** **

**Part 1 **

**(Academic work) **

** **

**STUDIES**

I obtained my
B.Sc. (1973) and M.Sc.(1974) from Imperial College, London University, and my Ph.D. (1977) under
the supervision of J. A. Erdos at King’s College,
London University.
The title of my thesis was *On some reflexive lattices and related algebras*,
and the topic was Operator Theory.

** **

**EMPLOYMENT
AND TEACHING**

My first position was at the
University of Crete, when it had just opened, in 1978. This was a fascinating
experience because we had to set up a Department from scratch: there was no
library, the courses had not been designed, student handouts were unavailable
etc. Everything had to be done ab initio. Although this took a disproportionate
amount of effort, the fascination and the experience gained made it worthwhile.

In 1985 I was promoted to an Assistant
Professor and in 1991 to an Associate, a position that I still hold. I spent my 1985/86, 1991/92 and 1998/99
sabbaticals at, respectively, the University of Alabama and King’s College
London (twice).
In the summer of 1988, 1990 and 1992 I was at the University of Western Australia, with
a research grant, to teach and collaborate with my colleagues there.

In the various places I worked, I have
taught a plethora of courses at the undergraduate or the graduate level, such
as Calculus, Real Analysis, Topology, Measure Theory, Functional Analysis,
Operator Theory, Analytic Number Theory, Set Theory, Functional and Theoretical
Numerical Analysis, ODE’s, PDE’s, Euclidean Geometry, History of Mathematics,
History of Calculus and others.

**SUPERVISION OF DOCTORATES**** **

N.K. Spanoudakis obtained his doctorate
in 1993 under my supervision. I have been in the committee (but not the main
supervisor) of the following other doctorates: E. Katsoulis (Athens
University), M. Papadakis (Athens University), E. Deligianni (University of
Crete), who worked in areas of Functional Analysis. I have also been in the
committees for doctorates in the History of Mathematics or in Pedagogical Studies, of N. Andreadakis
(University of Crete), F. Kalavasis (University of Athens), N. Kastanis (University of Thessalonica), M.
Terdimou (University of Ioannina), J. Thomaides
(University of Thessalonica) and A. Tokmakidis (University of Thessalonica).

** **

**PAPERS
IN RESEARCH JOURNALS**

My
published papers in mathematics are

1) “Complete Atomic Boolean lattices”,
Journal of the London Math. Soc., 15 (1977) 387-390. MR
57 #2891.

2) “Semi-simple completely distributive lattices
are Boolean algebras”, Proceedings of the Amer. Math. Soc., 68 (1978) 217-219.
MR 56 #3030.

3) “Rank one elements” (with J. A. Erdos and S.
Giotopoulos), Mathematika, 24 (1977) 178-181. MR 57
#7176.

4) “Non-trivially pseudocomplemented lattices are
complemented”,
Proceedings of the Amer. Math. Soc., 77 (1979) 155-156. MR 80j:03087.

5) “Abelian algebras and reflexive lattices” (with W. E. Longstaff),
Bulletin of the London Mathematical Society, 12 (1980) 165-168. MR 82b:47057.

6)
“Approximants,
commutants and double commutants in normed algebras”, Journal of the London
Math. Society, (2) 25 (1982) 499-512. MR 84f:47053.

7) “Completely distributive
lattices”, Fundamenta Mathematica, 119 (1983) 227-240. MR 85g:06008.

8)
“Strong
density of finite rank operators in subalgebras of B(X)”, Proceedings of the
Centre for Mathematical Analysis, 20 (1988) 83-99. MR 90e:47035.

9) “On the rank of operators in reflexive algebras”, Linear Algebra
and its Applications, 142 (1990) 211-235. MR 91k:47104.

10) “Counterexamples
concerning bitriangular operators” (with W.E. Longstaff), Proceedings of the
Amer. Math. Soc., 112 (1991) 783-787. MR 91j:47017.

