ARCHIVES

The purpose of this study is to investigate the importance of model scale in solving challenging mathematical problems, identifying the four most significant elements: learnt model scale, computational time expectation, search diversity, and verification. Results from the harder twenty problem set saw the Ministral 3.5 comparator obtain 19/20 while the GPT counterpart got 16/20, pointing towards the possibility of lower-scale models being able to solve many hard problems. However, the outcome was different when examining 5 constant problems, with Ministral proving correct in 3/5 cases, but failing in a logarithmic integral (T9) and constrained global optimization (T18), while the later GPT model was accurate on all 5 problems. The use of repeated search methods in Ministral allowed for the improvement of the results of combined T9+T18 from 10/40 (25%) to 25/40 (62.5%) without any changes in the model parameters used; later attempts of the GPT using different approaches also yielded a much higher percentage of 39/40 (97.5). Being aware that the later records were not independent and controlled tests of model size also allow us to draw the conclusion of the study itself, which states that although scale contributes significantly to the development of the most complicated problems, search technique and verification practice assist in minimizing a gap by eliminating.