GPT-4.5 and GPT-4 both demonstrate advanced capabilities in solving complex mathematical problems, including calculus. However, their performance can be distinguished based on specific improvements and focus areas.
**GPT-4 is known for its significant advancements over its predecessors, particularly in handling complex mathematical and scientific tasks. It can effectively solve advanced calculus problems, simulate chemical reactions, and analyze complex scientific texts. This model's ability to process nuanced instructions and its enhanced contextual awareness make it more reliable for complex problem-solving compared to earlier versions like GPT-3.5[1][5][7].
**GPT-4.5 builds upon the strengths of GPT-4 by offering improvements in several areas. It shows a notable increase in mathematical performance, with a 27.4% improvement over GPT-4o in math-related tasks[2]. This suggests that GPT-4.5 is more reliable for factual reasoning and mathematical problem-solving. However, it is designed more as a general-purpose model, adept at creative and nuanced tasks rather than detailed step-by-step logic or multi-step reasoning[6].
In terms of calculus specifically, while GPT-4.5's improvements in math are significant, it is not specifically tailored for advanced logical reasoning or multi-step mathematical derivations like some other models (e.g., o-series models). Therefore, for tasks requiring detailed calculus derivations or complex mathematical proofs, GPT-4 might still be competitive, but GPT-4.5's broader improvements could make it more versatile for a wider range of mathematical and scientific applications.
Overall, GPT-4.5 offers enhanced performance in math and science compared to GPT-4, but its strengths lie more in its general-purpose capabilities and reliability across various tasks rather than specialized mathematical problem-solving.
Citations:
[1] https://www.searchenginejournal.com/gpt-4-vs-gpt-3-5/482463/
[2] https://www.vellum.ai/blog/gpt-4-5-is-here-heres-how-good-this-model-is
[3] https://pmc.ncbi.nlm.nih.gov/articles/PMC10884900/
[4] https://cdn.openai.com/gpt-4-5-system-card.pdf
[5] https://openai.com/index/gpt-4-research/
[6] https://help.openai.com/en/articles/10658365-gpt-4-5-in-chatgpt
[7] https://www.kommunicate.io/blog/chatgpt-4-vs-chatgpt-3-5-key-differences/
[8] https://www.techtarget.com/searchenterpriseai/tip/GPT-35-vs-GPT-4-Biggest-differences-to-consider
[9] https://neoteric.eu/blog/gpt-4o-vs-gpt-4-vs-gpt-3-5-comparison-in-real-world-scenarios/