11) “Unit Ball density and the
operator equation AX=YB” (with W.E. Longstaff), Journal of Operator Theory, 25
(1991) 383-397. MR 94c:47026.

12) “Atomic Boolean subspace
lattices and applications to the theory of bases” (with S. Argyros and W.E.
Longstaff), Memoirs of the Amer. Math. Soc., 445 (1991) 1-96. MR 92m:46022.

13) “Finite rank operators
leaving double triangles invariant” (with W.E. Longstaff), Journal of the
London Math. Soc., (2) 45 (1992) 153-168. MR 93e:47056.

14) “Spectral conditions and
reducibility of operator semigroups” (with H. Radjavi and W.E. Longstaff),
Indiana Univ. Math. Journal, 41
(1992) 449-464. MR 94a:47069.

15) “The decomposability of
operators relative to two subspaces” (with A. Katavolos and W.E. Longstaff),
Studia Mathematica, 105 (1993) 25-36. MR 94h:47082.

16) “On some algebras
diagonalized by M-bases of *l*_{2}” (with A. Katavolos and M.
Papadakis), Integral Equations and Operator Theory, 17 (1993) 68-94. MR
95c:47048.

17) “On the reflexive algebra
with two invariant subspaces” (with A. Katavolos and M. Anoussis), Journal of
Operator Theory, 30 (1993) 267-299. MR 95i:47082.

18) “Spatiality of
isomorphisms between certain reflexive algebras”(with W.E. Longstaff),
Proceedings of the Amer. Math. Soc., 122 (1994) 1065-1073. MR 95b:47053.

19) “Some counterexamples
concerning strong M-bases of Banach spaces” (with W.E. Longstaff), Journal of
Approximation Theory, 79(1994)243-259. MR 96k:46014.

20α) “Spectral synthesis and reflexive
operators” (with J. Erdos and N.K. Spanoudakis), Comptes Rendus Mathématiques
La Société Royale du Canada, 18 (1995) 193-196. MR 96h:47008 (this is a preliminary version of the next
paper).

20β) “Block strong M-bases and spectral synthesis” (with J. Erdos and N.K.
Spanoudakis), Journal of the London
Math. Soc., 57 (1998) 183-195. MR 99e:46012.

21) “Spectral decompositions of
isometries on c_{p}” (with D. Karagiannakis and E. Mageiropoulos),
Journal of Mathematical Analysis and its Applications, 215 (1997) 190-211. MR
99i:47067.

22) “Non-reflexive pentagon
subspace lattices” (with W.E. Longstaff), Studia Mathematica 125 (1997)
187-199. MR 98f:47006.

23) “Pentagon subspace lattices
on Banach spaces” (with A . Katavolos and W.E. Longstaff), Journal of Operator
Theory, 46 (2001) 355-380. MR 2003a:47137.

24) “Small transitive families of
subspaces in finite dimensions” (with W.E. Longstaff), Linear
Algebra and its Applications, 357 (2002) 229-245.

I also have a) the paper “Automatic continuity
and implementation
in normed algebras”, which I circulated as a report at the University of Crete,
b) four papers submitted. For two of them I am a single author and for the
other two I worked with N.K. Spanoudakis.

My work is in the Theory of Invariant Subspaces, in Spectral
Theory, in Basis Theory, in Banach Algebras and in Lattice Theory. Below I include the reviews of my papers 1 to 23 as they
appeared in *Mathematical Reviews*. I also add a brief description of my
most recently published paper (which has not been reviewed yet) and of my
report “Automatic continuity and implementation in normed algebras”
(which is a research paper, often quoted in the literature).

** **

**PUBLICATIONS
IN THE HISTORY OF MATHEMATICS**

** **

One of my research interests is in
the History of Mathematics. My publications there are all in Greek, so I
include a brief description of each of my papers.

