Of course, she admits the best part of her job is the research, but she greatly enjoys the opportunities to teach and interact with students - adding that the immediate rewards that come with teaching can sometimes be more satisfying than the occasional \u201cEureka!\u201d moments one has when doing research. <\/p>\r\n
\u201cI love seeing the stars in the students\u2019 eyes when they learn a new concept\u201d <\/p>\r\n
she adds with a smile. <\/p>\r\n
Whether it\u2019s undergraduate classes, more advanced optional classes or research seminars, she thrives when presenting mathematics - from the very fundamental to the arcane details of her own work. Her favourite, though, is working with first-year Bachelor students - \u201ca big audience of young people that are new to the field\u201d, in her own words. She recalls her own first year and how it felt like her brain was being reset, and takes great joy in initiating the same in the new generations of scholars at UniGe. <\/p>\r\n
Her own choice to study math happened by chance: Professor Bucher knew she was good at the subject, but wasn\u2019t certain what she wanted to do, and picked mathematics as a solid place to start. For her, the moment when she realised that she wanted to do research as a career was not an instant in time, but rather a continuous process and the culmination of various motivating factors. She enjoyed the subject, her professors encouraged her to stay in the field, and it was a natural step forward. Not everything was perfect: at one point, she found herself limited in options and applied for a single position, with the mindset that she would quit math if she didn\u2019t get it. Professor Bucher laughs as she recalls the anecdote: she isn\u2019t sure if she would have followed through with that decision. Thankfully she didn\u2019t have to, as she got the job.<\/p>\r\n
This article is part of a three-part series by volunteers Yuta Mikhalkin and Tanish Patil. Read the conversations with David Cimasoni <\/a>and Anders Karlsson<\/a> as well! <\/p>\r\n Explaining what you do to a layperson is always a challenge, but Professor Bucher is more than up to the challenge. \u201cI work in the intersection between geometry and topology, and one concept which comes up regularly in my work is called the Euler characteristic\u201d. You may have already heard of the famous equation that relates the faces, edges and vertices of a polyhedron: F - E + V = 2. Where does this come from, though, and what is the significance of the 2? Professor Bucher asks us to imagine \u201cprojecting\u201d the polyhedron onto a sphere - drawing 8 points, and 12 lines connecting them - and remarks that having the sphere as a basis on which to draw our polyhedra makes proving the combinatorial fact that F - E + V = 2 much easier. Furthermore, it\u2019s now easy to see that the value 2 is intimately associated with the sphere - if we change the surface we\u2019re projecting onto (for example, a torus, or donut) we\u2019d instead get a different value (namely, 0). The fact that the value is equal to 2 for the sphere has further implications: one, says Professor Bucher, is the famous \u201chairy ball\u201d theorem (you cannot comb a ball covered in hair without creating a cowlick - or, in mathematical terms, \u201cthere is no nowhere vanishing vector field on a sphere\u201d.) And why restrict ourselves to two dimensions? We can stretch our analysis to higher dimensional objects as well - with a little imagination and a lot of math! Professor Bucher might feel right at home with topological invariants, but during her Master\u2019s thesis, she did a lot of work in geometric group theory, and admits she returns to it from time to time. Mathematicians don\u2019t have to restrict themselves to their specialisation. Her work has had applications in a variety of fields, though she considers \u201cthe most exotic application to have been in combinatorics, in counting problems.\u201d <\/p>\r\n When it comes to research, many wonder whether certain branches of mathematics offer more opportunities than others. According to Professor Bucher, open questions can be found everywhere, even in fields often considered \u201cclosed,\u201d such as linear algebra or general topology. <\/p>\r\n \u201cI feel many people get the wrong impression of some subjects taught in the first or second year of university \u2013 those courses make them seem so concise that it looks as though they extend only as far as what has been taught.\u201d <\/p>\r\n In particular, nearly every branch reveals numerous applications as time goes on: \u201cfor example, linear algebra is very active right now, applied to various algorithms for data processing and machine learning.\u201d Of course, at times certain topics become trendier than others, meaning that at a given moment more people focus on them \u2013 sometimes because they offer more applications in connection with current technology advancements \u2013 but that does not mean they have more to offer overall. Although Michelle Bucher is a pure theoretician \u2013 she has only ever collaborated with fellow mathematicians and never with researchers from other fields \u2013 she considers the applications of mathematics, and the new fields they generate, to be truly beautiful. The rise of branches combining mathematics with sciences such as biology or chemistry (such as mathematical biology <\/i>or mathematical chemistry<\/i>) represents highly interesting projects, as long as they are not motivated by funding solely: indeed, universities tend to devote far more resources to research that involves applications. Ultimately, she sees mathematics as a living discipline, one that continually expands its horizons \u2013 whether within its own foundations or through the bridges it builds to other sciences. <\/p>\r\n Why do research, as opposed to working in industry? Professor Bucher offers two answers.