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Zoltán Kovács

Publications and source records attributed to Zoltán Kovács.

At least 19 recordsLinked to original sources

Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs

Following the recent achievement of gold-medal performance on the IMO by frontier LLMs, the community is searching for the next meaningful and challenging target for measuring LLM reasoning. Whereas olympiad-style problems measure step-by-step reasoning alone, research-level problems use such reasoning to advance the frontier of mathematical knowledge itself, emerging as a compelling alternative. Yet research-level math benchmarks remain scarce because such problems are difficult to source (e.g., Riemann Bench and FrontierMath-Tier 4 contain 25 and 50 problems, respectively). To support reliable evaluation of next-generation frontier models, we introduce Soohak, a 439-problem benchmark newly authored from scratch by 64 mathematicians. Soohak comprises two subsets. On the Challenge subset, frontier models including Gemini-3-Pro, GPT-5, and Claude-Opus-4.5 reach 30.4%, 26.4%, and 10.4% respectively, leaving substantial headroom, while leading open-weight models such as Qwen3-235B, GPT-OSS-120B, and Kimi-2.5 remain below 15%. Notably, beyond standard problem solving, Soohak introduces a refusal subset that probes a capability intrinsic to research mathematics: recognizing ill-posed problems and pausing rather than producing confident but unjustified answers. On this subset, no model exceeds 50%, identifying refusal as a new optimization target that current models do not directly address. To prevent contamination, the dataset will be publicly released in late 2026, with model evaluations available upon request in the interim.

cs.CL↗

Automated proving in planar geometry based on the complex number identity method and elimination

We improve the complex number identity proving method to a fully automated procedure, based on elimination ideals. By using declarative equations or rewriting each real-relational hypothesis $h_i$ to $h_i-r_i$, and the thesis $t$ to $t-r$, clearing the denominators and introducing an extra expression with a slack variable, we eliminate all free and relational point variables. From the obtained ideal $I$ in $\mathbb{Q}[r,r_1,r_2,\ldots]$ we can find a conclusive result. It plays an important role that if $r_1,r_2,\ldots$ are real, $r$ must also be real if there is a linear polynomial $p(r)\in I$, unless division by zero occurs when expressing $r$. Our results are presented in Mathematica, Maple and in a new version of the Giac computer algebra system. Finally, we present a prototype of the automated procedure in an experimental version of the dynamic geometry software GeoGebra.

cs.CG↗

GNU Aris: a web application for students

We report on recent improvements to the free logic education software tool GNU Aris, including the latest features added during the Google Summer of Code 2023 project. We focused on making GNU Aris a web application to enable almost all users to use it as a standalone offline web application written in a combination of HTML, JavaScript, and WebAssembly. We used the Qt Quick framework with Emscripten to compile the application to WebAssembly. In the report we summarize the user feedback of university students given during a course on logic.

cs.LO↗

A note on Erdős's mysterious remark

We give an alternative proof of the statement, by using elimination from algebraic geometry, that the only set $S\subset\mathbb{R}^2$, $\left|S\right|=6$ such that all subsets that form a triangle are isosceles triangles, is the regular pentagon with its center. Our proof can be extended to answer some related questions raised by Erdős.

cs.CG↗

The Effect of Ga-Ion Irradiation on Sub-Micron-Wavelength Spin Waves in Yttrium-Iron-Garnet Films

We investigate the effect of focused-ion-beam (FIB) irradiation on spin waves with sub-micron wavelengths in Yttrium-Iron-Garnet (YIG) films. Time-resolved scanning transmission X-ray (TR-STXM) microscopy was used to image the spin waves in irradiated regions and deduce corresponding changes in the magnetic parameters of the film. We find that the changes of Ga$^+$ irradiation can be understood by assuming a few percent change in the effective magnetization $M_\mathrm{eff}$ of the film due to a trade-off between changes in anisotropy and effective film thickness. Our results demonstrate that FIB irradiation can be used to locally alter the dispersion relation and the effective refractive index $n_\textrm{eff}$ of the film, even for submicron wavelengths. To achieve the same change in $n_\textrm{eff}$ for shorter wavelengths, a higher dose is required, but no significant deterioration of spin wave propagation length in the irradiated regions was observed, even at the highest applied doses.

physics.app-ph↗

Solving with GeoGebra Discovery an Austrian Mathematics Olympiad problem: Lessons Learned

We address, through the automated reasoning tools in GeoGebra Discovery, a problem from a regional phase of the Austrian Mathematics Olympiad 2023. Trying to solve this problem gives rise to four different kind of feedback: the almost instantaneous, automated solution of the proposed problem; the measure of its complexity, according to some recent proposals; the automated discovery of a generalization of the given assertion, showing that the same statement is true over more general polygons than those mentioned in the problem; and the difficulties associated to the analysis of the surprising and involved high number of degenerate cases that appear when using the LocusEquation command in this problem. In our communication we will describe and reflect on these diverse issues, enhancing its exemplar role for showing some of the advantages, problems, and current fields of development of GeoGebra Discovery.

cs.SC↗

Solving Some Geometry Problems of the Náboj 2023 Contest with Automated Deduction in GeoGebra Discovery

