere and subject to the following natural laws: the temperature is greatest at the center and decreases uniformly, as we move away from it, to reach the absolute zero at the sphere’s surface […] All bodies in this world have the same expansion coefficient, such that a rod’s length is proportional to its temperature. Finally, let us suppose that an object, moving from one point of this world to another, of a different temperature, automatically adapts to the new thermal environment of its new position. […] Thus, an object moving towards the outer surface keeps shrinking.

If this world is finite, from our own geometric point of view, it will seem infinite to its inhabitants. Indeed, as they approach the outer surface of the sphere, they keep getting colder and smaller. Hence, their steps also become constantly smaller and they can never reach the outer sphere.

Of course, it is perfectly possible that Escher was informed of Poincaré’s ideas by his other Mathematician friends. However, the artistic depiction of the hyperbolic geometry model is purely his own work, a work in fact that was proven, in 1995, by Coxeter himself to be, from a mathematical angle “…absolutely correct in every inch… It is a pity that he did not live long enough to witness his mathematical justification”.

For Escher, another important mathematical encounter was the one with British Mathematician, Roger Penrose. Together they conceived the idea of the twisted triangle – the tribar – the basis for Escher’s impossible buildings. Three points in space always define a single plane and thus, contrary to the skew tetrahedron (the tetrahedron whose 4 peaks are not on the same plane), the skew triangle is impossible. However, when we depict three-dimensional space on a plane, violating the rules of perspective can create the illusion of a skew triangle and through it, the image of a self-sustained waterfall, a circular, perpetually upward or downward trajectory, or a tower that, when climbed “from the inside”, leads you “to the outside”.

Escher’s last mathematical encounter is also limited to the world of ideas. We cannot know whether Escher ever met Russel or Gödel. We do know, however, that all three dabbled in self-reference. Russel used it to show the contradiction inherent in the idea of “the set of all sets that do not contain themselves”, Gödel used it to prove that a theory cannot guarantee, in and of itself that it is non-contradictory and Escher created two beautiful hands that draw one another with it. If self-reference is a nightmare to Mathematicians, shaking the foundations of their science, Escher uses his carving tools to send them a hopeful message: “When looking at things from the right perspective, all paradoxes are mere illusions”.

INFO: You can view all Escher’s graphic work by visiting the official M. C. Escher Website, here

My novel “Symmetry and the Expatriate” (currently available only in Greek) describes an encounter of a fictional character with Escher, in Siena.

Math fiction revisited

Posted in Books, Fiction with tags , , , , , on March 11, 2019 by tefcros


What Is Math Fiction, And Why Are Greeks So Good At It?

A wonderful article describing math fiction and especially the work of Greek authors written by E. L. Meszaros, may be accessed here

Many many thanks to E. L. Meszaros

Yunan karasi: an anthology of crime fiction stories by Greek writers, published in Turkish

Posted in Books, Fiction with tags , , , , , on December 17, 2018 by tefcros

My short story “Twin Primes” is included in the just published Turkish anthology of Greek crime fiction writers. Many thanks to the editor, Vasilis Danellis and to the Istos editions. Yunankarası 1


Petits meurtes entre mathematiciens (Pythagorean Crimes in French)

Posted in Books, Fiction with tags , , , , , , , on July 16, 2017 by tefcros

I was happily surprised discovering this small video on You Tube. A teacher used my novel in a classroom. How exciting!

The video includes some wonderful pictures

Thanks to Sara Dostie!

Spherical Mirrors, plane murders

Posted in Books, Fiction with tags , , , , , , , , , , on July 10, 2017 by tefcros

New book

08 Σφαιρικά κάτοπτρα, επίπεδοι φόνοι

Spring 1191: In a commandeered mansion at Limassol, Cyprus, the newly wed king Richard, whom they have called the Lionheart, enjoys the fruit of his recent conquest of Cyprus. However, another war is raging in his surroundings. Intrigues, conspiracies, alliances forged and immediately broken; and to top it all off, a murder. The victim is the fiendish Laure, confidant of the queen mother Eleanor and concubine to her son. The main suspect is Dona Estephana, a doctor, once pupil of Averroes, attached to the newly wed Berengaria of Navarra.

Mid 1950s: An English Byzantine scholar, a French paleographer and a young Greek mathematician are urgently invited to Cyprus in order to evaluate a manuscript dating from the Third Crusade. It contains the solution to a difficult problem concerning spherical mirrors, stated by Ptolemy and solved by the Muslim scholar Alhazen. The manuscript also contains references to a murder. Things get more complicated when the three experts witness a second murder, eight hundred years after the original one…

Two interwoven stories, eight hundred years apart. Richard’s conquest of Cyprus during the Third Crusade and the 1955 – 1959 war of independence are bridged through the famous Kitab al Manazir (The book of optics), with its spherical mirrors problem. The solution to both mysteries can be found in this manuscript, provided one can read it properly!


