A. Muhammed Uludağ
Muhammed Uludag
Galatasaray
University

Mathematics
Department

Vita   

Publications
Favorite
Quotes
Contact
Info
Tubitak
projeleri

Some
Links

- Caddebostan Fossils
- Yahya Efendi


Yükseköğretim politikaları hakkında görüşler
olmak ya da olmamak


Research Interests

my personal research logo

I am interested in everything connected to the modular group (which includes mathematics and more). These days I am working on an exotic involution -jimm- of the real line and an associated dynamical system which is non-topologically conjugate to the Gauss map. I also have some dreams about a space I call "Heyula", on which the general linear group over Q acts, hoping that I can prove via this action my conjectural presentation for the latter group. All these are related to dessins, binary quadratic forms, dynamical systems, transfer operators, Gauss-Kuzmin theorem, the Selberg zeta function, the Fibonacci and the Lucas zeta functions, Thompson's groups, Minkowski and Denjoy measures and to some aspects of the Teichmüller theory.

Over the time I worked on algebraic geometry, orbifolds and all that is hyper: hypergeometry, complex hyperbolic geometry, hyperplane arrangements, topology of hypersurface complements. I was initiated to research in complex analysis.
Motto: Knowledge without research eventually stagnates!

         
themapstalpha            conjugateListen!
  

A Visualisation of PSL(2,Z)


Here is a modular group toy (developed by Ayberk Zeytin and Hakan Ayral) Enjoy! (needs flash) The cells in the "slit" disc represents the elements of the modular group; in fact, what you see is nothing but a very fat Farey tree. Fat branches meet along the slits. Clicking on a cell brings it to the center and this way you can travel to infinity. Venture beyond the numerical limit and you will be rewarded! Continued fractions and congruence subgroups animations will appear soon! Prize question. Find explicitly the conformal isomorphism between the Poincaré disc and the (properly defined) slit disc. Here is a simpler version modular group toy and here's a free android version.

Android app on Google Play




Scientific Events



Publications


cobweb plot
  • A conjectural presentation of the group PGL(2,Q) (submitted)
  • The class groupoid and Thompson's groups (under progress, with Ayberk Zeytin)
  • A deformation of Lebesgue's measure on the boundary of the Farey tree (under progress, with İsmail Özkaraca and Hakan Ayral)
  • Some deformations of Lebesgue's measure on the boundary of the Farey tree (under progress, with Hakan Ayral)
  • A subtle symmetry of Lebesgue's measure, (with Hakan Ayral, 2016).
  • Testing the transcendence conjecture of Jimm and its continued fraction statistics (with Hakan Ayral, 2016).
  • Dynamics of a family of continued fraction maps, (with Hakan Ayral, 2016).
  • Jimm, a fundamental involution, (with H. Ayral), arxiv preprint 2015), (visit the jimm page for some codes, algorithms and graphics related to jimm. Tablet computer applications will appear soon). We have been unable to publish this paper thanks to its "weird notation" and its length. We are forced to split it into at least two papers. This longer paper will eventually become a survey/lecture note.
  • On possible deterioration of smoothness under the operation of convolution, C.R. Acad. Sci. Paris, t.322, serie I, (1996) 173-17


Editorial Work



Books

  • Modüler Grup (Under preparation, with Irem Portakal)  (A book project in Turkish on the modular group, estimated to appear in 2015)


Teaching


Probability, Complex Analysis, Discrete mathematics, Automata and theory of languages, Introduction to Cryptography, Complexity and theory of languages, Numerical Analysis, Introduction to Mathematical Logic and Set Theory, Linear Algebra, Calculus, Real Analysis, Complex Analysis, Functional Analysis, Riemann Surfaces, Abstract Algebra, Ergodic Theory and counting..
Motto: To inspire is more important then to teach!



