A "reduced fraction" is a fraction that has the smallest possible integer numerator and denominator for its value.
For example:is not a reduced fraction, because there is another fraction equal to it but with smaller numerator and denominator:
Hilbert's tenth problem is decidable for quadratic equations Updated 2025-06-17 +Created 2024-07-12
TODO is it or is not:
- mathoverflow.net/questions/207482/algorithmic-un-solvability-of-diophantine-equations-of-given-degree-with-given
- math.stackexchange.com/questions/181380/second-degree-diophantine-equations
- mathoverflow.net/questions/142938/is-there-an-algorithm-to-solve-quadratic-diophantine-equations
- math.stackexchange.com/questions/798609/is-there-any-solution-to-this-quadratic-diophantine-equation
mathoverflow.net/questions/11540/what-are-the-most-attractive-turing-undecidable-problems-in-mathematics/11557#11557 contains a good overview of the decidability status of variants over rings other than the integers.
Decidability of Hilbert's tenth problem of a given degree and number of variables Updated 2025-06-17 +Created 2024-07-12
Decidability of Hilbert's tenth problem in modular arithmetic Updated 2025-06-17 +Created 2024-07-12
E.g. International Mathematical Olympiad, International Physics Olympiad, competitive programming, etc.
Events that trick young kids into thinking that they are making progress, but only serve to distract them from what really matters, which is to dominate a state of the art as fast as possible, contact researches in the area, and publish truly novel results.
Financially backed by high schools trying to make ads showing how they will turn your kids into geniuses (but also passionate teachers who fell into this hellish system), or companies who hire machines rather than entrepreneurs.
The most triggering thing possible is when programming competitions don't release their benchmarks as open source software afterwards: at least like that they might help someone to solve their real world problems. Maybe.
Some irrelevant people highlight that knowledge Olympiads can have good effects, because they are "an opportunity to meet university teachers and their research organizations". Ciro's argument is just that there are much more efficient ways to achieve those goals.
As an alternative way to get into university, this is not 100% horrible however, e.g. the University of São Paulo accepted students from olympiads in 2019 and then again 2023: jornal.usp.br/institucional/usp-oferece-200-vagas-em-mais-de-100-cursos-de-graduacao-para-alunos-participantes-de-olimpiadas-do-conhecimento/?a
Resources to study for knowledge olympiads:
- savchenkosolutions.com contains collaboratively created solutions to the Savchenko Problems in Physics. It appears to be a frontend for: github.com/savchenko-physics/savchenko-solutions. Closed license, kind of sad.
There are unlisted articles, also show them or only show them.