Journey of the Guinea Pig, Volume 2: The Ph.D. Adviser

By Denka Kutzarova

With a fresh undergraduate degree in mathematics, Svetlana Nikolova embarks on her next journey, the quest for a Ph.D. This requires solving some mathematical problems which have never been solved before. She must also survive a tense relationship with her adviser and several bureaucratic roadblocks. And should she succeed, then what next?

• Language: English
• Publisher: Denka Kutzarova
• Release date: Dec 23, 2022
• ISBN: 9781005674113

Book preview

Journey of the Guinea Pig

Volume 2.

The Ph.D. Adviser

by Denka Kutzarova

Copyright © 2022 by Denka Kutzarova

Svetlana’s rules for dealing with her adviser:

. Never forget that he is only human.

. If he gets on your nerves, avoid him as much as possible.

. Don’t believe everything he says about you.

In case the above is not sufficient, apply the ultimate:

. Do the opposite of what he tells you to do.

to Kevin,

who encouraged me to write this book

Dedicated to my parents,

Nikolai Kutzarov and Dimitrinka Kutzarova

"What is a woman mathematician?

She is like a Guinea pig -

neither a pig, nor from Guinea."

(a folklore joke)

Sea Magic

I stand before the sea and wait

for winds to turn and blow my way.

Day after day - is it too late?

My doubts condense in charcoal grey.

How long my launch will I postpone?

A raging storm - would I endure?

I dread of sinking like a stone.

My longings only time will cure.

I need no dreams! Yet at the shore,

sea waves arrive in constant action;

I watch them coming more and more

and can’t escape from their attraction.

The Mathematical Modeling section

I already know who will be my future adviser and I’m still nervous as hell. I wonder how my fellow students feel who’ll learn in a few minutes the names of theirs! thought Svetlana Nikolova while stealthily glancing the anxious faces of the twenty-some students from her year who were admitted to the Master’s program of the Mathematical Modeling section. It didn’t even cross her mind that the choice of an adviser could determine one’s whole professional life. She was just curious about her friends and competitors.

The seminar room on the fourth floor of the Institute of Mathematics was packed with professors and students who were waiting impatiently to be matched by the authorities of their section. Inquisitive eyes from both sides of the aisle stared at each other. Svetla’s eyes briefly stopped at the front table by the windows. As usual, Grigor looks unperturbed, she mused, and couldn’t help a faint smile. Grigor Petrov, the top student of their year, was courted by two girls, but his attention was directed at the young assistant and associate professors.

Svetlana suddenly shrank down when Boyan Vladimirov approached Katya Mitova, who shared her table. Bittersweet memories from Svetla’s undergraduate years rushed through her mind. Boyan used to be her best friend from their recitation group, and they had a great math cooperation. He even courted her for a while and she was very fond of him, but then his last girlfriend got pregnant, he married, and for no reason he interrupted all connections to Svetla. Their friendship turned sour, but she still liked him and was sorry that everything ended that way.

Academician Simov agreed to take me as his student, Boyan boasted to Katya, but it was not clear if he did so because of her, since his head was turned more towards Svetla. My Master’s thesis will be based on problems he’ll pose to me.

Simov will be my adviser, too! Katya replied immediately with a triumphant grin. Boyan didn’t linger any longer and sat at another table.

Wow! That’s a big deal! Svetla congratulated Katya for becoming a student of the rector (president) of Sofia University. She was not surprised, since Katya was a former Olympian and also Simov had worked in math biology, the topic that Katya wanted to study. Nevertheless, the news about Boyan slightly puzzled her. He was an excellent student, but not among the nominated stars like Grigor. How did he get to Simov? Never mind, she suppressed her thoughts, good for him. She didn’t want to dwell on past feelings; besides, it was partly her fault that it happened that way.

Lanich, Katya turned to Svetlana using that strange nickname which she invented during their first year as undergraduates and which only she used. You know how it is with big bosses. He’ll probably ask someone else to supervise me, since he’s very busy. See, he’s skipping this orientation meeting. What about you? Will you work with Dobrin Belov? Didn’t Boris Popov suggest him when we traveled to Shumen?

Yes, he did, in the restaurant. But he said someone else would be my official adviser. I don’t even see Belov here. He’s in Taggy’s section, and apparently Taggy doesn’t let younger faculty become advisers; he takes all the students himself.

By the way, Saveliev and Aneta are admitted to the Math Logic section. They’ll both be under the supervision of the section’s chief, continued Katya. Saveliev is already thinking about a project related to Turing machines.

Yeah, he once wrote on the board that the theorem of N. Saveliev is better than the theorem of S. Nikolova. But I don’t have any theorem yet.