1) One field of my interests is mathematics in
Greece during Ottoman occupation, that is, in the period 1453-1821. During this
time many of the mathematical works remained unpublished, because authorities
did not allow a printing press in Greece, or where published abroad, mainly in
the Latin West. In any case, their source was western and they all attempted to
revive the interest in mathematics of the ancient ancestors. For example, as
mentioned in the introduction of one such book, the aim was “to help the Muses
return to their original home, Mount Parnassus, as they flew away in these
challenging times the nation goes through”. For my researches I had to study
manuscripts that are to-day scattered in public or in monastic libraries,
throughout Greece. As a matter of fact, I have discovered in small libraries
some unknown till then manuscripts as, for example, early 19^{th}
century translations of Christian Wolf’s *Arithmetic* and Voucerer’s *Physics*.

Some of my research results are included in my article ** “Non-elementary
mathematics during Ottoman times: the case of Nikephoros Theotokis” **(National
Research Council, 1990 ). In this article I study the context and influence (as
seen for example in correspondence between scholars of that time) of the first
calculus book in modern Greece, the celebrated three volume

A second paper concerning mathematics in the
same period is “** An attempt to duplicate the cube during Ottoman times,
and the text of ‘Antipelargisis’ ”**. (

In
the book *“Sciences during Ottoman times”* (collective work, edited by J.
Kara’s, 750 pages, to be published in 2003) I have written three articles, a) *“ Trigonometry in Ottoman times” *, b)

With the same team I have worked to
create a large data bank of all scientific publications in pre-Revolution
(1821) modern Greece. For each book we recorded a) all it’s
classification data (such as title, author,
translator, publisher, printer etc), b) it’s number in the various catalogues of the time or modern (such as *Bibliographie
Hellénique* of E. Legrand or Elliniki
Vivliografia of D. Ginis and V. Mexas), c) all public or monastic libraries
that posses a copy, d) all definitions within the text (so one could see, for example, when mathematical concepts unknown
to the ancients were introduced to modern Greeks), e) each and every name
mentioned (more than 1500)
and
their original version for the case of hellenized ones (for example: Xylander = Holtzman), f) all place names
appearing.

In co-operation with I.
Mountriza I am preparing a critical edition of the oldest mathematical text in
modern Greece. It is the elementary work ** Eisagogi
Mathematikis**, dated
1695, by
Anastasios Papavasilopoulos. The text survives in six manuscripts. For the
edition I have compared word for word the manuscripts to prepare the apparatus criticus and I have written extensive annotations.

2) I have also worked in ancient
Greek mathematics. In
this direction I have published (in Greek) “** The cattle problem of Archimedes**”.
This includes a) rich bibliography since antiquity b) the forgotten article of Lessing who
discovered in 1773 the
manuscript of the Platonic

I have also published on* **“**Archimedes’ palimpsest**”*** . **There I have the history of the manuscript,
including some behind the scenes activities, before the auctioning of the
manuscript in 1998.

**EDITOR OF JOURNALS**

I am a member of
the editorial board of the *Bulletin of the Greek Mathematical Society*, a
research journal, and for many years I have been at the editorial board of two
journals on elementary mathematics, the *Euclidis (Section C)* and *Mathimatiki
Epitheorisis,* published by the Greek Mathematical Society (these last two
resemble, more or less, the *Mathematics Magazine* of the AAM).

I am also an
editor of the electronic journal *Forum Geometricorum* (http://forumgeom.fau.edu/ ) which
publishes original articles in modern Euclidean Geometry. Other editors include
J.H. Conway, R. Guy, Paul Yiu etc. Finally, I am an editor for the
Romanian journal on elementary mathematics, *Lucrarile** **Seminarului** **de** **Creativitate** **Mathematica*.

** **

**(popularising)**

I have spent much of my time in popularising mathematics at all levels. This is reflected by the books I have written, the translations, the editing, my work with Mathematical Olympiads, the training of gifted school students, the teaching of refresher courses to Secondary School teachers, a large amount of public lectures, a series of articles in popular topics etc.