FAVORITE QUOTE
Not everyone is able to pass through all these stages quickly and to cut through all these veils easily during the (process of) instruction. Disputes often cause the mind to stop at the veils of words. Disturbing quarrels and doubts cause it to fall into the nets of argument, so that the mind is prevented from attaining its objective. Rarely do more than a few (individuals), who are guided by God, succeed in extricating themselves from this abyss. If you are afflicted by such (difficulties) and hampered in your understanding (of the problems) by misgivings or disturbing doubts in your mind, cast them of ! Discard the veils of words and the obstacles of doubt! Leave all the technical procedures and take refuge in the realm of the natural ability to think given to you by nature! Let your speculation roam in it and let your mind freely delve in it, according to whatever you desire (to obtain) from it! Set foot in the places where the greatest thinkers before you did! Entrust yourself to God's aid, as in His mercy He aided them and taught them what they did not know! If you do that, God's helpful light will shine upon you and show you your objective. Inspiration will indicate (to you) the middle term which God made a natural requirement of the (process of) thinking, as we have stated. At that particular moment, return with (the middle term) to the molds and forms (to be used) for the arguments, dip it into them, and give it its due of the technical norm (of logic)! Then, clothe it with the forms of words and bring it forth into the world of spoken utterances, firmly girt and soundly constructed! Verbal disputes and doubts concerning the distinction between right and wrong logical evidence are all technical and conventional matters. Their numerous aspects are all alike or similar, because of their conventional and technical character. If they stop you, (you will not be able) to distinguish the truth in them, for the truth becomes distinguishable only if it exists by nature. All the doubts and uncertainties will remain. The veils will cover the objective sought and prevent the thinker from attaining it. That has been the case with most recent thinkers, especially with those who formerly spoke a language other than Arabic, which was a mental handicap,  or those who were enamored with logic and partial to it. They believe that logic is a natural means for the perception of the truth. They become confused when doubts and misgivings arise concerning the evidence, and they are scarcely able to free themselves from (such doubts). As a matter of fact, the natural means for the perception of the truth is, as we have stated, (man's natural ability to think, when it is free from all imaginings and when the thinker entrusts himself to the mercy of God. Logic merely describes the process of thinking and mostly parallels it. Take that into consideration and ask for God's mercy when you have difficulty in understanding problems! Then, the divine light will shine upon you and give you the right inspiration. God guides in His mercy. Knowledge comes only from God (Ibn Khaldun, al-Muqaddimah).



FAVORITE QUOTE
The sole means now for the saving of the beings of the planet Earth would be to implant again into their presences a new organ ... of such properties that every one of these unfortunates during the process of existence should constantly sense and be cognizant of the inevitability of his own death as well as the death of everyone upon whom his eyes or attention rests. Only such a sensation and such a cognizance can now destroy the egoism completely crystallized in them. (Gurdjieff, All and Everything, via Alan Watts, On the taboo against knowing who you are) - upon my meditations on what positive thing one should fathom from some unfortunate decapitation scenes I have seen on the media.


FAVORITE QUOTE
BOOK XI
As to living in the best way, this power is in the soul, if it be indifferent to things which are indifferent. And it will be indifferent, if it looks on each of these things separately and all together, and if it remembers that not one of them produces in us an opinion about itself, nor comes to us; but these things remain immovable, and it is we ourselves who produce the judgements about them, and, as we may say, write them in ourselves, it being in our power not to write them, and it being in our power, if perchance these judgements have imperceptibly got admission to our minds, to wipe them out; and if we remember also that such attention will only be for a short time, and then life will be at an end. Besides, what trouble is there at all in doing this? For if these things are according to nature, rejoice in them, and they will be easy to thee: but if contrary to nature, seek what is conformable to thy own nature, and strive towards this, even if it bring no reputation; for every man is allowed to seek his own good.

Consider whence each thing is come, and of what it consists, and into what it changes, and what kind of a thing it will be when it has changed, and that it will sustain no harm.

