text: **Mathematics**
  In mathematics, special forms of formal step-by-step reasoning are used.[154] In contrast, LLMs such as 
  *GPT-4 Turbo*,*Gemini Ultra*,*Claude Opus*,*LLaMa-2*or*Mistral Large*are working with probabilistic 
  models, which can produce wrong answers in the form of hallucinations. Therefore, they need not only a 
  large database of mathematical problems to learn from but also methods such as supervised fine-tuning or 
  trained classifiers with human-annotated data to improve answers for new problems and learn from 
  corrections.[155] A 2024 study showed that the performance of some language models for reasoning 
  capabilities in solving math problems not included in their training data was low, even for problems with 
  only minor deviations from trained data.[156] 