Mathematical Genealogy

Contents:

• A mathematics professor fights stereotypes
• How a mathematician searched for his roots and created a global project
• What mathematicians do with their family trees

Professor of mathematics in the fight against

Linda McGuire, a mathematics professor at Muhlenberg College in the United States, annually challenges her students to a unique project: writing their own mathematical biography. As part of this assignment, students answer a variety of questions about their personal experiences studying mathematics. They reflect on what moment in their "mathematical journey" they consider the most significant, who inspires them, what role mathematics plays in their daily lives, and what advice they would give their former selves about studying mathematics. This project not only helps students gain a deeper understanding of their relationship with mathematics but also develops their analytical and writing skills, which are important aspects of a STEM education.

At first glance, it may seem that essay writing is irrelevant in subjects like algebra or geometry. However, reflection in these areas can also play an important role. Understanding mathematical concepts and processes requires not only the mechanical assimilation of formulas but also an awareness of their application and significance. Essays help students not only develop critical thinking skills but also deepen their understanding of the subject matter. They teach students to analyze, compare, and express their thoughts, which facilitates deeper understanding of the material and the development of analytical skills. Thus, reflection is an important element of the educational process, even in such seemingly strictly scientific disciplines.

McGuire emphasizes that social stereotypes dominate the STEM (science, technology, engineering, and mathematics) fields. There is a perception that the sciences are exclusively for men, particularly white men in multicultural societies. As a result, women and ethnic minorities are often underrepresented in these fields, unrelated to their abilities or desire to advance in these fields.

Stereotypical thinking has a negative impact on the educational process, excluding those who do not meet established norms. McGuire cites the definition of a former president of the American Mathematical Association, who characterized such manifestations as "mathematical microaggressions." This is a situation when teachers, through their words or actions, make it clear to a student that they do not fit into the educational environment. Such manifestations can significantly reduce student motivation and limit their opportunities for development in mathematics and other disciplines.

Stereotypes about gender roles sometimes have a significant impact on career choices, especially in the sciences. Many potential professionals fear a negative reaction in advance and decide to study other fields. This is confirmed by the UNESCO report "Cracking the Code," which highlights the problems of girls' and women's education in STEM disciplines. The report's authors emphasize that the gender gap begins in primary school, where teachers often underestimate girls' abilities, and this gap becomes especially noticeable at universities. Ensuring equal opportunities for all genders in STEM fields is an important task for the development of science and technology.

Research shows that specific stigmas are formed in children at an early age. For example, by the age of six, many children begin to accept the idea that boys are more intellectually gifted than girls. This belief can cause girls to lack confidence in their abilities and reluctance to face negative situations. It is important to recognize how such stereotypes can influence children's self-esteem and development, shaping their perception of themselves and the world around them.

According to McGuire, mathematical biography aims to change established stereotypes. However, it is not limited to essay writing; the instructor offers students additional tasks that promote a deeper understanding of the topic.

During the lesson, students are divided into pairs, where each participant shares their mathematical biography, highlighting the key points they consider important. The interlocutor listens attentively and then briefly recounts what was heard, clarifying any details that interest him or her. After this, the students switch roles. Each person is given about five minutes to tell their story, while interruptions and random remarks are not allowed to create a comfortable atmosphere for communication. This approach promotes the development of self-presentation and active listening skills, and also strengthens interaction between students.

Throughout the lesson, group members frequently switch places, which encourages an active exchange of opinions. At the end of the lesson, the group discusses the knowledge gained, shares impressions of what seemed interesting, what common ideas were identified, and what experiences surprised them. The instructor can also share their "mathematical biography," which helps create an atmosphere of trust and friendliness. This approach not only promotes better understanding of the material but also fosters a cohesive team capable of collaborative problem-solving.

The second assignment from McGuire involves creating a personal mathematics tree. Students can include both famous mathematicians and those who have significantly influenced them, and they must justify their choice. Project presentations usually take place at the end of the semester, and beforehand, the instructor conducts several check-ins, allowing students to discuss their ideas and developments during the preparation phase. This assignment helps deepen their understanding of the history of mathematics and develop critical thinking skills.

Students most often include in their projects people with whom they identify. For example, female students often mention famous female scientists, while international students or children of immigrants often mention researchers of the same nationality. In this context, it's worth noting that "forgotten" heroes of mathematics often appear in mathematical trees. These include teachers at the African Free School and female computer scientists who made significant contributions to programming during World War II. Furthermore, some students add talented relatives and ancestors to their tree who were unable to receive a full education or pursue a scientific career. These examples highlight the importance of identity and heritage in the educational process and inspire a new generation of researchers.

Assignments aimed Breaking down stereotypes encourages students to seek support in the mathematical community. This can be achieved through participation in various mathematical associations and communities. Such activities not only develop skills but also build self-confidence, which is especially important for successful mastery of mathematics.

Despite common stereotypes that claim the opposite, mathematics classes are a highly social activity. It is important for students to recognize that mathematical communities are engaging intellectual spaces. This awareness can promote the development of collaboration and knowledge sharing skills, which makes learning mathematics a more engaging and productive process.

How a mathematician searched for his roots and created a global project

Mathematical genealogy is a phenomenon that emerged almost three decades ago, in 1996. The founder of this field was the American mathematician Harry Coons. Inspired by the work of his supervisor, he began to reflect on his own mentor. This quest for roots led him to recognize the need to create a database of mathematicians. However, his idea was not supported by his colleagues, who considered it unrelated to mathematics and doubted the feasibility of such a project. Nevertheless, mathematical genealogy continues to evolve, opening new horizons for researchers and mathematics enthusiasts, allowing us to trace the influence of scientific ideas and the relationships between scientists over time.