If any have offended against thee, consider first: What is my relation to men, and that we are made for one another; and in another respect, I was made to be set over them, as a ram over the flock or a bull over the herd. But examine the matter from first principles, from this: If all things are not mere atoms, it is nature which orders all things: if this is so, the inferior things exist for the sake of the superior, and these for the sake of one another.

Second, consider what kind of men they are at table, in bed, and so forth: and particularly, under what compulsions in respect of opinions they are; and as to their acts, consider with what pride they do what they do.

Third, that if men do rightly what they do, we ought not to be displeased; but if they do not right, it is plain that they do so involuntarily and in ignorance. For as every soul is unwillingly deprived of the truth, so also is it unwillingly deprived of the power of behaving to each man according to his deserts. Accordingly men are pained when they are called unjust, ungrateful, and greedy, and in a word wrong-doers to their neighbours.

Fourth, consider that thou also doest many things wrong, and that thou art a man like others; and even if thou dost abstain from certain faults, still thou hast the disposition to commit them, though either through cowardice, or concern about reputation, or some such mean motive, thou dost abstain from such faults.

Fifth, consider that thou dost not even understand whether men are doing wrong or not, for many things are done with a certain reference to circumstances. And in short, a man must learn a great deal to enable him to pass a correct judgement on another man's acts.

Sixth, consider when thou art much vexed or grieved, that man's life is only a moment, and after a short time we are all laid out dead.

Seventh, that it is not men's acts which disturb us, for those acts have their foundation in men's ruling principles, but it is our own opinions which disturb us. Take away these opinions then, and resolve to dismiss thy judgement about an act as if it were something grievous, and thy anger is gone. How then shall I take away these opinions? By reflecting that no wrongful act of another brings shame on thee: for unless that which is shameful is alone bad, thou also must of necessity do many things wrong, and become a robber and everything else.

Eighth, consider how much more pain is brought on us by the anger and vexation caused by such acts than by the acts themselves, at which we are angry and vexed.

Ninth, consider that a good disposition is invincible, if it be genuine, and not an affected smile and acting a part. For what will the most violent man do to thee, if thou continuest to be of a kind disposition towards him, and if, as opportunity offers, thou gently admonishest him and calmly correctest his errors at the very time when he is trying to do thee harm, saying, Not so, my child: we are constituted by nature for something else: I shall certainly not be injured, but thou art injuring thyself, my child.- And show him with gentle tact and by general principles that this is so, and that even bees do not do as he does, nor any animals which are formed by nature to be gregarious. And thou must do this neither with any double meaning nor in the way of reproach, but affectionately and without any rancour in thy soul; and not as if thou wert lecturing him, nor yet that any bystander may admire, but either when he is alone, and if others are present...

Remember these nine rules, as if thou hadst received them as a gift from the Muses, and begin at last to be a man while thou livest. But thou must equally avoid flattering men and being veied at them, for both are unsocial and lead to harm. And let this truth be present to thee in the excitement of anger, that to be moved by passion is not manly, but that mildness and gentleness, as they are more agreeable to human nature, so also are they more manly; and he who possesses these qualities possesses strength, nerves and courage, and not the man who is subject to fits of passion and discontent. For in the same degree in which a man's mind is nearer to freedom from all passion, in the same degree also is it nearer to strength: and as the sense of pain is a characteristic of weakness, so also is anger. For he who yields to pain and he who yields to anger, both are wounded and both submit.