APMEP in Marseille, France

Posted in Uncategorized with tags , , , , on October 8, 2013 by tefcros

Le Lundi, 21 Octobre, je vais participer au Souk des Maths dans le cadre des Journées Nationales de l’ APMEP (Association des Professeurs de Mathématiques de l’ Enseignement Public) qui auront lieux a Marseilles.2013-10-21 - APMEP Marseille

Symmetry and the Expatriate

Posted in Books, Fiction on July 16, 2013 by tefcros

Symmetry and the Expatriate - CoverThis is the story of an expatriate from Asia Minor, obsessed with symmetry, forced to leave his fatherland during the ethnic cleansing directed by the Turks in 1920 – 1922. He finds himself in Siena, Italy, where he meets with M.C. Escher, with whom he shares the interest in symmetry. In 1936 he is forced to flee again, due to his opposition to the fascist regime.

His next destination is Spain, where he becomes a member of the International Brigades defending the Spanish Republic. There he meets Rachel, a Jewish girl from Thessaloniki, the love of his life. He also meets Simone Weil, as well as the parents of Alexander Grothendieck, the most eminent and unconventional mathematician of the 20th century.

After the victory of Franco he flees once more, this time to France, where he is involved in the underground resistance against the Nazis and meets with the famous mathematicians of the Bourbaki group.

It is the story of a fictional hero as well as a chronicle of the 20th century.

Table of Contents

1. The Expatriate

2. Ex oriente lux

3. An exile’s paradise

4. The beetle

5. Al Andalus

6. No pasaran

7. Paris, ville ouverte

8. Interdit d’ interdire

9. … and the symmetry


The important thing is that the author dissolves the main aspect of positivism, that is, the mentality of strict sense and enriches it with many elements of sensibility. Of course, I am not referring to cheap melodrama but living, breathing setting of the scene that evokes emotion in moderation. This emotion stems from the tragic elements of the story and the harsh fate reserved for humans, seemingly so unfair when juxtaposed to the symmetrical justice of geometric shapes. (George Perantonakis, Efimerida Sintakton, 16 – 17 /2)

Tefcros Michaelides is back to mathematics literature. In his “Symmetry and the Expatriate” fiction mixes admirably with history. Places and eras mix equally well: Asia Minor, Italy between the two wars, Spain during the Civil War and France during the resistance. At the center of the story, the Bourbaki movement which used mathematical rationalism to understand everyday events. (Antaios Chrisostomides, Avgi, 23/12/2012)

Is symmetry understood in the same way by everybody, or at least by those who study mathematics. The graphic artist Escher and the mathematician Alexandre Grothendieck who share the interest for symmetry with the central hero of the novel understand it differently. The best way to understand it is of course to consider it as a game. Then following the ways to leave footprins on the sand you discover seven different ways to proceed: Hop, step, sidle, spinning hop, spinning sidle, jump, spinning jump. However, mathematical rationalism is not used in general at play but for much more serious reasons. One of these is to analyze the historical facts that determined the events of the 20th century. (Ilias Kanelis, The Books’ Journal, #26, December 2012).

He manages to keep the reader’s interest as the process of simultaneous examination of so different items as are mathematics, history and art as well as the viewpoint of each one of these separately create a peculiar suspense. The research for freedom at all levels in correlation with the purity of science open new paths in understanding things. Delicious and deprived of difficulties even to those with a bad relation with mathematics – including myself. (Titika Dimitroulia, Kathimerini, 10/02/2013).

The “Expatriate” of mathematician Michaelides is first of all a hymn to humanity and secondly only a “mathematics fiction”. It contains so many real facts that nobody will consider it as fiction. An the narrative recipe of the author is so ancient and so successful that no one will consider it as a “boring biography”. Michaelides immediately introduces us to the mood of the Socratic dialog teacher – student, reminding us of the valuable role of a mentor, so much neglected in our days. And then he uses another forgotten valuable ingredient, the dialog of friendship. He bases his story on a mathematical background that floods it. A background that would remain unnoticed to the reader but which, according to the author is strictly linked to the evolution of history. It is the eternal fight between symmetry and disorder, beauty and ugliness, goodness and violence, love and height rid. The book is not only extremely well written and cleverly structured but moreover it is a mirror to the generations that built the 20th century. ”. (Tasos Kafantaris, TO VIMA, 05/01/2013). The author manages to combine the square mathematical way of thinking to a tragic mood developing emotion and humanity (George Perantonakis, Book Press, 16/12/2012).