The conversations stopped when professor Boris Popov, Simov’s former student and current right hand, entered the seminar room, walked to the front desk and immediately began his speech with general facts about the section. Svetlana’s eyes fixed on his imposing figure and especially on his face. His chubby cheeks didn’t evoke the standard association with a good-humoured character. Popov’s powerful, serious eyes were partly distorted behind his thick, black framed glasses. Svetla was afraid of him, yet she felt secure in his presence among the unfamiliar faces of the members of her new section. She tried to lift her own spirits by recalling her former exploits, especially her first place with a perfect score at the last National Olympiad in Shumen, a single point ahead of Grigor - the only time he was second. As if this happened not five months ago, but years and years away.

Svetla briefly scanned the faces of the young faculty. Most were men, but there were a few women as well. Her former assistant professor Valeria Toneva was still in Moscow, working on her Ph.D. Ha, Svetla thought, and I was certain that I’d never be in the same section with Toneva. I’ll specialize in a different topic, but we’ll still belong to the same social circle. I’m glad we overcame the initial misunderstanding and are now on better terms.

Apart from Popov, Svetlana knew only Branislav Banchev, their last assistant professor in numerical analysis, who was now Dozent (Associate Professor). He also looked at her and grinned with his friendly, radiant smile and she felt slightly less frightened by the new environment.

Boris Popov finished his speech and then read from his list the names of the students together with the names of their proposed advisers and pointed at them. When her turn came, he announced the name of Rosen Todorov, but didn’t point at anybody in the room. Svetla had never heard of Todorov and she wondered who he was. She looked around, but nobody got up from his seat and that caused her to panic. The meeting ended as the professors shook hands with their future students and walked them to their offices. Popov, before walking away with Grigor, approached Svetlana and quietly told her:

You’ll be officially a student of Rosen Todorov. I chose him, since his research is mainly in collaboration with Dobrin Belov. They are the same age, but Rosen’s Ph.D. thesis was based on joint results with Dobrin, so basically he was Dobrin’s student. You’ll work with Dobrin, yet you can also talk math with Rosen. He’s waiting for you in his office. It’s on the this floor. Todorov is a young man with a mustache.

That’s not a good start - I don’t like men with mustaches, Svetla thought while looking for Todorov’s office. For a brief moment, she was again disappointed that Popov didn’t himself become her adviser, but she had to agree with what he had said in Shumen - she was better at the more pure type of mathematics, which she found more beautiful. In the corridor, the space on the walls between the pale-green painted doors was covered by framed pictures of famous mathematicians: Newton, Gauss, Laplace, Euler, Markov. The girl blushed when she saw the profanity which someone, probably drunk after a party in the Institute, had scratched on the picture of Sofia Kovalevskaya. She decided to clean it up some day when nobody was around. Svelta read the names on each door; each room was shared by two or three researchers from the section, while only Simov and Popov had single offices. Finally Svetla found the name of Rosen Todorov. She knocked and a soft, melodious voice answered, Come in. Surprisingly, Svetlana immediately liked Todorov, despite his mustache. She couldn’t determine why she felt so, but there was something comforting about him. He was dressed in a sport jacket, had nice features and hazel eyes, more green than brown.

So you are Svetlana, he smiled reassuringly, glad to meet you. I’ve heard a lot about you. I suppose Boris Popov explained to you that you’ll actually be Belov’s student, but you can always talk to me, too. I’d be happy to help as much as I can. This academic year you’ll take graduate classes, and the next semester Dobrin will also give you a research project to think about. He has an office in the math department building, but he often comes to the Institute, so you may see him here, if that’s more convenient for you.

Yes, indeed. I live very close to the Institute. Thanks.

The meeting didn’t last more than fifteen minutes, but it felt like a whole hour. Just before Svetlana left the office, she noticed on Todorov’s desk, among notes and research papers, a little bottle with herbal valerian pills which are known for their calming effect. She almost laughed - she was not the only one who worried.

In the meanwhile, in the large open space on the fourth floor of the Institute, between the two wings of the new L-shaped building, a small crowd of excited students was sharing first impressions of their advisers. The divisions between recitation groups and the two streams of their undergraduate years were in the process of being replaced by those between different research areas.

You, lucky guys! Maxim Tolev teased Katya. It has its perks to be in the section of the big boss Simov.

Matso, Katya countered, if you wanted to be in Math Modeling, why did you apply to the Optimization section?

Because that’s what I want to do!

Don’t complain then. Besides, your section is not bad itself - your chief Ivan Kesarov is the vice-director of the Institute!