But if thou wilt, receive also a tenth present from the leader of the Muses (Apollo), and it is this- that to expect bad men not to do wrong is madness, for he who expects this desires an impossibility. But to allow men to behave so to others, and to expect them not to do thee any wrong, is irrational and tyrannical. (The Meditations By Marcus Aurelius)




ALL-TIME FAVORITE QUOTE

Cosmic Unification in the Presence of the Eye-witnessing through the
Assembly of the Human Tree and the Four Spiritual Birds

"....
From my impossibility to my validity, and from my validity to my deficiency.
I am no one in existence but myself, so-
Whom do I treat as foe and whom do I treat as friend?
Whom do I call to aid my heart, pierced by a penetrating arrow,
When the one who shot the arrow is my eyelid, striking my heart without an archer?
Why defend my station? It matters little to me, what do I care?
For I am in love with none other than myself, and my very separation is my union.
Do not blame me for my passion. I am inconsolable over Him who has fled me. -
- In this epistle I never cease addressing myself and returning to myself from my very self.
...
I am my beloved and my lover; I am my knight and my maiden.
....
I praise God who has "fashioned" me and "balanced" me, and made me enter upon "the most beautiful of constitutions." For He made me know myself through myself and caused me to appear to myself, so that I became enamored of only myself. Between my distance and my proximity I have become mad with love for myself, and I address myself alone.

Were I to see myself when I in my Essence, came to myself, secretly or openly,
And said, "Greetings" and answered, "At your service,"
And if my turning were from me to me, my very "Here I am!" would annihilate me,
My enemies and my trusty friends, my threat of punishment and my surplus grace,
My paradise of delights and my promised recompense, my witnessing and my testimony.
What wonderful favor would be mine through myself!
Oh I! Return me by me to me until I see my stability.
He returned me by me to me from me, and only my qualities subsisted in me.
...
When the signs of witnessing were lifted from me and the suffering of spiritual combat was removed, and harmony and succor began to flow through me, I mounted the Burâq of my spiritual aspiration and departed from the cycle of this grief. I fell into the sea of matter, and beheld the next world and the present one.

Then I shouted: "Oh alas!" and "Alas, my burning heart. I fled from the universe and here I am in it. Where is what I seek?"

I heard a voice coming from me-but neither inside me nor outside me-say: "Why do you demand a high station when you are on the road?
...
I answered: "Oh you who obstruct me, your words have wounded me. Do you not know that you speak from your own station? You are in the presence of the essential being, divested of time and place, while I am in this dark sea, in this thick gloom and this fearful calamity, in this mine of lies and doubt, this place of faults and vices. Does not the one who is prisoner of quantity and quality and precepts of wisdom cry out: Woe!? If you extract me from the crashing waves and deliver me from the horror of this gloomy night I will never more pronounce the adverb or the preposition of place."
...
Through his irresistible power he attracted me to himself and said to me: "You are vanquished, so seek help!"
...
When he attracted me to himself I saw myself in another form than my previous one and I established myself there, firmly and steadily.

I said: "Oh I!"

He said: "I, welcome!"

I said: "No welcome, no greetings, no make yourself at ease!"

He said: "Oh eye-balm, what is the doubt that assails you? Oh prisoner of creation, what is afflicting you?"

I answered: "You do not cease from veiling me from myself. Unveil me to myself so that I can know myself!"
...
When I heard that there was still a trace of createdness before me, I feared that it would cut me off from my cognizance. So I rose from that gloomy darkness, leaving the Burâq of my aspiration in it. I was transported to the thrones of subtle grace and the cushions of the celestial couches, until I reached the station of rejoicing where I set myself to oscillate like a hanging lamp. I said: "What do I have to do with the state of audition?"

Someone said: "It is the beauty of the rhythm that has set you in motion."

I said: "I didn't feel it."

Someone said to me: "Be careful! For you are in yourself and not in him!"

I said: "Reality is beyond the rhythms of song. What it demands is extinction within extinction."

No sooner had I pronounced these words than a veil was lowered between my essence and his essence and a condition was set between him and me.
...
Then the Universal Tree of the garden, described as the Likeness, was unveiled to me
I observed a tree "whose root is firm and whose branches are in the heavens." Its fruit is in the hand of the Deity, established on the Throne. Among its branches sat the Crow and the strange Anqâ, and in the shelter of its boughs perched the Eagle and the Ring Dove. I greeted the Tree and it answered, greeting me even more finely.

