Start at number 14 of 21/04/2016
... "The bells, the bells! .. And you are powerless to stifle, to erase the memory of experiences ..."
Professor Phakadze did not leave the operating table for five hours. Five hours he did everything to save Eugene’s life. He saw, he realized that the hope of success would be self-deception, but his hands, his hands were doing.
... Eugene returned to his homeland happy and elated. Warsaw remained behind, he was sitting in a wagon of train and thought about one thing: how to meet his mother, his dear sister. They returned earlier and lived in Kyiv, in fact, not far from Kyiv – in the hamlet of Shevchenko. Eugene was born there. He knew every path, remember all the trees that grew on the surrounding hills. So he immediately recognized the hut that was hidden in the old garden. He threw his suitcase in the yard and not enter, but flew into the room. The mother stood at the table with a towel in her hands and froze.
- Eugene, my son ..
Long, long time she could not say a word. She looked, examined as if not recognize her son and was crying. She calmed down and asked:
- Tell me what hurts you? What is with your face?
- Nothing hurts. It is because of the road - said Eugene and felt embarrassment because he lied to his mother.
- Where are you going now? – She asked covering the table.
- I will learn.
- To the eighth grade? You are already twenty two ...
- I will try extern - for ten.
Eugene passed his exams brilliantly. Having received the gold medal he applied for the Kyiv Pedagogical Institute. The memory about Vasyl Myronovych whom he has not sought, induced him to such a choice still in German. No Vasyl Mironovich - now he will teach children not only geography, and mathematics. Vasyl Myronovych is dead, now he will teach children not geography, but mathematics. Student life captured and spun Eugene. It was no use thinking about spare minute. From home - to the institute, from the institute – to the library, and then when it was late – to home. Mother worried. Exams for three school years were so easy but so difficult in college. And everything because of the math that he likes. Sometimes he sits until the morning at those formulas. She was more worried that son could go all days without eating. No matter what she cooked, he did not eat. And sometimes at night she listened and heard groan and her heart was bleeding. Eugene did not tell his mother about disease. He did not visit doctors. In Brandenburg one military doctor told him that everything will be okay if he did not smoke and did not eat spicy food. He has never smoked, and he did not want spicy food. And disease does not matter when there is such amount of work. Especially work, but not reading of boring textbooks.
Also he did not tell his mother about his first problems with studying. It happened on the third lecture. Young, spruce associate professor made two mistakes when writing on the blackboard the proof of theorem. Eugene was anger, he stood up, went to the board and quietly corrected the error. The students began to laugh, and the teacher apologized and thanked Eugene. But the next day the same thing happened. But this time instead of gratitude Eugene had to leave the class. Students did not laugh. When he was leaving someone considered him to be strange, somebody viewed with conviction: like he got a smattering and boasts. The dean found it out, called Eugene and without going into details said:
- Viktorovskyy, you was accepted to the institute not to teach the teachers. If you want, you will pass the exams at the department, in the presence of the commission. So choose or the other ...
- Thank you. I will pass it in the presence of the commission. But lectures of honored associate professor are just fun.
- I say it quite seriously.
- And I'm not kidding.
Then dean invited professor Remez. When he entered, Eugene recognized professor whom he visited with his father before the war. But Remez didn’t even looke at Eugene who was standing near the door. After greetings he asked why he was invited.
- Sorry, Eugene Yakovych, that I disturbed you. But just look at smarty pants whom we have. He obstructs the lectures. It’s a report here. I say that he has to pas an exam in the presence of commission, and he agrees. Maybe you can help to decide. He turned round, came to Eugene, went around in a circle and asked:
- Are you that boy who came to me?
- Yes I am.
- I see. I remember your eyes. You are fair, and your eyes are black. Well, well ... now you are here? That's good! .. - And you are already at the dean’s office: - Let me talk with him by myself, I just have a break.
They left the institute and were slowly walking along Shevchenko boulevard. Eugene told about his ordeals in Germany, the military service, and, of course, about the incident at the lectures on higher mathematics.
- And your life has not teach you? - said Eugene Yakovych.
- In this no.
- Okay. And in mathematics have you gone further?
- How shall I say. Slightly. In Brandenburg I came across a library. Not a library but a real treasure. I bought a few books there. Two of them impressed me. I even tried to prove something in my own way ...
- Tell, tell me. What is this book?
- First is Perron’s, second is Carathéodory’s.
- Oh, these are the old problems. You see how it is in mathematics: since these books came out, it took more than three decades. Thirty years, and no one has yet managed to come close to those problems. But, excuse me, do you have any records?
- Everything survived, Eugene Yakovych.