**BOOKS**

** **

I have
written the following books (all in Greek, so I will need to say a few word
about each):

1)
** Mathematics for fourth grades in High Schools **(National
School Book Publishing House, Ministry of Education, 1985). All schools books
in Greece are published by the Government. For each course there is a unique
official textbook, followed by all students, which is given to them for free.
This set textbook is chosen after a national competition or by direct
assignment, by an official committee of the Ministry of Education. Authors get
a, once and out, nominal fee. For the above book I worked with three school
teachers and I was the main author. The book was taught for six years to 16
year olds, nationally.

2)
** Elements
of Pascal language **(1990). It is for 15-16 year olds.

3)
** English-Greek
Dictionary of Mathematical Terms** (Athens 1992). I co-authored this dictionary with two other
mathematicians and a philologist. For each mathematical term in English, we
give its translation into Greek, various contexts in which it appears and its
correct pronunciation (using the international phonetic alphabet). The book is
still in circulation, and quite successful.

4)
*Mathematics
for the “second chance” school.*** **((National
School Book Publishing House, Ministry of Education, 2000). The book is the set mathematics
textbook for people who did not complete their mandatory secondary education
but decided to do so later in life.

**CONTRIBUTIONS
IN ENCYCLOPAEDIAS**

** **

1) I have contributed
the article *Hypatia* in *Encyclopedia of Greece and the Hellenic
Tradition*, Fitzroy Deaborn Publishers, London-Chicago, 2000.

2) I have contributed three articles, the *Emil Borel*, *Leopold
Kronecker* and *Ferdinand Lindemann*, for the current issue of *Encyclopedia
Americana*. This last can be accessed electronically at ( http://auth.grolier.com/cgi-bin/authV2 ).

**NOTES FOR STUDENTS**

** **

I have written notes for 8
courses. Some is standard material, but I believe my notes on:

α) Functional and Numerical
Analysis,

β) Analytic Number Theory,

γ) O.D.E’s and P.D.E’s,

δ) History of ancient mathematics

have some merits of originality.

** **

**TRANSLATIONS**

** **

I have
translated into Greek the following:

1) The classic
booklet of G.H. Hardy, *A** **Mathematician**’**s** **Apology** *(Cambridge University Press), for which I also
wrote extensive notes. The Greek edition was published by the University of
Crete Press (the translation, but not the notes, was in co-operation with
another colleague).

2) The book of R.
Smullyan, *The lady or the tiger? And other logic puzzles.* (Alfred Knopf,
N.Y.). Published in Greece by Katoptro (the translation was in co-operation
with another colleague).

3) The classic
booklet of P. Alexandroff, *Topology* (Dover). Published here
by Trohalia (the translation was in co-operation with another colleague).

Also I have
translated the following that have not appeared in print yet, but soon will:

4) R. G. Bartle, *Elements of Integration* (John Willey).

5)
The edition by G. Toomer of * Diocles, On Burning Mirrors* (Springer-Verlag). This is an
ancient Greek book on conic sections whose Greek original is lost, but it
survives in an Arabic translation. Toomer rendered it into English and my
translation is, of course, back into Greek.

**EDITORIAL WORK**

** **

I have edited the Greek
version of the following books, for some of which I also provided detailed
annotations that supplemented the text:

1)
*H**oward** Eves,* *Great Moments in
Mathematics* (2 volumes, Mathematical Association of America).

2)
*Martin Gardner, Aha! **Gotcha* (W.H. Freeman & Co).

3)
*Philip
Davis and Reuben Hersch, Mathematical Experience *(Penguin).

4)
*E.
Nagel and J.R. Newman, Gödel’s Proof** *(New
York University Press).

5)
*Hermann
Weyl, Symmetry*
(Princeton University Press).

6)
Michael
Spivak, *Calculus** *(Addison Wesley).

7)
*D.E.
Littlewood, The Skeleton Key of Mathematics* (Hutchison University Library).

8)
*Yakov Perelman, Mathematics can be Fun *(2
volumes, Mir).