It said: "Listen, O wayfarer, O king."
Discourse of the Universal Tree, described as the Likeness
"I am the universal tree of synthesis and likeness. My roots are deep, my branches are lofty.
..
The spirits blow on me from all directions. They disarrange the order of my branches. In striking against one another they make one hear such melodious sounds that they enrapture the supreme intellects in the utmost heights, and set them circling in accordance with what is inscribed in their scroll. I am the music of wisdom that removes care through the beauty of its melodious rhythm."
...
Discourse of the Royal Eagle
"I was still nonexistent as an entity in one of the degrees of creation when the divine solicitude came and made my existence the Beginning. Having manifested Himself to Himself, my existence was prolonged in self-contemplation."
...
Oh, Sakhr ibn Sinân, I have explained to you some of the stations of the sources of the creatures: the universal man, the first intellect, the unique soul, prime matter, and universal body. Investigate them like an intelligent man who seeks the salvation of his soul.
Peace be upon its author and upon us!
(al-Ittihad al-kawni fi hadrat al-ishhad al-ayni bi-madhur al-shajara al-insaniyya wa-l-tuyur al-arbaa al-ruhaniyya)

I heard a voice coming from me-but neither inside me nor outside me-say: "Why do you demand a high station when you are on the road?
...
I answered: "Oh you who obstruct me, your words have wounded me. Do you not know that you speak from your own station? You are in the presence of the essential being, divested of time and place, while I am in this dark sea, in this thick gloom and this fearful calamity, in this mine of lies and doubt, this place of faults and vices. Does not the one who is prisoner of quantity and quality and precepts of wisdom cry out: Woe!? If you extract me from the crashing waves and deliver me from the horror of this gloomy night I will never more pronounce the adverb or the preposition of place."
...
Through his irresistible power he attracted me to himself and said to me: "You are vanquished, so seek help!"
...
When he attracted me to himself I saw myself in another form than my previous one and I established myself there, firmly and steadily.

I said: "Oh I!"

He said: "I, welcome!"

I said: "No welcome, no greetings, no make yourself at ease!"

He said: "Oh eye-balm, what is the doubt that assails you? Oh prisoner of creation, what is afflicting you?"

I answered: "You do not cease from veiling me from myself. Unveil me to myself so that I can know myself!"
...
When I heard that there was still a trace of createdness before me, I feared that it would cut me off from my cognizance. So I rose from that gloomy darkness, leaving the Burâq of my aspiration in it. I was transported to the thrones of subtle grace and the cushions of the celestial couches, until I reached the station of rejoicing where I set myself to oscillate like a hanging lamp. I said: "What do I have to do with the state of audition?"

Someone said: "It is the beauty of the rhythm that has set you in motion."

I said: "I didn't feel it."

Someone said to me: "Be careful! For you are in yourself and not in him!"

I said: "Reality is beyond the rhythms of song. What it demands is extinction within extinction."

No sooner had I pronounced these words than a veil was lowered between my essence and his essence and a condition was set between him and me.
...
Then the Universal Tree of the garden, described as the Likeness, was unveiled to me
I observed a tree "whose root is firm and whose branches are in the heavens." Its fruit is in the hand of the Deity, established on the Throne. Among its branches sat the Crow and the strange Anqâ, and in the shelter of its boughs perched the Eagle and the Ring Dove. I greeted the Tree and it answered, greeting me even more finely.

