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Tag: mathematics

  • The Mathematics Journal

    The Mathematics Journal

     

    In its almost 250-year long history, the Romanian print media records the longest uninterrupted publication of a magazine: “Gazeta Matematica” (The Mathematics Journal), a specialised magazine for mathematics lovers, published in 1895 in Bucharest at the initiative of a group of mathematicians and engineers. The five founders were the engineers Victor Balaban, Vasile Cristescu, Ion Ionescu, Mihail Roco and Ioan Zottu. After Balaban’s untimely death, the mathematician Constanța Pompilian was co-opted into the group. Soon, the original group broadened to include the engineers Tancred Constantinescu, Emanoil Davidescu, Mauriciu Kinbaum and Nicolae Niculescu and the mathematicians Andrei Ioachimescu and Gheorghe Țițeica.

     

    In the 129 years of continuous publication, “Gazeta Matematica” was the platform for Romania’s best mathematicians, researchers, teachers, engineers, economists, students and other lovers of the field to express themselves. The magazine also features the work of foreign mathematicians. “Gazeta Matematica” educated generations of enthusiasts and organised competitions for them. At first, the magazine was published in 16 pages, with a circulation of 144 copies, which were sold on subscriptions. Then, the number of buyers increased, with the highest circulation recorded in the 1980s, when an issue was published in 120,000 copies.

     

    With such a tradition, “Gazeta Matematica” is also a source for research into the development of education in Romania. The mathematician and writer Bogdan Suceavă cites the wealth of information that “Gazeta” provides in this regard:

     

    Bogdan Suceavă: “The fact that there is a database with a lot of problems, spanning 129 years, means that one can look at various historical layers, at various ways of thinking about education, and of finding problems suitable for a certain age range. These models are in the Gazeta. For more than a century, there have been enough examples, enough strategies have been tried, and an interesting population sample has been seen to respond to them. The fact that we have so many examples, so many ways of thinking about the Gazeta enables us to see how this experience is of interest in a broader context.”

     

    Over its long history that carries on today, the “Gazeta Matematica” has had high standards and has constantly encouraged creative thinking. Bogdan Suceavă recalls such an episode of original thinking:

     

    Bogdan Suceavă: “An interesting case was Sebastian Kaufman, who forgot some trigonometry formulas during an oral exam. He was criticised, he couldn’t het away with it. No problem, Kaufman learned trigonometry and ended up doing research using techniques that have to do with the polar coordinate system. His work was published just months before Romania entered World War I. What was his paper about? Just as we have the power of a point with respect to a circle, a concept introduced by Jakob Steiner in 1826, we can have the power of a point with respect to a plane algebraic curve. He proposed to write it in polar coordinates and see what happens. It was an extraordinary paper, written by a remarkable high school student. This was the Gazeta environment. He prepared for the competition, for the Gazeta contest, he met with evaluators, he was far from perfect. He was criticised and felt compelled to improve, and out of this environment something creative emerged. The same Kaufman problem was later on studied after World War II, and I don’t think we can find anything else published about this before 1956. The fact that a high school student was doing something like this in Bucharest is quite remarkable.”

     

    “Gazeta Matematica” is also linked to the emergence of the influential International Mathematical Olympiad. Romania has participated in all editions so far and has won 78 gold medals, 146 silver, 45 bronze medals and 6 honourable mentions, thus ranking 6th in the all-time ranking. Romania hosted 6 editions, in 1959, 1960, 1969, 1978, 1999 and 2018. Bogdan Suceavă:

     

    Bogdan Suceavă: “The idea of the International Olympiads came from the Romanian Society of Mathematical and Physical Sciences, the talks took place between 1956 and 1959. The first edition was in ’59. At that time, the president of the Society was Grigore Moisil, with Caius Iacob and Nicolae Teodorescu as vice-presidents. From a political point of view, it was not easy to organise an international event at that time, there were multiple constraints. The first of them was to obtain all the necessary approvals. The second was that of international contacts and the level of prestige required in order to start an international project of such magnitude. They used the Gazeta contest as a model and if we compare the format, this was the initial pattern: there were not many problems to solve in a very short time, but rather problems that required a lot of thinking time, about an hour and a half per problem. This was the initial concept and it was very similar to what had been attempted before World War I in Romania. The proponents of the idea felt that the Gazeta model could be of international interest. This is worth noting, compared with other competitions that existed at the time.”