Have you seen him? Svetla’s best friend from high school, Rachel Aaron, interfered. Very few students had met Kesarov, since he hadn’t taught them as undergraduates. He looks like a young Cary Grant, the famous Hollywood actor! In fact, even more handsome. Rachel was also admitted to the Optimization section.

I heard that Math Modeling and Optimization were once one section, and it split when it became too big, Katya informed them.

But they still drink together, Matso winked. And besides, our section is more exclusive - they admitted only eight of us.

And I know why, grinned Boyan, who was passing by. The rumour says that at the department meeting, when the secretary told Boris Popov that twenty people had applied, he responded ‘We’ll take them all.’ When the turn came to the Optimization section and the vice-chief of the section was told that there were eight candidates, he exclaimed ‘Eight - what are we going to do with so many?’ I can picture him, with a cigarette glued to his lips, and his soft, phlegmatic voice.

Nobody had any doubts, as they knew the vice-chair of the Optimization section from his lectures. The friendly teasing continued for a while, but they were all proud that they were among the one hundred students who made the grade average cut needed for becoming Masters students. The other hundred would graduate at the end of that academic year.

On the way out of Todorov’s office, Svetlana accidentally bumped into the woman who taught them geometry during their Olympiad training in the Rila Mountains two years ago.

Hello, Svetla, how are you doing? the woman greeted cheerfully.

We had our orientation meeting, the girl explained.

So you are in the Math Modeling section, after all. I have to tell you something, since you might not be aware of it. About the department meeting this September, when representatives of all sections distributed the new Masters students among themselves.

I haven’t heard anything. What happened? Svetlana asked, slightly frightened.

Nothing to worry about, but you have to know all your options. At the meeting, Professor Tagarinski asked his colleagues from all sections to see the lists of their applicants. Tagarinski doesn’t usually look for particular students, so everybody noticed that. Apparently, he was looking for you! What’s even more remarkable about it is that he never wants to take female students. Then he had an argument with Boris Popov after he learned that you applied to Math Modeling. He tried to persuade Popov that you would be better suited for functional analysis than for approximation theory. Everybody at the meeting was stunned when Popov rejected the request.

I had no idea about this, replied Svetlana, equally surprised. I did what one of my professors advised me to do. Actually, it was Boris Popov who told her what to write in her application and she complied.

Now it’s late to change sections, but it’s worth thinking about and perhaps reconsider. Good luck, girl.

Svetlana walked slowly in the corridor, still processing the news. Boris Popov never shared this story with her. What a show it must have been - Taggy looking for her! She felt proud, but also even more doubtful and scared than before. Did she do the right thing? She hoped that Popov had made the best choice for her. At least, she was certain that he wished the best for her.

The crowd on the fourth floor had already dispersed when Svetlana approached the foyer. Only two girls, one of them Rachel, were still there. Svetla joined her high school friend and they stopped in front of the large windows next to the stairs. The peaks of Vitosha, against the bright blue sky of the warm October day, dominated the horizon to the south. A tall birch stretched towards the glass its delicate branches with golden autumn leaves. Living on the first floor at home, in the Institute Svetla enjoyed the beautiful view above the nearby buildings. The two girls discussed briefly their new sections and then switched to their favourite topic - Grigor. Although they never discussed their feelings, each of them suspected that the other one was also in love with him.

His girlfriend was admitted as a Master’s student, announced Rachel with a hint of regret in her voice. Svetlana didn’t harbour very warm feelings towards Grigor’s girlfriend after that girl made fun of her before the second round of the math Olympiad the last academic year, especially since Grigor’s girlfriend was not among the best students and never participated in any math competition. On the other hand, Svetla mused, I might have not done so well in the Olympiad if she hadn’t made those belittling remarks. After all, I should be thankful to her.

Who will be Grigor’s adviser, Simov or Popov? Rachel interrupted Svetla’s distraction.

He’ll be working mainly under the guidance of Popov, but he said he’d also discuss math with Simov, Svetla informed her curious friend.

It’s good for Grigor that Simov took him under his wing. Simov supports people who don’t have a Communist background, since he had to struggle himself before he achieved his high position.

If you mean Boris Popov, you’re right. Decades ago, his father was considered by the Communist government as an ‘enemy of the people’. But I don’t know anything about Grigor. You’ve once told me that his parents are both doctors and divorced, but that’s all. She skipped sharing the fact that later Grigor had told her himself that his parents were separated.

Don’t you know that Grigor’s father emigrated to the West? Once you leave the country, the government doesn’t let you visit Bulgaria any more, nor can you take your family.

