20 - An Insipid Prize

Kazantzis whose entire professional life was devoted to teaching maths with remarkable intensity and passion, inspired me more with the ingenuity, sharpness and acuteness of his brain than the undisputable breadth and depth of mathematical knowledge in his possession. I would have been unable to grasp a chunk of the latter without becoming myself a mathematician, which was not on the table and my career plans. On occasions, subtly encouraged me in that direction: by posing complex problems, which before I even had the time to comprehend its structure and formulation and begin to develop of response, being generally considered slow-witted, he promptly presented the solution himself –with a cigarette permanently between the fingers of his left hand. And he formulated it within minutes in the excellent calligraphy that distinguished him, either with a gold-plated Parker on a white sheet of paper that he laid on his imposing mahogany desk, or on the blackboard in an empty classroom, where I stood beside him. I envied his mathematical brain and tried in vain to emulate his quick and methodical thinking process. Hundreds of problems passed before me, with the crafting of their solutions inflicting considerable mental torture, would serve no practical purpose whatsoever –at least in real life beyond school. They were mostly pickings from Kazantzis' books: the ‘Functions’, the polytomous ‘Algebra’, the ‘Number Theory’, the ‘Polynomials’, and so on, which filled an entire shelf of my bookcase. He was a proliferate author of mathematical textbooks and he duly appreciated me buying his oeuvre and, perhaps, felt flattered seeing his model-student with another of his books, well-read, with main points underlined, marginalia scrawled across pages, and worn out from studying. He often rushed to forewarn me for errors I would spot in those books –and there were plenty: ‘I already made a note of those; they will be corrected in the next edition!’, he would add. With admirable perseverance and tenacity, unprecedented levels of concentration, and the organization and method in studying, attributes I prided myself on, I managed to tame most of their content. The lack of great cognitive processing speed and agility was counter-balanced by perseverance and depth in thought, in proportion to the knowledge I had accumulated from hard study. For that nebulous ‘someone’ in science and engineering I was aspiring to become that maths was more than enough; in fact, superfluous by most professional standards.

The inspiration from Mr. Kazantzis led to some modest success, albeit at national level, in mathematics of course, in that last year of school and adolescence. It now looks as an insignificant dot from the time gap of decades, but it then solidified temporarily an always fragile self-confidence; it even inflated an otherwise skillfully suppressed and hidden ego. It led me to believe in a kind of potential at that threshold of life proper. Delving into the maths itself and study them in depth, as I did for two years thanks to Kazantzis, by a person who was by no means a prodigy, if anything else, formed a hardworking and persistent character, unyielding in the face of problems of any kind, which first and foremost require patience and exhaustive analytical processing, before a final solution is reached. People who can spend hours and even days grappling with a difficult mathematical problem display no less tenacity when confronted with complex situations of a different kind.

In the final year of my high school studies, I was awarded the second national prize in the low-profile and barely publicized annual competition of the Hellenic Mathematical Society. It spread the wings of confidence in mathematics and life beyond. It was unexpected and I felt, based on my own perception of my performance in the competition, a simple commendation would be more appropriate. I suspected Kazantzis, an active and prominent member of the Mathematical Society had a hand in all this, a terrible thought which I struggled not to entertain. Despite my doubts about whether I truly deserved such an accolade, I was basking for days and months in that familiar feeling of self-pride in more or less to everyone at such moments in life for an apparent talent and worth recognized beyond the narrow boundaries of school or the suffocating family environment. I did not boast but Kazantzis did, and surprisingly my parents ignored it: Mother did not understand what it was all about, whilst for both it was seen as a distraction ahead of the university exams.