     

    “Gazeta Matematica” is the benchmark publication of Romanian mathematicians, of the Romanian school of mathematics. There is mathematics, but there is also education, there is also history, there is also collective mentality, there is also generational change. And, above all, it is a tradition that carries on. (AMP)

  • The National Evaluation Exams – 2024

    The National Evaluation Exams – 2024

    In a country where functional illiteracy and school dropout, especially in the rural and disadvantaged areas have the tendency of getting chronic, the results in the National Evaluation exams involving eighth graders are a relevant indicator of the education quality. Three quarters of the students have this year got over 5, a mandatory mark for their further high-school accession, one percentage lower than in the past three years.

    The results published on Wednesday show that the students found the mathematics exam more difficult, as the percentage of those clearing the admission threshold or those who scored above proved to be lower as compared to 2023 and 2022. Roughly 78% of the students fared better in the Romanian language exam, whereas only 69% of them obtained the minimum required score in mathematics.

    Roughly 400 eighth graders got the maximum number of points in the Romanian Language exam, and over 1,000 in mathematics. However, only 65 of them managed to get the maximum number of points in both exams.

    Education Minister Ligia Deca, sees the glass half full and says that although lower than in the past years, the number of those who cleared the threshold is higher than in the simulation exam.

    Results obtained by children in the rural area continue to be weak though: only 40% of these managed to get the needed number of points in the aforementioned exam. Ligia Deca has also referred to the attempted frauds and their outcomes.

    Ligia Deca:” It happened as every year that subjects had been leaked before exams kicked off. However, that didn’t happen before the students had been placed under supervision in the exam halls. These cases have been identified because now we have methods to quickly discover the centre, which leaked the subjects. And we cooperate with police in this respect. The students attempting frauds are being eliminated from the exams and aren’t allowed to take the next sessions. Those who are members in various commissions and provide the subjects ahead of the exams are being prosecuted.”

    Nearly 153 thousand students have attended the National Evaluation Exam this year, which accounts for 95% of the total number of eighth graders. 8,300 of them took the exam in their mother tongue. Bucharest and other five counties have reported the highest attendance, over 98% and for the first time this year, exam papers have been graded by means of a digital platform. Thursday, July 4th, was the last day when the students dissatisfied with their results could apply for a remark.

    (bill)

  • Mathematician Gheorghe Țițeica

    Mathematician Gheorghe Țițeica

    The history of the Romanian school of mathematics begins somewhere in the late 1810s, with the establishment, in 1818, of the Polytechnic University of Bucharest under the name of the Higher Technical School. Here and in other higher education institutions established later, entire generations of Romanian engineers and mathematicians were trained. One of the names that made history in the development of mathematics in Romania is Gheorghe Țițeica.

     

    He was born in 1873, in Turnu Severin, a city on the Romanian bank of the Danube Gorge, and passed away in Bucharest in 1939, at the age of 66. From an early age, he showed a great interest in mathematics and the so-called “hard sciences”, that is, the formal sciences and the natural sciences that are based on methodological rigor, accuracy and objectivity. He was the first to be admitted to the Bucharest Normal School, the future PolytechnicUniversity, and studied mathematics at the Faculty of Sciences in Bucharest. Among the professors at the University of Bucharest, he was closest to mathematician and astronomer Spiru Haret, the most important reformer of the Romanian education system.