It said: "Listen, O wayfarer, O king."
Discourse of the Universal Tree, described as the Likeness
"I am the universal tree of synthesis and likeness. My roots are deep, my branches are lofty.
..
The spirits blow on me from all directions. They disarrange the order of my branches. In striking against one another they make one hear such melodious sounds that they enrapture the supreme intellects in the utmost heights, and set them circling in accordance with what is inscribed in their scroll. I am the music of wisdom that removes care through the beauty of its melodious rhythm."
...
Discourse of the Royal Eagle
"I was still nonexistent as an entity in one of the degrees of creation when the divine solicitude came and made my existence the Beginning. Having manifested Himself to Himself, my existence was prolonged in self-contemplation."
...
Oh, Sakhr ibn Sinân, I have explained to you some of the stations of the sources of the creatures: the universal man, the first intellect, the unique soul, prime matter, and universal body. Investigate them like an intelligent man who seeks the salvation of his soul.
Peace be upon its author and upon us!
(al-Ittihad al-kawni fi hadrat al-ishhad al-ayni bi-madhur al-shajara al-insaniyya wa-l-tuyur al-arbaa al-ruhaniyya)
(Epistle on Cosmic Unification - Muhyiddin Ibn 'Arabi translated by Angela Jaffray) top



FAVORITE QUOTE

"My Friend!
What I have so often told you, I say it once more, or rather I cry it to you: Either-Or! On me these words have always made a strong impression. - I think of an early youth,where, without really understanding what it is to choose in life, with childish confidence listened to the speech of my seniors, and the moment of choice became to me solemn and revered, even though in choosing I only followed somebody else's directions. I think of the moments in later life, where I was in the dividing path, where my soul was matured in the hour of decision. I think of the many, less important, but to me not uninteresting cases in life, where choosing was the issue; for even if there is only one context where this word has its absolute meaning, namely every time on one hand Truth, Justice and Holiness, on the other hand Lust and Inclinations, obscure Passions and Perdition,show up, then it is always important also in things, where it is in itself innocent, which one chooses, to choose right, to test oneself, so that one shall not painfully retreat to the point of departure, and thank God if one has not more to reproach oneself than having wasted one's time.
The choice itself is decisive for the contents of the personality. - If you imagine a helmsman of a ship at the moment when it has to cross over, then he may say, I can do either this or that; but if he is not a mediocre helmsman, then he will also be aware that, during all this, the ship is going at its usual speed , and that thus there is only a moment where it does not count whether he does this or that. So it is with Man, if he forgets to take this speed into account, then at last a moment comes, where there is no more talk of an Either-Or, not because he has chosen, but because he has left it out, which can also be expressed in this way, because others have chosen for him, because he has lost himself. Now if you will the understand me right, then I can willingly say that in choosing it is not so much the matter of choosing the right thing, as of the energy, the seriousness and the pathos, by which one chooses. In this the personality proclaims itself in its inner infinity, and thereby again the personality is consolidated. So even if a person chose the wrong thing, then he will still, even because of the energy by which he chose, find that he chose the wrong thing. Since indeed the choice is undertaken with the whole intensity of the personality, his being is purified, and he himself brought into an immediate relation to the eternal power that ever present pervades the whole existence. So for freedom I fight, for the future time, for Either-Or." (Soren Kierkegaard) top




FAVORITE QUOTE

"How does a normally talented research scientist come to concern himself with the theory of knowledge? Is there not more valuable work to be done in his field? I hear this from many of my professional colleagues; or rather, I sense in the case of many more of them that this is what they feel. I cannot share this opinion. When I think of the ablest students whom I have encountered in teaching - i.e., those who have distinguished themselves by their independence and judgement and not only mere agility - I find that they have a lively concern for the theory of knowledge. They like to start discussions concerning the aims and methods of the sciences, and showed unequivocally by the obstinacy with which they defend their views that this subject seemed important to them. This is not really astonishing. For when I turn to science not for some superficial reason such as money-making or ambition, and also not (or at least exclusively) for the pleasure of the sport, the delights of brain-athletics, then the following questions must burningly interest me as a disciple of science: What goal will be reached by the science to which I am dedicating myself? To what extent are its general results <<true>>? What is essential and what is based only on the accidents of development?... Concepts which have proved useful for ordering things easily assume so great an authority over us, that we forget their terrestrial origin and accept them as unalterable facts. They then become labelled as <<conceptual necessities>>, <<a priori situations>>, etc. The road of scientific progress is frequently blocked for long periods by such errors. It is therefore not just an idle game to exercise our ability to analyze familiar concepts, and to demonstrate the conditions on which their justification and usefulness depend, and the way in which these developed, little by little..." (Albert Einstein) top