<\/p>\r\n \u201cOn a personal level, you should do it if you like it. But in general, research in fundamental mathematics is important and ideas should develop freely, without considering what the applications might be down the line - and many results that are today considered useful fall into this category.\u201d <\/p>\r\n Professor Bucher lists knot theory as an example \u2013 both useful in other areas of mathematics (topology, in particular for studying three-dimensional manifolds) and other sciences (for instance, in biology, when studying the structure of DNA). And where does Professor Bucher find new challenges at the end of a long paper or research project? She describes it as a continuous process: the end of one question opens doors to a world of new inquiries. How can you generalise your result? What other corollaries follow from your work? Are there any natural conjectures to make? Mathematics is collaborative, and colleagues are a valuable source of inspiration for what to do next.<\/p>\r\n Over the past ten years \u2013 and especially during the pandemic \u2013 the ways of communicating in mathematics have changed drastically. Instead of always having to travel across the world to take part in a conference on a topic of interest, it has now become possible to share ideas or attend such events online. In Michelle\u2019s opinion, although it is sometimes convenient to call a colleague over Zoom to discuss a topic or a question, in-person conferences should forever remain a major part of a mathematician\u2019s work life. \u201cIt\u2019s not only about the talks themselves or the few questions you might ask the lecturer after them, it\u2019s also the minor interactions you have at coffee breaks when you\u2019re discussing the talks, and then all of a sudden you have a new idea, or another question just pops. Or you could be talking to someone about what you\u2019re currently working on, and they could ask something you haven\u2019t thought of or mention they know someone working on a related problem.\u201d As for collaborations, the professor believes that video calls can certainly be helpful and speed up progress, but they typically begin in person, where the main ideas are first discussed and developed, in the same room, with the blackboard and over coffee. Also regarding attention, it is naturally much easier to concentrate during an in-person lecture, where there are no distractions or temptations to take a \u201cquick break to grab a snack.\u201d Reciprocally, when teaching or giving a talk online, you cannot see your listeners\u2019 reactions in the same way as when you are physically in front of them. \u201cSo overall, it\u2019s just not as pleasant\u201d \u2013 says Michelle Bucher. Regarding her own travels around the world during her studies, she sees a great value in visiting many places and learning from the way things work at different math departments around the world. \u201cIt can happen [that someone spends their entire career in one institution] but I think it\u2019s important to go abroad, to get ideas from other universities, see how teaching can be done differently.\u201d <\/p>\r\n When asked whether she believes we should fear AI gaining dominance in mathematical fields, Michelle Bucher replies that we should rather learn to coexist and work with it instead. Just as we first adapted to calculators and then to computers, we can adjust to AI so that it handles tasks we theoretically know how to do but find tedious or simply lack the time and memory to complete. \u201cI definitely think it can be a big help,\u201d she says. \u201cIt will in my opinion never be more than just a tool \u2014 we always need, and will always need, a human brain to guide the machine and check its work. I do not think that there\u2019s any risk of it replacing us\u201d. Ultimately, it\u2019s not a threat but a powerful tool that, when guided by human insight, can enhance our capabilities without ever replacing the need for human reasoning. <\/p>\r\n The question was: \u201cIs it possible for two different and incoherent theories to be built on the same base?\u201d Michelle Bucher\u2019s answer was simple: <\/p>\r\n \u201cIf the logical axioms are the same and consistent, then no \u2013 and that\u2019s what\u2019s beautiful about mathematics. When I first entered the field, that\u2019s exactly what I loved the most about it: everything is either true, false, or unknown; there\u2019s no half-truth. That\u2019s why you know that if something doesn\u2019t add up, then there\u2019s necessarily a mistake somewhere.