Koons didn't abandon his original idea. In the spring of 1996, he sent several hundred letters to mathematicians using the American Mathematical Society's professional directory. He asked for the title of their dissertation and the name of their supervisor. Initially, only 25-30% of the recipients responded, but by September of that year, Koons had published the first 3,500 names. Thus began The Mathematics Genealogy Project (MGP), which has become an important resource for studying connections in mathematics and the history of the dissertation process.

Koons continued to develop his project, launched a website, and even received initial funding from the University of Minnesota, where he worked. However, after his retirement, the university decided to discontinue its support for the project. One of the university's deans explained this move by arguing that "the project has no academic value." In response, Koons posted an announcement on the website urging anyone who disagreed with this opinion to write to the dean. As a result, he received numerous letters of support.

Koons received support from the University of North Dakota, and the project continues to operate under its auspices. Over time, it has gained increasing international popularity. Currently, the MGP database contains over 275,000 names of mathematicians from around the world, significantly simplifying the process of finding participants, eliminating the need for email. Each entry in the database includes the scientist's full name, the name of the university that acknowledged their degree, the year it was awarded, the title of the dissertation, and the name of the supervisor. Some entries also contain links to the MathSciNet and MacTutor History of Mathematics Archive databases, which contain biographies of famous mathematicians. The project continues to evolve, providing access to important information about mathematical achievements and researchers.

Not everyone has complete data on Russian mathematicians. For example, the pages of famous mathematicians may look different.

What mathematicians do with a family tree

This tool allows you to clearly trace the relationships between scientists and the evolution of various areas in mathematics. This allows for a better understanding of how ideas and theories develop and influence each other, an important aspect in studying the history of mathematics.

In 2016, a study found that 65% of scientists in the MGP database belonged to just 24 "mathematical families," while the total number of such families was 84. Interestingly, the founder of the largest family was not a mathematician, but rather the physicist Sigismondo Polcastro, who taught medicine at the University of Padua (Italy) in the 15th century. The second-largest "descendant" was Ivan Dolbnya, a Russian mathematician and director of the Mining University in the late 19th century. However, after a revision of the data, their positions changed. While Dolbnya had nearly 19,000 "descendants" in 2016, today their number has dropped to 827. This is due to the fact that the database is constantly updated, new names are added, and the geography is expanding, allowing for more precise connections between scientists.

The analysis revealed the most important historical changes that influenced the development of mathematics, as well as changes in key scientific directions over the past two centuries. During the Industrial Revolution, the focus was on areas such as thermodynamics, mechanics, and electromagnetism. In the 1950s, the emphasis shifted to telecommunications and quantum physics, while in the mid-2000s, mathematicians began actively exploring statistics and computer science. These transformations highlight the dynamism of scientific progress and the shifting priorities in mathematical research.

Over the past decades, the MGP has been used to analyze the productivity of academic supervisors and assess the prestige of specialized departments at major universities. Researchers use the MGP to identify key indicators that allow for more accurate assessments of scientists' performance and the reputation of educational institutions. This makes the MGP an important tool in the scientific community, contributing to the improvement of the quality of education and scientific research.

The database is used not only for scientific research but also for personal purposes. For example, Russian mathematician Ekaterina Kukina studied it out of pure curiosity. Evelyn Lamb, a mathematician and journalist, decided to create a genealogical chain consisting exclusively of female scientists. The longest chain turned out to be that of Soviet mathematician and RAS Academician Olga Ladyzhenskaya, which counts six female scientific successors. It is important to note that the database contains more than 275,000 names, which highlights the scale of the gender imbalance in the scientific field.

The imbalance in mathematics extends beyond gender. In 2021, researchers from Dartmouth College presented a paper titled "Elitism and Inequality in Mathematics," based on data from the Mathematics Genealogy Project (MGP). This study focuses on the Fields Medal, considered the most prestigious award in mathematics and playing a key role in shaping the field's elite. The paper highlights the importance of examining the inequality and elitism that influence the development of mathematics and its practitioners.

Research shows that French students studying at leading universities where faculty have won awards have the greatest chance of entering the "elite" mathematical circle. Those from Eastern Europe, including Russia, have only slightly lower chances. At the same time, scientists from Arab, African, and Asian countries face significantly fewer opportunities to achieve such excellence in mathematics.

An Indian mathematician with a typical university education is six times less likely to enter the elite than a French mathematician with a similar level of education. This underscores the significant influence of geographic and educational context on the career prospects of mathematics specialists.

The opportunity to participate in prestigious scientific awards directly depends on the educational institution, the academic supervisor, and the openness of these awards to scientists with diverse national and cultural backgrounds. The authors of the study emphasize that both universities and award committees should address this issue and expand opportunities for those underrepresented in the scientific community. This will ensure a more inclusive approach and fair competition in scientific achievements.

Genealogical projects are also beginning to develop in other fields, such as astronomy. These initiatives provide an opportunity to explore the lessons of our own history in depth, draw important conclusions, and, following Professor McGuire's example, set ourselves up for a positive and progressive future. Studying genealogy in the context of astronomy helps us better understand our place in the universe and fosters a deeper appreciation of the connections between historical events and modern achievements.

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