     

    In 1895 he graduated in mathematics and the following year he went to study in Paris. He specialized in differential geometry. Țițeica wrote about networks in a space with “n” dimensions and introduced new classes of surfaces, curves and networks. He issued the “five-lei piece problem” or “Țițeica’s theorem”, and the concepts of “Țițeica surface” and “Țițeica curve”. He also dedicated himself to popularizing science and raising the level of mathematical education in Romania. One of his great passions was the “Gazeta Matematica” magazine and he was among the founders of the publication “Mathematics”.

     

    Bogdan Suceavă is a mathematician and writer and an expert in the history of mathematics in Romania. He defines Țițeica’s study period in the West as decisive for his career and and the development of scientific education in Romania: “The first decades of “Gazeta Matematica” are linked to Gheorghe Țițeica’s name. He benefited from scholarships all his life. He grew up without a father. He graduated from the school in Bucharest and in 1896, and, when he arrived in Paris, the first thing he was recommended to do was study at the Ecole Préparatoire. On that first year, he met Henri Lebesgue, who six years later would become the author of a very important chapter in mathematical analysis. Țițeica, being of the human quality we know, followed two sets of courses, those at the École Préparatoire and those at the École Normale. The first year was hell. He coped at the highest level and the question is why was he recommended to take more courses? Between Bucharest and Paris there was a certain difference. In July 1897, he quickly passed the certification exams in differential and integral calculus, mechanics and astronomy, all in a single year. He was first in an extraordinary generation, occasion on which he received a scholarship, plus a fee exemption. This experience would be important at a formative level. He understood very quickly how things were, how he had to prepare, what level the French school was at and where the Romanian school was at, during that time. This was happening before 1900.”

     

    Romania was moving at full speed towards the West and Romanian mathematics was one of the sciences in great expansion. And Țițeica’s generation sought to reduce the huge differences between Western society, the French one being the great model, and the Romanian one. As Bogdan Suceavă also noted, Țițeica met top mathematicians in France and learned from them everything that he brought to Romania: “Who did Gheorghe Țițeica work with? He worked with Gaston Darboux, who at that time was not only dean of the Faculty of Mathematics at the Sorbonne, he was also the author of a four-volume treatise on differential geometry in which the unifying theme is the following: how to choose the most appropriate benchmarks for various problems of differential geometry? The subject he studied was a whole philosophy, he was a very influential author who had many talented students, Țițeica being one of the best. He also studied with Henri Poincaré, Edouard Goursat, Charles Hermite, Émile Picard, Jules Tannery, Paul Émile Appell, the best mathematicians. After which, in 1899, he returned to Bucharest. He would write until 1937, over 100 works. In the last two years he did not work at all. He started collaborating with “Gazeta Matematica” while he was in Paris. The mathematics competition with the same name owes a lot to him. The editorials he wrote during that period described everything, including how the candidates behaved in the oral exams. It’s the kind of comments that no one would publish today, but which Țițeica, did.”

     

    Gheorghe Țițeica could not have become anything other than a university professor, a member of some academies and an honorary doctor of some universities. He was also among the ranks of the Romanian Society of Mathematical Sciences, whose president he was.

  • A Solar System Replica in downtown Bucharest

    A Solar System Replica in downtown Bucharest


    They thought they could even set a Guinness World Record with what they intended to do, but more than that they decided to experiment and play with other children as well. We are talking here about a project put together by the StartEvo Association, which, through the Kidibot education platform jointly with the Bucharest Astro-clubs partners and the Science and Technology magazine managed to build a 1: 1, 392, 700,000 replica of our solar system in downtown Bucharest.


    I met Constantin Ferşeta, vice-president of the StartEvo Association at kilometer zero in the Bucharest city center while he was trying to inflate a yellow balloon, one meter in diameter, which was going to represent our Sun. Here is what he told us.


    Constantin Ferşeta: “We are trying to do here something children usually dont do in schools. An experiment. We are trying to put up some posts with balloons, which are representing the planets in our solar system. We have calculated their scale, so we start here with the Sun and are going to end in the Herastrau park, where we are putting up Pluto, the last planet in our solar system. Now, every planet is also representing a fruit so that children may understand better the huge distances in our solar system. Weve also made an XL chart with all the information about the planets dimensions their diameters and orbits. Then we calculated the real proportions of our objects and children are now going to plant these posts which will also comprise information about these planets. And if anyone wants they may cover all the distance between them so that they may get a clear picture of our solar system.”


