Honestly, I have had issues with the standard models too. It is quite disappointing that OpenAI ChatGPT Plus with GPT-4o still hallucinates complex proofs despite the hype. I tried relying on it for stochastic differential equations last semester, but the logic was frequently flawed. Unfortunately, even Anthropic Claude 3.5 Sonnet fails when the LaTeX strings get too dense, often losing track of signs during long derivations. If you want something reliable, you really need to use the Wolfram integration. I eventually moved to a Wolfram Alpha Pro Subscription for the heavy lifting. The main drawback is that it wont explain the logic as intuitively as a dedicated LLM. For a more integrated experience, the Wolfram GPT within the ChatGPT interface is likely your best bet, though it still requires you to manually verify that the tool actually triggered. It isnt as good as expected, but it beats double checking every sign yourself.

Jumping in here because I have been down this exact rabbit hole way too many times while working on quant finance papers. In my experience, the biggest mistake is treating an LLM like a calculator when its really just a spicy autocomplete engine. Over the years, I have tried basically everything to get stochastic calculus right without pulling my hair out. I actually had some decent luck with Google Gemini 1.5 Pro. Since it has that massive context window, you can feed it whole chapters of a textbook for context which helps it stay on track. It still trips over the actual Itos Lemma derivations sometimes tho, so you gotta be careful. Ngl, its way better at explaining the theory than actually grinding out the proofs. If you need actual symbolic reliability, I usually tell people to skip the chat bots and use MathWorks MATLAB R2024a with Symbolic Math Toolbox. It isnt a chat AI, but its the only way I have found to get 100 percent accuracy on long derivations without the hallucinations. Another one I used back in the day was Maplesoft Maple 2024 Symbolic Computation Software. Its a beast for stochastic differential equations if you know the syntax. Honestly, using a pure LLM for high-stakes thesis work is risky... usually ends up being more work to double check the AI than to just use a proper symbolic engine from the start.

Like someone mentioned, these models are basically just spicy autocomplete, and honestly? I disagree that finding a better model is going to solve the problem right now. I would suggest being super cautious about trusting any AI with stochastic calculus derivations for a masters thesis. The logic is just too fragile. You might want to consider using them only for high-level conceptual summaries rather than the actual math. I have seen way too many people get burned by trusting the pretty LaTeX output, only to find a sign error on line two that ruined everything. Also, be careful with those premium math-specific tools... they are often expensive and still trip over the same hurdles as the standard LLMs. It can become a real money pit for a student. TL;DR: Be cautious with your budget and your logic; dont trust AI for multi-step calculus without checking every single character manually.