Wabisa ibn Ma’bad Al-Asadi reported: The Messenger of Allah, peace be upon him, said to him, “Have you come to ask about righteousness and sin?” I said, “Yes." So he brought his fingers together and struck his chest three times, saying, “Consult your soul, consult your heart, O Wabisa. Righteousness is what is satisfying to your soul and your heart. Sin is what wavers in your soul and causes hesitancy in your chest, even if the people give you a judgment (justification-m.u.), and again give you a judgment.” [Sunan Ad-Darimi, Book of Trade, Number 2533, Hasan]top


talfa


Tübitak Projeleri

Burada yürütmüş olduğum TÜBİTAK projelerime ait bir kısım evrakı (başvuru formları, sonu raporları vs), Hakan Ayral ile yazdığım proje rehberini ve 1001/1002 projeleri için kaynak LaTeX şablonları bulabilirsiniz. ULAKBIM veritabanı arayüzüne de buradan erişebilirsiniz.



Some Books

Nasr ad-Din Tusi on Spherical Geometry
Kitab-ı Menalous fil ashkal al-kurriya (al-Harawi)
Riemann Yüzeyleri ve Fonksiyonlar Teorisi (Cengiz Uluçay)
Hendese Kitabı (Ahmed Nazmi ve Hilmi)



Contact Info


Galatasaray University  Department of Mathematics  Ciragan Cad. No.36, Besiktas, Istanbul, 34357 Turkey   
Telephone: + 90 212 227 44 80 - 462 g-mail: muhammed.uludag



Some Links


Istanbul Matematik Doktora Okulu  (Istanbul Graduate School of Mathematics)
Fasikül (Journal of the GSU Maths Department)
turkmath.org (Mathematical events in Turkey)
Matematik kafası Mathoverflow in Turkish)
Türk Matematik Derneği (Turkish Mathematical Society)
Istanbul Matematiksel Bilimler Merkezi (Istanbul Center for Mathematical Sciences)
Nesin Matematik Köyü (Nesin Mathematics Village)


talpha


(arka komşum) Yahya Efendi

Ademün bünyâdını kıldukda Hak
Sanmanız ki eyledi bi-hendese

Taliba ömrün mühimme sarf kıl
Yelme hayranlar gibi olmaz sese

Yol mıdur İslâm ehli âkibet
Olalar muhtac cuhud-ı nakese


.... tekkesinin yanında inşa ettirdiği medresede Âşık Çelebi'nin de belirttiği üzere, "her fenden istifâde eden yüz kadar talebesi" bulunmaktadır. Hatta Aşık Çelebi, astronomi, matematik ve geometride Yahya Efendi'nin zamanının en mühim isimlerinden biri olduğunu, geometride Micasti (Almagest, Ptolemy) ve Uklidis'den üstün olduğunu söyler.... (BEŞİKTAŞLI YAHYA EFENDİ, Müslüm Yılmaz, Dergâh Yayınları, 2014). Menkıbelerine göre Yahya Efendi Rumca da bilir ama Batlamyus ve Uklidis'i o devirde bilinen yegâne nüshaları olan Arapça tercümelerinden okumuş olmalıdır.