\u201d <\/p>\r\n Such a situation has happened to the researcher herself: \u201cI had found that a certain invariant was equal to something like 6, which contradicted a published result, and I had triple-checked all my work. So I somehow naively sent the authors an email, suggesting that their proof might be wrong, which they naturally though politely dismissed \u2013 the thing was, I couldn\u2019t publish my paper as long as theirs was still out there as two contradictory results cannot hold simultaneously, and not many would have believed a young inexperienced researcher. A few months later, I had identified the issue in their proof and after pointing it out, they immediately wrote a correction, and I could finally publish my results.\u201d In research, such situations occur fairly often, but they are usually resolved quickly. \u201cAnother thing is there\u2019s a remarkable honesty about mistakes in the mathematical community. We make mistakes, and to be honest I\u2019m glad I\u2019m not a medical doctor\u201d \u2013 shares Bucher.<\/p>\r\n About a hundred years ago, building a career in science as a woman was nearly impossible. While things have generally improved with time, Michelle Bucher believes that being a woman in mathematics actually offered more advantages when she was a student than it does today. Back then, if you were bright, you would automatically attract more attention \u2013 in a positive way \u2013 than a man. Now, however, disparaging remarks abound. <\/p>\r\n \u201cSo if I were to give advice to young girls, I would say: if you like maths go for it, let the passion for the subject be stronger than any discriminative comments you might get \u2013 an advice that holds for men as well as for women.\u201d<\/p>","datetime":1763478600,"datetimeend":0,"newstype":1,"newstypetext":null,"links":"","subjects":["Sapere","Pari opportunit\u00e0","Suggerimenti"],"image":["https:\/\/science.olympiad.ch\/fileadmin\/_processed_\/2\/a\/csm_Michelle_Bucher_photo_22d134f3c3.png"],"link":"https:\/\/mathematical.olympiad.ch\/it\/notizie\/news\/everything-in-mathematics-is-either-true-false-or-unknown-theres-no-half-truth","category":[{"uid":10,"title":"Matematica"},{"uid":5,"title":"Startseite"}]},{"uid":4774,"title":"Jetzt f\u00fcr die Vorrunde der Philosophie-Olympiade 2025\/2026 \u00fcben","teasertext":"Letztes Jahr hat sich die Philosophie-Olympiade ver\u00e4ndert. Zum ersten Mal startete der Essaywettbewerb mit einer Vorrunde. Diese bliebt auch im kommenden Schuljahr bestehen. Wer schon ein bisschen \u00fcben und den Stil der Fragen kennenlernen will, kann jetzt den Test vom letzten Jahr l\u00f6sen.","short":"Letztes Jahr hat sich die Philosophie-Olympiade ver\u00e4ndert. Zum ersten Mal startete der Essaywettbewerb mit einer Vorrunde. Diese bliebt auch im kommenden Schuljahr bestehen. Wer schon ein bisschen \u00fcben und den Stil der Fragen kennenlernen will, kann jetzt den Test vom letzten Jahr l\u00f6sen.","body":" Letztes Jahr startete die Philosophie-Olympiade erstmals mit einem Multiple-Choice-Test vor der ersten Essayrunde. Diese Vorrunde wurde entwickelt, weil der Aufwand f\u00fcr die Bewertung der Essays mit steigenden Teilnahmezahlen f\u00fcr unsere Freiwilligen nicht mehr zu bew\u00e4ltigen war. <\/p>\r\n Wir wollten nicht nur Vorwissen pr\u00fcfen, daher haben wir einen Test konzipiert, von dem wir hoffen, dass er F\u00e4higkeiten testet, die einem auch dabei helfen, einen guten Essay zu schreiben. Zum Beispiel logisches Argumentieren oder das philosophische Verst\u00e4ndnis von Zitaten aus Prim\u00e4rtexten, die oft als Essaythemen dienen. <\/p>\r\n Die neue Vorrunde fand grossen Anklang: 1123 Sch\u00fcler*innen aus \u00fcber 80 Schulen in 24 Kantonen und dem F\u00fcrstentum Liechtenstein haben den Online-Test gel\u00f6st. Der bisherige Teilnahmerekord der Philosophie-Olympiade lag bei 172 Teilnehmenden letztes Jahr. Durch die Einf\u00fchrung einer neuen Vorrunde und die Teilnahme vieler Lehrpersonen mit ihren ganzen Klassen hat sich diese Zahl fast um das 7-fache erh\u00f6ht!<\/p>\r\n Daher bleibt die Vorrunde im Schuljahr 2025\/2026, mit einigen Anpassungen basierend auf dem Feedback von Lehrpersonen und Teilnehmenden. Zum Beispiel dauert der Test neu 45 statt 30 Minuten, mit mehr Fragen, um die Bedeutung des Zufalls zu reduzieren.<\/p>\r\n Die Vorrunde 2025\/2026 finden vom 1. September bis 5. Oktober 2025 auf OlyPortal<\/a> statt. Mehr erfahren.<\/a><\/p>\r\n Wer sich jetzt schon vorbereiten m\u00f6chte, kann sich auf <\/font>OlyPortal <\/font><\/a>registrieren und dort als Probetest den Test vom letzten Jahr l\u00f6sen. So kann man sich nicht nur mit dem Stil der Fragen, sondern auch mit der Plattform vertraut machen, auf der der Test stattfinden wird. Bewahre die Login-Daten gut auf - du wirst sie im September wieder brauchen!<\/font><\/p>\r\n Wenn du dich noch nicht registrieren magst, findest du den Test und das Bewertungsschema auch als PDF im <\/font>Brain Food Archiv.<\/font><\/a> Liebe Lehrpersonen, falls Ihnen eine Frage gef\u00e4llt, d\u00fcrfen Sie diese gerne weiterverwenden. <\/font><\/p>","datetime":1751990940,"datetimeend":0,"newstype":1,"newstypetext":null,"links":"","subjects":["Sapere","Compiti ed esercizi"],"image":["https:\/\/science.olympiad.ch\/fileadmin\/_processed_\/0\/4\/csm_54375739399_879faf15c3_c_8761e4ce47.jpg"],"link":"https:\/\/philosophy.olympiad.ch\/it\/news\/news\/jetzt-fuer-die-vorrunde-der-philosophie-olympiade-2025\/2026-ueben","category":[{"uid":1,"title":"Filosofia"},{"uid":5,"title":"Startseite"}]}],"offset":3,"hasmore":1}