My school, of course, remained nonchalant to the news. For most teachers it meant nothing; they had no contribution in the small yet nationwide success of one of their students. The teaching profession and employment in the high-school system was no more than at day-to-day job to make a living; it was the routine work of a civil servant. I did not expect any congratulatory mention and recognition in front of the school assembly, neither did I desire it, because of the modest and extremely reserved character. Nevertheless, in the manner of Mr. Notarides, the somehow dignified Mathematics teacher of my last years in Lyceum, I often discerned smiles of approval, perhaps even a recognition and maybe a slight admiration for that achievement. But Mr. Notarides, who imposed himself on an unruly class more by his portly figure than by a gift in teaching maths, was the most relevant to what was all about amongst the ragtag of teachers, and held me in high esteem: I could see it in his eyes when he was seeking a deliverance from the torment of a teacher in front of a non-responsive and indifferent class. Mr. Notarides’ implicit praise I sensed was a scant reward for the support I reluctantly contributed to his uninspiring teachings.

My imagination for its part, still immature as much as vivid, was weaving dreams of broad recognition and fame, gazing at the peaks of mathematics and science, involving the establishment of an own magna theory, attaching my name to at least a theorem and its elegant proof, even the solving of a hitherto unsolved theoretical problem that tormented, if not humanity, the circles of prestigious mathematical intellects. Where were those naïve thought and preposterous ideas rooted? The world of science and mathematics seemed vast in its diversity of domains and disciplines, while I only had a blurred picture through the small loopholes presented to me in the few books I studied here and there, usually school and tutorial textbooks: from Father's bookcase, and whatever interesting ‘aid’ the eye caught in bookstores of Thessaloniki. With the few mathematical tools and knowledge acquired, and indeed consolidated to a basic level, I endeavored lame-crookedly, but with intellectual effort of commendable perseverance as much as vanity, as in some afternoons of earlier yeas when I was trying to understand and naively expand theories of modern Physics, to prove Fermat's famous theorem that tormented the minds of great mathematicians for centuries. To no avail, of course, here too, as with particle physics some time back, despite the dozens of false starts and pages of scribbled notes with symbols and equations that filled the floor of my room. Whom did I think I become after that low-key award?

Not much fuss, not a single announcement about the Mathematical Society's award at the school assembly or class was made, thankfully for the shy and modest character who trembled in front of and amongst people. The praise and the smiles and the friendly pats on the back came less from the family environment than Kazantzis himself, who showed more pride than close relatives. And his praise counted the most given the great mathematician he was. Possibly he considered himself the mastermind behind my success, which was unprecedented for a student of his small tutoring school. The wings the prize spread would not take long to be clipped, at least partially, and for me to land onto realistic levels of self-awareness and self-esteem, and become again rational and level-headed vis a vis my mathematical genius. The illusions a young man, perhaps justifiably, cultivates around himself for success and glory in his life and the self-centered thoughts he harbors about a special and gifted personality, talent and intellect, would soon be suppressed. The narcissism that followed this and a similar minor success in the university entry exams was henceforth exhausted in temporary reflections of the self with consciousness, on the four walls of my room, without much resonance outside those walls. But that prize had somehow shielded my ego for the battles in the arenas of adult life.

Eight of us, the Society's awardees, eight ‘mathematical talents’ so to speak who excelled in that year's competition, would represent the country at the annual International Mathematical Olympiad, which in July 1981, after the most welcome end of high school studies, ahead of university enrolment and the enticing student life (or the beginning of ‘academic’ life, as my parents liked to put it), in Washington DC. For me, a lonely person for the best part of those years, with a non-existent social life and intimate friendships and especially female ones, a teenager starved of the experiences and sensations of love often the butt of tasteless jokes by the two or three bullies in the class, who had spotted and sneered at my ‘virginity’ (or incel as called today) and the pimples of my face, which their theory went had no other cause than systematic masturbation in my room or a seedy cinema auditorium, the anticipation a trip to America and the student life that would immediately follow flooded my being with enthusiasm and a longing for the future, for after school life. It was state of an unprecedented bliss, beyond and above the school routine I would soon leave behind, once and for all, as a thankless and gray and depressing part of life. I drew little satisfaction from the thought that many of my schoolmates who mocked my social isolation and celibacy might feel a little envy, now that the chains of school would be shaken off, as they would face up to a future of different and less attractive prospects.

