- Theorem: Every girl is blonde 1
- Proof. It is sufficient to show that in every set of girls, any two members have the same hair color. As there exists at least one blonde girl. And all the girls form a set.
- We prove the italicized statement by induction on the size of the set. If the size is one, the statement is clearly true. Suppose that the statement holds for every n element set of girls, and consider an n+1 element set: S = {Kate, Julie, Ann, Elisabeth, …}. If Kate is dropped from S, then an n element set remains, and by the induction assumption, every girl in this subset has the same hair color, say X. Similarly, if Julie is dropped from S, then in this subset the hair color is uniform. But Ann’s hair is of color X, and so the same holds for Kate. Therefore, the hair color is uniformly X in S, too.
For many the above proof might look correct, but it is trivial that the statement is not true.
To start the page with this math ‘joke’, I wanted to point out the importance of logical thinking, because what would happen to us in a world where there are only blond girls:)
Section is under development
My goal is to organize some of my notes into accessable format, write about topics I am interested in and create though provoking articles. The writing of such things take time and I only have little time to spare for such efforts, but I hope with time I will realize at least some of my ambitions to share knowledge in my site.
For now, I am updating the extended version of my handwritten lecture notes on Latin squares, which can be found here.
Recommendations
General recommendations
- I strongly recommend to all the videos of Grant Sanderson on the channel of 3blue1brown
- For computer assisted problem-solving tasks I recommend the Project Euler site
- If you want to learn about LLMs and modern AI systems in depth I strongly recommend Andrej Karpathy's videos
For non-Hungarian high school students and teachers
As a current organizer, I can recommend to all interested in competitive math at the highest level to participate in the international edition of the Durer competition. For participants, it is free, and there are usually many interesting problems created by former Hungarian IMO team members.
As a teacher, you can also apply to be an official location where local children can participate in person. In this case, the possibility to translate the problems into your own language is given. Details can be found at durerinfo.hu. If you have any questions, email maths@durerinfo.hu.
For STEM students at ELTE
- I can only encourage peoples interested in pursuing a STEM career in Hungary to attend the math BSc at ELTE as there are great teachers and great students. As the program structure has changed a few years ago, so I am only partially up to date with the current structure, but if you have questions feel free to reach out to me.
- I strongly recommend joining an advanced study college there. Either the Bolyai Collage focusing on STEM or the Eötvös College, which is interdisciplinary and welcomes nearly any discipline.
- I can suggest participating in some voluntary program / extracurricular activity such as joining the Matematika Összeköt egyesület, or programs of the Joy of Thinking Foundation, such as organizing the Durer competition or the Repülő Iskola. Helping with the KöMaL edition or problem correction is also a good way to engage with the STEM community. Most of these organizations can be welcoming even if your main interest is not in mathematics.
For Hungarian school students
For Hungarian high school students interested in the STEM disciplines, I am wholeheartedly recommending all activities of the Joy of Thinking foundation. If you are interested in math competitions, you should visit the Joy of Thinking Medium site, where there are suggested competitions and activities based on age groups and interests from the beginning of school up until adulthood.
If you are not looking to make the team for the Olympiad, but just want to enjoy interesting math problems and have fun, I recommend the Durer Competition, which is a team competition in math, physics, and chemistry. Its final is a two-round competition with lots of fun and free-time activities over three days. I, like most, started volunteering as an organizer after having an amazing experience during the competition as a participant. I would also strongly suggest the events of Medve Matek. Even though I only have limited experience with it, I have heard many great things about it from both participants and organizers. Both of these organizations operate mostly through the voluntary work of university students and fresh graduates enthusiastic about math.
If you are more interested in higher-level competitions, the monthly problem-solving competitions of ABACUS (3rd–8th grade) and KoMaL (9th–12th grade) provide a good opportunity to regularly work on interesting problems aimed at your skill levels.
If you are interested in the highest level of competitive high school mathematics and aiming for the Olympiads, then visit the official site of the Olympiad preparation. I strongly recommend for all girls interested in competitive math the preparation for EGMO. Since 2019, there has been a specific program for this, and I have heard from many girls who participated in the preparation that it had a lasting effect on their motivation to solve problems. For the most ambitious, I can recommend the Olimpiai Iskola program, organized by András Imolay and other former IMO participants, with the aim of preparing current students to achieve their best through rigorous preparation.
If you are looking for math activities for yourself or for your children in Hungary and couldn’t determine the best possibilities based on the above, feel free to reach out to me or to the Joy of Thinking foundation.