- Then, dear colleague, incidents are incidents but science is science. I think you have nothing to do at the lectures on mathematics. The course that is taught now, you knew even when you came to me. You will pass the exam for commission only for formality. Meanwhile take up the theorem, general theorem of existence of solutions of differential equations connected with integral inequalities. If you prove this theorem, you will take, perhaps the first step to creation of a new theory ... Well, I, in turn, ask the rector to allow you to study individually.
- You say so, Eugene Yakovych ... Maybe it's beyond the scope for me?
- Maybe yes. But you are young. You have a phenomenal memory, logic. Appreciate it. And then ... then, remember what Goettingen spike wrote about arguments about consistency of non-Euclidean theorems of geometry? The possibility of error, he wrote, exists forever. You are young people, he addressed to those like you. Your name is not canonized, you can afford to print nonsense. I highly recommend you to devote all your energy to this problem ...
- It was easier for Carl Gauss ...
- You think so? And do not you think that he wrote it, maybe with a sadness. When you become known, famous, you will know how difficult it is to admit that there is something that you can not do ...
Eugene did not tell his mother about the conversation with professor Remez. He did insufficiently for his mother, so he wanted to comfort mother’s heart with success. And the mother won’t know what forced him not to sleep until he finds, proves his theorem.
A lot has already been done. He went further than Perron and Carathéodory. The proof of the theorem led to new problems. But he knew that the main thing in mathematics is to articulate the problem. Without outlining and comprehension of those problems you can’t specify the tasks. It is not necessary to search analogies in nature. After all, if he found what they are worth in the world of his abstractions?
But Eugene again and again opened a book of lectures by Rene Baire. In a small preface a prominent French scholar wrote: "In mathematical descriptions of natural phenomena we constantly deal with continuous medium, with discrete points. Of course it is only about approximation, but that is just the point that such approximation equally gives us in some cases - a real environment, while in others - some moments. Some theories of physics, chemistry, mineralogy is similar to the mathematical concept of discreteness. In any case, contrary to former belief that is now rejected nothing gives us the right to say supposedly that "nature does not make leaps." In this case is not the duty of mathematician to proceed with the study, in abstracto, of relationships that take place between these two concepts, continuity and discretness - concepts which, being opposed to each other are so closely connected ? Maybe it would be the best way to ensure the background for a new mathematical physics in which the role of the hypothesis would be minimized." Well, it appears as if the river flows, and on the surface of the field there is no discontinuities. There is plenty of mathematical methods to describe a field. But if the river faces the banks? If the field is broken? Can you describe it? It turns out that such theories do not exist. Half a century has passed since Rene in Bair called for their creation, but no one, no one in the world did not dare.
"Of course, - said Remez, when Eugene shared with him his thoughts. - It must be difficult theory, the world of exceptional mathematical abstractions. I'm afraid that when you get them, you will have very few people who can understand you. But everything - then. In the meantime prove the theorem ... " Eugene presented the proof of the theorem at the Academic Council of the faculty. The rumor about a student of physics and mathematics faculty, who made some discoveries was spread through the whole institution. There was not free seat in the audience. Even a professor who wrote a report to the dean has come. He came to Eugene, smiled, wished good luck and sat in the first row.
The meeting of the council was chaired by professor Shymansky. He said that he did not remember when scientific work of students were presented at Academic Council. He was extremely pleased to present the audience Eugene Viktorovsky who proved a new theorem in hardly explored field of pure mathematics. Then he gave a word to Viktorovsky. Eugene went to the blackboard, took a piece of chalk and began with agetation:
- As I know by this time nobody found any distribution of the method that was applied by Perron for the proof of the existence of solutions of differential equations - he wrote that equation on the blackboard - with continuous arguments on both the right side, in fact a related technique invented by Chaplygin in one thousand nine hundred fifth year for the approximate integration of differential equations, for the more general case " Carathéodory conditions" …
Eugene’s voice became more confident and blackboard was covered by new equations. Students and most teachers hardly understood what the speaker said. But all of them were fascinated and followed his arm. But he turned to the audience, as if to say: "Here I see no need to dwell on quite apparent from the preceding" - he wrote and wrote. Both of blackboards are already written. Eugene took a rag, wiped everything and continued to write. In his hand was no compendium or any other records. It was even more impressive especially for students. One of them whispered to friend: "Keep all that in mind, perhaps, is more difficult than the score of the opera." When Eugene finished applause appeared. Eugene Yakovych Remez applauded most of all. He even did not listen to the speaker, but observed the audience. He took the floor as nobody wanted to speak.
- Welcome, welcome Eugene Eugenovych! - said he sublimely. - Today we are the witnesses of the birth of a talented mathematician. His theorem is worth to be published in the most respected scientific journals. So I suggest to recommend it to print, and, Eugene Evgenovych, I advise you not to stop. The assault of discontinuous field began and I believe that success is for you ...
(To be continued)