That poor country, my homeland, still held a small, albeit shrinking place in my heart. The rare distinctions of Greek athletes and teams in international competitions still stirred some patriotic emotions of pride, and that country, with its scarce means, would pay for our Olympic Airways' tickets to New York. The expectations of the few, who had a concept of what this international competition was all about, were low from the onset, and the publicity our participation received non-existent: taking part in the so-called Mathematical Olympiad was a small internal affair of the insular family of the Mathematical Society, comprising a sub-section of maths teachers, along with some hobbyists and dilettantes of mathematics with a residual passion for the subject. The school, as long as it was not yet formally finished, kept its distance from my participation in that unknown international arena, indifferent to any kind of individual distinction -no matter how small or large. The reasons were various and explicable. The root causes were to be found: in the structure of the educational system and its chronic inability to inspire and mold talented students and even identify their talents and inclinations; in the body of generally mediocre and unqualified teachers, a homogeneous and amorphous body, which they viewed their profession through the prism of civil servant. With a unity in purpose and an unambiguous direction, and a disclaimer of responsibility for poor results without accountability or assessment, they had undertaken to teach to the letter, in the predetermined period of time of the school year, a predetermined syllabus bureaucratically dictated by the ministry. Those teachers, with a few exceptions, could well and perhaps have preferred to teach in half-empty classrooms, spared from the ordeal of ill-discipline from the bulk of unruly and inattentive teenage students. The indifference was mutual. A plethora of tutoring centers and private schools, those para-education establishments, had undertaken (with the accountability that the parents who paid tuition fees would demand) the assimilation of this exam material in every possible way and its implantation in young minds, mechanically and with over-the-odds intensity. A substantial and valuable education of young people was of secondary importance.  

19 - The Maths Teacher

The classical physics we were taught at school in the ‘bundle’ of subjects in science, like Chemistry and Biology, were relatively easy to walk through. Some basic intelligence and plenty of memorization, of the rote learning kind, almost guaranteed good grades in the university entry exams. Enlightenment from new knowledge and erudition in one of the more interesting modern fields in science would have to wait for admission to a decent university school. Therefore, the physics into which Father tried discreetly to introduce me took back seat in my studies for the exams, while mathematics, being at the core of the ‘positive’ sciences or rather engineering I was aspiring to study and, for that matter, the most challenging for the majority of the candidates, was brough under the spotlight -and rightly so. The maths questions and problems in our school textbooks the brain was called upon to deal with, some of which admittedly cumbersome, I did manage to grapple with, mostly thanks to tenacity and perseverence than genius. That embarrassing episode of one Saturday evening, with the problem I was presented with by Mr. N, our family friend, before going out with my parents, a problem, which, as I was told, Billy, his son, of the same age as me managed to solve with ease (as Mr. N told me, presumably either to put untoward pressure on me or brag about Billy’s brilliance or both) and I did not manage to answer after wrestling for an hour for a solution and had to abandon it unsolved before going to bed (naturally to the detriment of my self-confidence and the disappointment of my parents), that episode had long been forgotten.

The late mathematician of my last and most creative and knowledge-absorptive phase of late adolescence, Theodoros Kazantzis or ‘Roulis’ -for Father, friends and colleagues, in whose tutoring school I was enrolled free of charge, an honour bestowed from Roulis –due to my good performance and grades at school, and an above average intellectual ability (as I was embarrassingly touted outside our family circle by Father), and his previous acquaintance from their student days in the 1950s, Kazantzis, more than any other teacher, became an inspiration and gave me a direction at a critical junction in life. Famous theorems and the elegance of their proofs by mathematicians whose names filled Kazantzis’ mouth and opened his eyes wide in awe, each time he mentioned them with pomp, glorious names of his trade like Fermat’s, Kolmogorov’s, Leibnitz’s, Poincare’s et al. turned my aspirations and ambitions and a short-lived youthful devotion to mathematics instead, away from early literary explorations. The latter were considered by many in Greece shallow in terms of the depth of thought expended and lacking the wealth of mental permutation and combinations· for literature and language, Father and the broad wrinkled brows of mathematical intellects, saw them as something easy for the brain to grasp and deal with, as a more trivial and prosaic, but less abstract, formal and concrete way to communicate thought and ideas than that of mathematical symbols -the language of logic and reason. Whether this direction proved a posteriori right or wrong a posteriori does not matter. After all, it is pointless such choices to be the object of retrospective reflection, and any conclusions drawn such introspection is immaterial at later stages of life.