9)
*George Polya, Mathematical Discovery *(John
Wiley & Sons).

10)
*Malba Tahan, The Man Who Counted* (W.W.
Norton & Co).

11)
*Eli Maor, Trigonometric Delights *(Princeton
University Press)*.*

12)
*Waclaw Sierpinski, 250 Problems in Number Theory *(MacMillan).

13)
*Serge
Lang**,** The Beauty of Doing Mathematics* (Springer-Verlag).

14) *Paul Nahin, An Imaginary Tale: The story of *√(-1)
(Princeton University Press).

Also, I was the Editor in Chief of the Greek edition of the enormously
popular *QUANTUM* magazine (American Mathematical Association) for about 8 years. The Greek edition was a translation of the American but
with many additions and improvements, much the same way as the American edition
was to the corresponding Russian *KVANT*.

**MATHEMATICAL
OLYMPIADS, CRUX MATHEMATICORUM**

** **

For two years I was the trainer of the Greek
team that took part in the International Mathematical Olympiad (ΙΜΟ) and the corresponding Balkan (ΒΜΟ), and on four occasions I was the
Leader of the team (1996 IMO in Bombay, 1996 BMO in Bacau Romania, 1997 IMO in
Mar del Plata Argentina and 1997 BMO in Kalampaka Greece).

For many years I taught mathematic to gifted or
to motivated school children. This was on a voluntary basis, with regularity,
usually on Sundays.

My engagement with Mathematical Olympiads made
me an avid reader of the monthly magazine *Crux Mathematicorum* (www.cms.math.ca/CRUX/), which is devoted to problem-solving. I have submitted
solutions to more that 350 problems proposed in its problems section. In fact,
for two years running I had submitted the largest number of solutions among other
readers (the editors publish a statistic), and I had the largest number of
featured solutions appearing in the solutions section.

**POPULAR TALKS AND ARTICLES**

** **

I have given a
great number of talks, nationally or internationally, on topics in the History
of Mathematics and on Recreational Mathematics. The audience was the general
public or University students or school students, depending on the occasion. I
list here some of the more representative titles, which I have repeated many
times.

a) *“**Non elementary mathematics in
Greece during Ottoman times**”*.

b)*“What
is papyrology and how it helps us in the study of the History of Mathematics”*.

c) *“Ancient
Greek Mathematics”*.

d) *“Diocles
on Burning Mirrors”*.

e) *“**The** **birth** **of**
mathematical thinking”*.

f) *“**Archimedes**’**cattle** **problem**”*.

g) *“Archimedes’
palimpsest”*.

h) *“Burning
mirrors from Archimedes to Buffon”*.

I have written many articles (in
Greek) for the general mathematical public. The most representative ones are:

a)** “Polynomial
equations from the ancient Babylonians to Galois Theory”** (together with
S. Giotopoulos and S. Exarhakos, in

b) *“How much is sin**1*^{ο}** ?”** (together with N. Tzanakis, in

c) ** “The
mathematical work of Ptolemy”** (

d) **“ With
ruler and compass”** (a sequence of three articles,

e) ** “Mathematics in the 20^{th}
century: a quick journey through”** (

f) ** “The ‘Spherica’ of Menelaus”** (Quantum, May 2001). A
description and the achievements of Menelaus (2

g) In *Quantum* magazine I had a permanent column entitled ** Scripta
Manent**. Its purpose was to discuss proverbial phrases drawn from the
history of mathematics. For each phrase I traced it’s origin (for example, the
most ancient text that gives us the information), the story of the phrase, the
legends surrounding it, etc. Famous phrases that I discussed in length included

h) In the journal of the Greek Mathematical Society I had for many years
a column entitled “** Euclid answers**”. This was a queries column. Anybody could send
in mathematical questions for clarification or for answers to his problems.

Finally, I have written
shorter notes for the daily or Sunday press, such as “*Ada Lovelace, Lord Byron’s
daughter*” etc.