Yukarıda "Hak insanın temelini atarken hendesesiz (geometri) yaptı sanmayın!" diyen Kanuni'nin süt kardeşi Yahya Efendi'den (1495-1571) bize intikal eden beyitleri olsa da bildiğim kadarıyla teoremi yoktur. Hiç olmadığından mı, yoksa kimse onları aktarmaya değer bulmayınca kaybolup gittiklerinden mi? Aynı eserde, Galatasaray Üniversitesi Matematik Bölümü'nün arkasındaki tepede yer alan tekkenin burada meskun bazı keşişlerden istimlâk edildiği yazar -kimbilir onlar da bin sene evvel pagan rahipleri yerinden ederek oraya yerleşmiştir!-. Feriye köşkünden Çırağan sarayına kadar kalan bölgenin bu arazi içinde yer aldığı rivayet olunur.

"Müderris" mahlasıyla tasavvufî şiirler yazan Yahya Efendi'nin tekkesi günümüzde İstanbul'da düzenlenen manevi turların uğrak yeri olmuş ve Telli Baba, Yuşa as ve Üsküdar'daki Aziz Mahmut Hüdayi ile birlikte "Boğaz'ın koruyucu ermişi" mertebesine erişmiştir. Beşiktaş'taki Barbaros makamına yakınlığıyla pekişen konumu sayesinde leventlerin pîri ünvânını da elde etmiştir. Acaba bu ünvân ve makamların Bizans'taki kökenleri nedir?

Mezkûr mısra Da Vinci'nin (1452-1519) insan vücudunun nispetlerini gösterdiği meşhur Vitruvian Adamı çizimini çağrıştırıyor.. ki bu oranlar da meşhur Romalı mimar Marcus Vitruvius Pollio'nun (MÖ 80-10 civarı)  De Architectura  kitabından alınmıştır. Acaba Yahya Efendi Vitruvian adamı'nı görmüş müdür? Yoksa bu beyitte neyi kastetmektedir?

Son beyit, Devlet-i Ali'nin zirvede olduğu dönemde yazılmış olması itibarıyla ayrıca dikkat çekicidir. İlk başta, günümüzde onu okuyan matematikçiye sanki hendese bilgisinin eksikliğinden şikayet eder gibi görünse de, tahminimiz tababette Osmanlı tebası gayrimüslimlere muhtaç kalmanın kastedildiği istikametindedir. Kanaâtimiz; ilk beyit de tababet bağlamında tevil edilmelidir. Ancak tabiplerimizin kendisine sahip çıktığına dair bir emâre bilmiyoruz.

Şunu da eklemeliyiz ki, Roma ve Bizans'ın da matematikteki sicili pek parlak değildir: Van der Varden'in tabiriyle, 4 ve 5. asırlardak bazı katkılar olsa da “bu son pırıltılardan sonra Grek matematiği bir mum alevi gibi sönmüştür". Yahya Efendi'nin çağında Grek matematik geleneği çoktan Halifeliğe intikâl etmiş, oradan bir kısmı Orta Asya aydınlanmasına geçmiş, sonra da kitaplar kalsa da gelenek yitip gitmişti.

Uklidis'i okuduğunu bildiğim bir başka sufi de, Füsus'ta ondan "Hekim" diye bahseden İbni Arabi'dir (1165-1240).

Madem ki yukarıdaki beyitleri söylemiş, Yahya Efendi'nin ilmi mirasına asıl biz matematikçiler talibiz! Yahya Efendi'nin hendese çalışmaları hakkında malumatı olanlar şahsıma bildirirse minnettar kalırım. Yukarıda arzolunan malumat hakkındaki tenkit ve tashihleri de mutlaka duymak isterim.

Klasik eğitim veren medreseler dışında "her fenden istifâde eden yüz kadar talebesi" olan, kökleri Bizans'a dayanan (keşişler) bu kurum; şartlar müsait olsaydı belki bir üniversitenin temelini teşkil edebilecekti. Neden edemedi? İhtimal, zaman içinde tekkenin sûfî hüviyetinin baskın çıkmasıdır. Merak ettiğim bir başka husus, tekkesinde yetişen yüzlerce talebenin Osmanlı devlet teşkilâtında veya ilmiye sınıfında nerelere geldiği, ne gibi işler icra ettikleridir.