Kazantzis was an admirable personality, unforgettable by those who had the opportunity to be guided by him in maths, a bright star that illuminated for two, otherwise dim, years my journey along the never-ending path of intellectual development. He would influence and inspire any young person who might have displayed an interest in maths, provided he or she possessed sufficient intelligence and comprehension of them. Sadly, for the mass of students who attended those tutoring schools, such a thing, that special mathematical inclination and intelligence, let alone a talent in maths, Kazantzis was looking for (beside their tuition fees), were lacking. Widespread private tutoring, in ad hoc schools or, for the wealthy, at home, paper over the cracks of a deficient public educational system private was born out and flourished out of deep-rooted social issues and the economic reality in Greece and is persistent and still in high demand by students, whilst they are subjected to the stress and the incessant pressure by their families for a university place. In short, those schools offer to their students the crutches to walk through ominous university entry exams, success in which is deemed crucial (as they are told) for their future lives and well-being.

As a major attraction for a unique ability communicate complex concepts and magnetize his audience, but also being the owner and boss and absolute ruler in his school, Kazantzis entered and left the classrooms at will, without any regards to an agreed timetable, which he himself probably had drawn up at the beginning of the year, tailor-made to his personal needs, and subscribed to. Most of the time he did not show-up to deliver his lecture, without prior notice and to the dismay of his students waiting for him, like beggars stretching their hands for alms. My school mate Yiannis D, who had been influenced by the more than average inclination and good performance in maths I had shown, after some non sequitur reasoning regarding the choice of tutoring he decided to join me to Kazantzis’ school. Each time he did not turn up to the expectant class, Yiannis protested, complaining about the tuition fees he had already paid with an unfulfilled demand of being taught personally by him, given his transmissibility and communicative abilities. He somehow believed Kazantzis possessed the magic wand that would implant mathematical analytical thinking in a (put mildly) mediocre brain. Puffing and muttering in my ear every now and then, and especially with every no show of Kazantzis, he ‘threatened’ to move to a different tutoring school· something that, after a few fruitless months at a desk next to me he did, to the relief of those who had been directly or indirectly (like me) involved in his initial decision.

A silent dissatisfaction, followed by murmurs of discontent by Roulis’ students, who had been patiently waiting for his arrival. They could hardly be appeased by the appearance of a ‘relief’ tutor at his place, usually a young graduate, who, with a few minutes' notice, would take over the reins of teaching us maths. (Not necessarily well-off families had to pay handsomely for each hour of tutoring with the anticipation of success in the exams.) Often, the young Roulis’ substitute appeared accompanied by his boss, who, after a few excuses and lame explanations behind his artfully disarming smile of the reasons preventing him ‘this time round’ to deliver his lecture to the expectant class (’because something unexpected had cropped up’), a praise for the worthiness of the substitute apprentice tutor, and a brief prologue as to the intended content of the lecture, he left the room in the same way as he had entered it: with one hand in the pocket of his waistcoat and the other, inevitably, holding a cigarette.

He was barely one meter and sixty centimetres tall, but an erect posture, a large and well-shaped head, featuring a broad forehead furrowed by wrinkles, befitting deep thinkers and intellects, as in busts of famous philosophers of antiquity, the wavy and messy, blackish-gray hair, along with his expensive three-piece suit attire, enhanced his personality with an aura that disguised the short stature. His features and presence radiated mathematical ingenuity, intellectual energy and exuded a masculine charm and overshadowed his physical littleness in the eyes of women at least, as I later found out when I met his attractive and, of course, much taller wife. (The height of a man, we read in the popular press of the time, was one of the main physical characteristics that attracted women to a man, therefore what height my body would reach in adulthood was of appreciable concern and preoccupied me and family during adolescence. Consequently, I was convinced a short stature of Roulis’ level would be a serious impediment in attracting the female sex, and the existence of such a short man would fatefully and obsessively be absorbed by a job or a life-long interest, like maths. What a shame, I was thinking then along with the longings I was harbouring for the opposite sex, guiding then much of our teenage behaviour, even within the confines of my tutoring school, which, unlike my school, was mixed.)