    Constantin Ferșeta told us more about the aforementioned project


    Constantin Ferşeta: “On this project we are working with children from the third to the eighth grade of various schools in Bucharest. Hopefully this miniature solar system will remain in place for a while and not get vandalized. But we also want this project to be shared by students from other cities, because it is an extraordinary project and it is very useful to see Mercury for instance, which is as small as peas and I have to walk a lot to place it at some distance from the Sun, or Pluto, which is so far away! In this project Pluto is a mustard seed, 4.5 kilometers from the Sun, so to say. So, children will have to walk for two hours around the city to see Pluto, the last planet in our solar system.”


    After having completed 12 orbits around the Sun, at the age of 12, Ştefan, one of the students involved with the project, told us that he was interested in exact sciences, such as physics, chemistry and mathematics, the foundation of all.


    Ştefan: “Ive come here not only to learn something new but also to teach other children how to do it. I believe large-scale experiments arent very much used in the process of teaching and I believe they should be used more. Thats why I encourage people to do suchlike experiments because it is easier to learn things this way. At the beginning we mount the Sun, Mercury, Venus, Earth, the Moon, Mars, Jupiter, Saturn, Uranus and Neptune and the last one, Pluto.


    The 11 years-old Natalie would recommend experiments like these to anyone:


    Natalie: “I am here for this experiment first and secondly, wed like to celebrate the birthday of my colleague, Ştefan. I like this experiment because it is something different from what we do at school. They dont actually do experiments like these in schools nowadays, so its an entirely different thing.”


    Matei is 13 years old and told us what motivated him to join the project


    Matei: “I thought it was something interesting and I wanted to come and see for myself all the more so as there is a lot of action and exercise involved!”


    I understand the idea of the project was made public last year and its first implementation was in Turda, western Romania, following a Zoom meeting.


    Marian Neuman, an honorary member of the Bucharest Astroclub, the oldest organisation of this kind in our capital city, founded in 1908, shared with us the passion he has for astronomy and his motivation to participate in the project.


    Marian Neuman: “For the benefit of children first, as we wanted to make children understand the real dimensions of space, the distances between the Sun and the planets. Because only through an experiment like this they will fully understand how things are in outer space. The Astroclub is more of an association for the adults who share this hobby, astronomy, but we have lately focused on this age bracket, on children. So we have created a smaller club for them that we called Astroclub junior and which has members from four to thirteen years old.”


    Mihai Popa, who is teaching geology and paleontology at the Bucharest University, has told the children about the connection between geology and planets.


    Mihai Popa: “As you know our solar system is a heap of star dust. And in billions of years this heap of star dust materialized in the planets we see today. Rocky planets are closer to the sun as you know, whereas the gas giants, which are lighter, have been pushed farther from it. Today we are going to speak about geology and astronomy because these two sciences are tightly connected. And you are going to learn why. Welcome everyone!”


    And because Ive learnt that our solar system is at half of its life, I thing I am going to follow the example of the organizers and make plans to move in the future to a different galaxy, far, far away. “


    (bill)




  • On lost manuscripts with writer Bogdan Suceava

    On lost manuscripts with writer Bogdan Suceava


    “From Aristotle to Hemingway, there is an entire history of manuscripts that are forever lost and which might have revolutionised literature, philosophy, mathematics and physics. How tragic is the definitive loss of a manuscript? But what if the author of the lost manuscript wrote other invaluable works?” These are some of the questions posed by the writer and mathematician Bogdan Suceava in his new book published at the end of 2017 by Polirom, called “The History of Lapses. On Lost Manuscripts”. On 22nd December 1989, when the Romanian Revolution broke out, Bogdan Suceava, who at the time was a student at the Faculty of Mathematics in Bucharest, saw the Central University Library on fire. “In the middle of Bucharest, and no one could do anything about it. Lots of rumours circulated. I don’t know the cause of the fire, but I remember thinking: so that’s how libraries burn. That’s how the Library of Alexandria must have burnt”, writes Bogdan Suceava. That incident appears to be one of the triggers for his new book. A professor at the Department of Mathematics at the California State University in Fullerton and the author of 13 books of prose and several books on the history of mathematics, Bogdan Suceava tells us he believes a review of the most important lost manuscripts is more necessary than ever:



    “I thought this book was necessary first of all in order to clarify my own image about literature and the role of the novel today. At the end of the day, we can ask ourselves why we still read and why we still write novels. What if the future holds a world in which we will no longer read novels? Is this the time certain literary genres are beginning to die out and interest in the traditional values of literature begins to dwindle? I believe the short answer is no, I think people will keep on reading. I believe we will always be able to find a type of story, a type of novel that will be necessary in the future, just they have always been necessary in the past. And I said to myself books that are absolutely necessary are the books that help us reconstruct scenes from the past, moments that seem relevant for the world we live in. Filling up such obscure moments-episodes of the past with a well-written story seems to me absolutely useful and it’s all about a special kind of usefulness as regards culture. And I don’t think something like that could be replaced by social network posts, messages or video-clips. There are certain things which are purely literary, while the reconstruction of several important pages of the past seems to guarantee the viability of the novel as a genre.”



    “Once the book is lost, maybe the happiest twist in the tale could be fate of the second part of Aristotle’s Poetics, which means that another author, such as Umberto Eco, should invent a story over the ruins of absence. And that is not necessarily the initial book, about which we all agree it has been lost forever, but speculation on the context of its disappearance. And that could turn into a novel”, Bogdan Suceava writes.



    “With ‘The Name of the Rose’ I was lucky, I read it when I was seventeen, and I realized rather early in my life that there was something very important there. Yet there was another important moment, the moment I prepared a course in the history of mathematics, trying to compile a list of the things I would teach for that course. And that’s how I found out that many books from the Classical Antiquity period were missing. For instance, I discovered that a volume written by Cicero, a book that Saint Augustine liked a lot and which meant a great deal for the progress of young Augustine, was actually missing, it had disappeared. And that may really hurt you, at a very personal level. And you actually want to find out what has happened with the memory of humankind. But that dawned upon me very late in my life. I think you need to be old enough to be able to appreciate the true value of such a loss. I realized that over the past two years.”



    Bogdan Suceava chose to leave for the United States, as he wanted to study mathematics under the supervision of a famous Chinese specialist, whom he also mentions in his recently launched volume “The History of Lapses. On lost manuscripts”. Bogdan Suceava earned his PhD in Mathematics from the Michigan State University, in 2002. He currently holds a teaching position with the California State University. Notwithstanding, he has returned to literature from time to time:



    “I believe literature makes us more wholesome. I for one do need literature and I think that were I only to stick to my technical endeavour, that would mean way too little. It may come as some sort of impoverishment, as some sort of dwindling of one’s own self. There were years when I didn’t write anything. Between 1996 and 1999 I had to prepare for some exams in mathematics, that were very tough. It was very hard, very tough, I didn’t write anything for three good years. One of the most difficult exams was in May 1999. I was 28 and I suspected myself of being unable to memorize anything. Three days before that exam I started writing again. It was like a moment of liberation, of necessary liberation. We need to be wholesome and in order to be wholesome, we need literature.”



    The CopyRo Prize that Bogdan Suceava received in 2002 for the volume “The Empire of Tardy Generals and Other Histories”, the Bucharest Writers’ Association’s Prize for Fiction, awarded for his novel “Miruna, a Tale” and the Literary Network’s 1st prize for “The Night When Someone Died for You” are some of the prizes which reward Bogan Suceava’s literary activity. (Translated by C. Mateescu & E. Nasta)