In this article, we solve some of the geometry problems of the Náboj 2023 competition with the help of a computer, using examples that the software tool GeoGebra Discovery can calculate. In each case, the calculation requires symbolic computations. We analyze the difficulty of feeding the problem into the machine and set further goals to make the problems of this type of contests even more tractable in the future.

math.HO↗

The Locus Story of a Rocking Camel in a Medical Center in the City of Freistadt

We give an example of automated geometry reasoning for an imaginary classroom project by using the free software package GeoGebra Discovery. The project is motivated by a publicly available toy, a rocking camel, installed at a medical center in Upper Austria. We explain how the process of a false conjecture, experimenting, modeling, a precise mathematical setup, and then a proof by automated reasoning could help extend mathematical knowledge at secondary school level and above.

cs.RO↗

Showing Proofs, Assessing Difficulty with GeoGebra Discovery

In our contribution we describe some on-going improvements concerning the Automated Reasoning Tools developed in GeoGebra Discovery, providing different examples of the performance of these new features. We describe the new ShowProof command, that outputs both the sequence of the different steps performed by GeoGebra Discovery to confirm a certain statement, as well as a number intending to grade the difficulty or interest of the assertion. The proposal of this assessment measure, involving the comparison of the expression of the thesis (or conclusion) as a combination of the hypotheses, will be developed.

cs.SC↗

Open Source Prover in the Attic

The well known JGEX program became open source a few years ago, but seemingly, further development of the program can only be done without the original authors. In our project, we are looking at whether it is possible to continue such a large project as a newcomer without the involvement of the original authors. Is there a way to internationalize, fix bugs, improve the code base, add new features? In other words, to save a relic found in the attic and polish it into a useful everyday tool.

cs.PL↗

Proceedings 14th International Conference on Automated Deduction in Geometry

ADG is a forum to exchange ideas and views, to present research results and progress, and to demonstrate software tools at the intersection between geometry and automated deduction. The conference is held every two years. The previous editions of ADG were held in Hagenberg in 2021 (online, postponed from 2020 due to COVID-19), Nanning in 2018, Strasbourg in 2016, Coimbra in 2014, Edinburgh in 2012, Munich in 2010, Shanghai in 2008, Pontevedra in 2006, Gainesville in 2004, Hagenberg in 2002, Zurich in 2000, Beijing in 1998, and Toulouse in 1996. The 14th edition, ADG 2023, was held in Belgrade, Serbia, in September 20-22, 2023. This edition of ADG had an additional special focus topic, Deduction in Education. Invited Speakers: Julien Narboux, University of Strasbourg, France "Formalisation, arithmetization and automatisation of geometry"; Filip Marić, University of Belgrade, Serbia, "Automatization, formalization and visualization of hyperbolic geometry"; Zlatan Magajna, University of Ljubljana, Slovenia, "Workshop OK Geometry"

cs.LO↗

Towards understanding the central limit theorem by learning Python basics

We report on a first experiment about an email based course that connects learning Python basics and introductory probability theory. In the experiment 7 short sequences of homework were sent out to prospective mathematics teachers who did not have any programming background formerly, but already had some minor knowledge on probability theory. The experiment was about to decide if learning basics of programming can promote understanding main concepts of probability theory.

math.HO↗

Automated Discovery of Geometrical Theorems in GeoGebra

We describe a prototype of a new experimental GeoGebra command and tool, Discover, that analyzes geometric figures for salient patterns, properties, and theorems. This tool is a basic implementation of automated discovery in elementary planar geometry. The paper focuses on the mathematical background of the implementation, as well as methods to avoid combinatorial explosion when storing the interesting properties of a geometric figure.

cs.CG↗

Symbolic Comparison of Geometric Quantities in GeoGebra

Comparison of geometric quantities usually means obtaining generally true equalities of different algebraic expressions of a given geometric figure. Today's technical possibilities already support symbolic proofs of a conjectured theorem, by exploiting computer algebra capabilities of some dynamic geometry systems as well. We introduce GeoGebra's new feature, the Compare command, that helps the users in experiments in planar geometry. We focus on automatically obtaining conjectures and their proofs at the same time, including not just equalities but inequalities too. Our contribution can already be successfully used to support teaching geometry classes at secondary level, by getting several well-known and some previously unpublished result within seconds on a modern personal computer.

cs.CG↗

Online Generation of Proofs Without Words

Understanding geometric relationships with little mathematical knowledge can be challenging for today's students and teachers. A new toolset is introduced that is able to create a proof without words by combining the benefits of the Geometric Deduction Database method (to obtain a readable proof of a geometric statement) and the GeoGebra framework (that makes it possible to export these data as an online applet in a simple way).

cs.LO↗

GeoGebra Discovery in Context

In our contribution we will reflect, through a collection of selected examples, on the potential impact of the GeoGebra Discovery application on different social and educational contexts.

cs.HC↗

Supporting Proving and Discovering Geometric Inequalities in GeoGebra by using Tarski

We introduce a system of software tools that can automatically prove or discover geometric inequalities. The system, called GeoGebra Discovery, consisting of an extended version of GeoGebra, a controller web service realgeom, and the computational tool Tarski (with the extensive help of the QEPCAD B system) successfully solves several non-trivial problems in Euclidean planar geometry related to inequalities.

math.LO↗