Eccentric and uncompromising, he reserved the praise only for his colleagues - subordinates in his tutoring school and a few former associates in his ventures, in short, the few who managed to endure a partnership with a cumbersome and demanding character, and the few young mathematicians whom he nurtured in mathematics and had successful careers. Only a handful of personalities from the Greek mathematical world he would unreservedly praise and even dedicated some of his books to them: those whom he had the good fortune to meet or whose work he studied, from the pantheon of late great Greek mathematicians, such as Caratheodory, and a certain professor Varopoulos, his and Father’s teacher in the university and renowned like Kazantzis for his eccentricity. But for most of the people in his trade and his time and place, whether academics, tutors, or high-school teachers, he reserved derogatory comments and scorn, usually condensed into terse disapprovals and aphorisms and expressed without further elaboration –as if they were axiomatic, a priori given or too obvious to argue against: "The fool!", "A disgraceful character!", "An irrelevant person!", " The idiot!", "What a Karagiozis!", etc., were the kind of phrases he habitually used to degrade fellow mathematicians, low in his esteem.

The few times he turned up in the classroom to deliver his maths lecture to a restless and expectant class (few despite the grandiose commitments to the students and parents at the beginning of the school year), he entered the room several minutes after the scheduled start, dressed in his three-piece suit (if he was in a hurry) or in waistcoat or sleeveless sweater over his shirt and tie. And he managed to magnetize everyone from the very first moment, including the few studious amongst us, the nerds, so to speak, with a solid background and generally good understanding of high-school maths, but also the relatively indifferent or the desperate for tutoring with lower levels of understanding and perhaps intelligence.

Between the index and the middle finger of his left hand a cigarette was burning incessantly, a cigarette he was dragging at intervals of a few minutes, until its long column of ash fell off from the pull of gravity. In his right he held a chalk leaving white traces around the pocket of his waistcoat. He lectured without any written notes, with the confidence and arrogant spirit of a brilliant man he undoubtedly was, a grand-maître who had the theorems of mathematics in his fingertips, a man recognized by his professional circle, despite his controversial character and the intense competition in the trade of private tutoring -the shadow-education thriving in Greece to counterbalance the inadequacies of the public education system. I formed the belief then that his career was trapped in that rather ignoble sector for political reasons and poor public relations. He might as well had been ostracised from the community of university professors, although his genius and knowledge surpassed many of those. He would always start his lesson, writing from the upper right corner of the blackboard, where he posed the problem to be solved or the theorem to be proven· with remarkable agility in the use of chalk and unparalleled calligraphy, he ended up in the lower right corner, covering the board with three or four columns of mathematical symbols and equations, inserting at points emphatic adverbs, such as ‘therefore’, ‘consequently, etc., in the solution of the problem or the proof of the theorem, which triumphantly ended with a QED! During this process, which all of us followed in awe and silent behind our desks, some bewildered, he would occasionally turn towards the fascinated and enchanted class, in order (I thought) to reassure himself of our amazement at his intelligence and knowledge. Eventually, with his back turned to that work of art, a work of intellectual elegance and calligraphy as displayed on the blackboard, he would ask his class a question or two, which, however, after a few seconds of pause, when his restless and sparkling eyes shifted from left to right, he would himself answer. The completion of a proof on the board was accompanied by an abrupt, almost dancing 180-degree turn to face the class, accompanied by slight shaking of his untidy fringe by the centrifugal forces from his turn, the throwing of what was left of the chalk in the general direction of the blackboard, the extinguishing of his cigarette with his foot after one last drag, a triumphant smile, and the piercing rays from his gaze. Another lighting of a cigarette would follow, before his hasty departure from the room. The class, after the great mathematician’s departure was in a hurry to copy the contents of the artwork on the blackboard to the last letter. It would have been weeks before the students of his tutoring school would enjoy a similar sought-after performance.