No, I had no idea! Svetla immediately recalled how nervous Grigor was two years ago, when during their walk in the park he told her about his divorced parents. He didn’t mention anything about his father, but she could understand now why he was nervous - there was a stigma related to people who escaped to the West. She suddenly felt happy that, unknowingly, she was very supportive of him then.

You probably don’t pay attention to this, since we both come from left-leaning families. However, Grigor had some troubles, but don’t tell anybody else about this. Some guy from his native town wrote a letter to the Math Department that Grigor should be expelled because of his father.

What?! That’s preposterous! He is the best mathematician of our year!

Fortunately, it didn’t have any effect. A letter like that might have caused great damage years ago, but not any more. Yet, I can’t imagine what made that person attack him so viciously.

Maybe he studied in the same high school as Grigor and hated him for being much better. Maybe the father of this guy was a boss in their town, yet Grigor was the most distinguished pupil. And what if that person was not admitted to the University? Who knows, Svetla reasoned. Being deeply shocked by this, she forgot to ask Rachel how she knew about the letter.

It has to be something like that. Otherwise, why bother? People use politics to excuse their personal animosities.

On the way home, Svetla stopped for a couple of minutes to contemplate the blooming roses in the garden in front of the Institute. Too much information for one day. She was still thinking about the back-stabbing letter against her fellow student. Svetla admired Grigor for his determination and intellectual strength. Perhaps this episode made him even stronger and gave him the tenacity to win all the math competitions. Except the last one, she couldn’t resist saying silently in her mind.

Rock and Roll

The new snow gradually covered streets, roofs and trees. The snowflakes quietly rang through the air while the wind carried them in gentle swirls. All other sounds were muffled by the snowfall, as if they came from the distance. Vitosha was obscured by clouds and was not visible from the city. Not many people walked outside in the late morning; only occasional cars slid and splashed jets of snow behind them. Here and there between the blocks of flats, the chimneys of the remaining houses gave out curls of smoke. The tree branches in their sleepy gardens hid under the heavy blanket.

Svetlana was coming back from the department and felt lonely in the midst of the winter wonderland. She and her fellow students had the last common undergraduate lectures and recitations, and in a week or two there would be no streams, no recitation groups; only memories. On the other hand, she didn’t have to sit any more in her usual spot in the recitation classroom and try to avoid looking at Boyan’s shoulders in front of her; it was over. Svetla still had to attend the next semester a graduate class with him in the Math Modeling section, Simov’s course in Approximation theory, but Grigor would also be in the same class and that would provide different dynamics. Especially since Grigor’s current girlfriend was Boyan’s ex; to say nothing of the fact that Boyan and that girl broke up because she was jealous of his math conversations with Svetla. These few months had some peculiar feel - the students from Svetlana’s recitation group, with whom she spent the last three years, still took classes together, yet their lives were already diverging. Katya and Anton would get married after the end of the academic year, before their friends, who were not admitted to the Master’s program, would leave the university. Katya herself made the invitation cards for the wedding and invited the whole group. Svetla cringed when she thought that she would have to see Boyan’s wife for the first time - after all it would be natural for him to bring his wife to Katya and Anton’s wedding reception. For a moment Svetlana forgot where she was; then she turned her head to see her own tracks in the deepening snow and listened to the whisper of the falling snowflakes before she lifted the collar of her dark blue coat and hurried back home.

Around lunch time the phone rang. Hey, Lanich, Katya exclaimed, why don’t you come to my place to eat with me and Anton. I’m cooking moussaka.

Sorry, I don’t feel like coming. My mother is also cooking something.

Oh, come on! Besides, I’ll ask Anton to teach you to dance to rock and roll. I’ve been planning this for a while.

Svetla’s mother Minka saw that her daughter was not in a good mood and quietly suggested Go.

All right, wait for me, Svetlana replied on the phone and put on her boots and coat. In five minutes she arrived at Katya’s place, and the smell of fresh moussaka greeted her as soon as Katya opened the door.

My brother already ate his share, so he’ll not disturb us, Katya explained while serving the steaming plates to Svetla and Anton. We’ll have some dessert later, but now let’s go to the living room for the dance lesson. I don’t want to postpone this, since after the wedding, Lanich, I’ll leave my parents’ apartment and I won’t live so close to you any more. Anton and I will move initially to a special dormitory for young academic couples.

Katya, will you actually have rock and roll at your wedding reception?

No, because of our parents, Katya smiled, that’s why I’ll start the lesson with a waltz. Look at the steps, one-two-three, one-two-three, one-two three. You’re catching on fast.

I’ve watched waltzes on the TV.

Now the rock and roll. Anton, come here. You’ll dance with Svetla and I’ll watch and give instructions.

That lesson didn’t start well. Svetlana didn’t have any experience with rock and roll and she felt uncomfortable.

Anton, Katya shouted, you have to lead! Svetla doesn’t know how to dance it.

How can I lead when you watch and criticize, Anton complained as he and Svetla continued to step on each other’s toes.

That’s enough! Katya interrupted them, I’ll teach Svetla myself. Anton, don’t go to my brother’s room; he’s bothering me with a problem for his geometry homework assignment. Don’t become his next victim. I’ve had enough of solving his high school math problems!

Under Katya’s lead, the lesson went better. I think you’ve got it, she concluded in an hour. Where is Anton? Hey, did you go to my brother’s room?

Anton appeared from the other room with a guilty look on his face. I just briefly looked at the problem, but it seems hard.

I told you not to! Now you’re hooked, Katya protested, but it was too late. Soon after that, the three of them were sitting on the sofa staring at the text while Katya’s brother was hanging around and repeating Ha, the stars of the Math Department cannot solve a high school problem. Finally, the three mathematicians produced a solution and Anton explained it to his future brother-in-law. The boy listened carefully and then, with a smirk on his face, announced. Yeah, but you used a theorem which we haven’t studied in class yet!

You should have told us in the very beginning! What material have you covered so far?

I’ve warned you not to fall into my brother’s trap, but nobody listens, Katya complained.

Here’s the textbook, the boy handed it and showed them their current geometry lesson. Then he took his jacket and got ready to leave.

Where are you going?

I’m meeting a couple of friends. We’ll be skiing on Vitosha. If you find an appropriate solution, I’ll hear it in the evening when I come back from the mountain, he said with a grin.

I refuse to work on his stupid problem, Katya declared when the three of them remained alone. Anton, however, had to defend his mathematical pride, and eventually they all looked at the textbook before they found an acceptable solution. The reward for their efforts came in the shape of cake slices which Katya served with hot chocolate.

On the short way back home Svetlana wondered if she’d ever use her newly acquired dancing skills. She had heard from friends about the wild parties in the Math Institute, but didn’t quite believe it. She had something more pressing on her mind - soon Belov would give her a math research project, her very first one.

Intelligence test

On a late February evening, the bell rang and Svetlana hurried to open the door.

Grigor! she exclaimed in surprise as he had never come to her parents’ apartment before. What’s up?

May I come in? he asked with urgency in his voice.

Certainly, Svetla replied, letting Grigor enter the larger room, the only one apart from the kitchen.

Has Belov given you an intelligence test? Grigor started right away.

A what?

That is, to solve a research type problem which has already been done by someone else. Boris Popov just gave me one.

Not yet. But today Rosen Todorov mentioned to me that I’d soon get a similar type of problem in functional analysis from Belov. Todorov thought that I should be given a truly new research project. However he said that Belov insisted that I should be tested one more time.

Indeed, can’t they just pose unsolved problems to us and then see if we can do research. Nobody else got an intelligence test of this sort, nobody! Only you and I. Haven’t they tested us enough? We’re the only ones in our year with a straight 6 course average (6 is the top grade in Bulgaria); I’ve won so many math Olympiads, and you won the last one - isn’t this enough? I can even guess how they decided it. Boris and Dobrin got drunk together and looked for some amusement, so they invented it: ‘Let’s give them an intelligence test!’ Damn!

Is your problem hard?

Most likely. Here it is. Have you seen anything of this sort in some of the graduate classes you’re taking?

Sorry, I haven’t. Should I try to think about it, too?

No, thanks. I just wanted to vent some steam. It’s virtually impossible to find where Boris took it from. Probably some research paper and only he knows the coordinates. I’ll tackle it myself. You’ll have enough trouble when you get yours.

Grigor and Svetla talked for a while, both competitors and friends, both self-confident and scared, with him being more of the first type and her the second. They simply had to overcome one more hurdle. In this era before the Internet, it was extremely hard to search for anything.

A week later, Grigor, much calmer, stopped Svetla in the corridor of the Institute.

I solved my problem. Did you get your intelligence test from Dobrin?

Yeah, I did, three days ago. I’ve no clue about it.

I’m tempted to try to help you, but I shouldn’t. If I solve it and you don’t, you’ll feel horrible. And if you solve it and I don’t, then I’ll feel the same way. Good luck! Grigor added with soft, comforting voice, quite atypical for him.

That was so true what he said, Svetlana thought. Each of them had to win one’s own battle, fight one’s own war.

The girl went back home, sat on her bed in the kitchen, her usual desk, bent her back on the old refrigerator and put a notebook on her knees.