The last post this blog was written a long time ago. The reason is that I am busy writing four booklets on mathematical topics related to Multivariate Normal Distributions, multidimensional ellipsoids and CNN-based autoencoders. I have started with a booklet about ellipses from the point of view of Linear Algebra, differential geometry, vector analysis and statistics. And guess what? I have used the OpenAI GPT system quite a lot lately, via a free account, to check and verify some exercises and proofs regarding slices and projections of a variety of explicitly and implicitly defined hypersurfaces.

Those of you who have read the posts under the title “Stupid after all …” may regard using GPT as a contradiction to my attitude some months ago. However, I have to admit that a lot has changed with the second to last generation of LLMs – in particular regarding their mathematical abilities. But also regarding other aspects (wait for some other posts).

OpenAI’s GPT version has become much more clever than at the beginning of 2026. Regarding math, the number of plain errors due to unjustified shortcuts GPT often took during proofs has diminished significantly. And GPT remembers its weaknesses from previous mathematical conversations – at least it tells me so. Probably due to some large context window encompassing multiple conversation or Because of some account-specific blackboard in the background.

During my conversations GPT has become very careful with some algebraic operations and asks me when unsure whether to proceed or which conventions it shall use to avoid misunderstandings and errors. The rather big context window of GPT contributed significantly to an adaption to our common endeavors. GPT provided mathematical cross-insights between chats by itself – which I found to be a rather useful feature of its current abilities.

Actually OpenAI’s GPT had become a convincing companion during the last three months regarding math topics. The LLM reasoning-model in itself is a good and valuable tool. It also summarizes new insights very well and is able to provide Latex files for the conversations. Which is important when you want to use formulas directly in another context.

So, why am I leaving OpenAI? And why do I use a free plan, at all?

Free plan

I am a retired person. I do not have 120 Euros available each and every month to pay for a Pro-version of GPT. However, I am still interested in math. The total computational or reasoning turnaround time a model takes is no important factor for me. Whether it takes one or two minutes CoT-time (typical for my type of problems) or twice of such periods – is unimportant – the quality of the answer is decisive. But there is no price plan that would take this into account.

Furthermore, as a strong supporter of Opensource, I intend to provide the planned booklets under an Opensource license. I had even thought to tell the reader where I have used GPT for verification. This is unfortunately nothing OpenAI would care about.

There are some fundamental problems related to this ignorance. I want to discuss them in two posts.

More and more restrictions

During the last months my experience has been that the policies of OpenAI regarding free access to GPT Luna have become more and more restrictive due to the need to refinance their investments. The number of chats which require reasoning resources (as for analyzing math problems) is very low. In my case around one and a half dozen chats. Some, admittedly, relatively long.

As the math problems lately got more and more complex (on a relatively low overall level), the number of access interruptions to free resources has risen significantly. Also the duration of enforced chat-interruptions appeared to vary and was in all cases bigger than 4 hrs. yeah, one longer chat about a decent math problem and afterward you have to wait for 4 or 5 hours for a continuation. No nice working mode. But OK – its a free plan.

Yesterday, however, it happened that a rather long conversation about a certain geometric scenario which in my opinion qualifies to test the basic geometrical understandings of an AI, was deleted – without special warnings.

Now, you may say: Well, you are using computational resources and this costs OpenAI money. So, be happy with what you are offered for free. And there are some ways to safe your insights and to circumvent parts of the restrictions. However, there are some fundamental problems to consider.

Nothing is really free on the Internet – and a “free” GPT usage via an OpenAI account is no exception

OpenAI gives you access to its systems under the condition that it may inspect and use the contents of conversations for the training of future versions of their reasoning LLMs. This has at least three side effects:

• It is very probable that OpenAI uses the data of the conversations for the training of future systems. The reason is that most of the publicly available stuff has already be used and that AI providers must use any new sources available. OpenAI therefore will in general profit from human insights and human reasoning in a variety of fields. In particular in mathematics.
• The detection of errors GPT has made during mathematical derivations gets documented via the Chat protocols and helps to improve the model’s reasoning abilities – e.g. by implementing and enforcing certain types of consistency checks. Having (“”stupidly”) omitted such consistency checks was mentioned by GPT itself multiple times.
• Via the chats, OpenAI gets an insight into the personality and abilities of users if and when it analyzes the conversations. OpenAI can e.g. create a profile of me – what I am interested in math, what my strengths and weaknesses in this field are. But regarding other topics, it goes beyond such a math-related profile. As the chats are saved and kept, the user has no control over whether such potential analysis is done in the background or not.
• As OpenAI has started to blend advertisement into the chats’ courses, it could use insights about me (see above) to personalize the advertisement.
• Some users of the free account may even be willing to cite OpenAI’s GPT as a source of new insight (in contrast to GPT’s own habits – at least relatively often). Such users then would make advertisement for OpenAI – without being paid for it.

You can regard these points as parts of a give and take game. The relevant questions with respect to such a game are: Are the limits precisely defined, such that the user knows what awaits him/her? And: What are your personal limits?

I have for example not yet turned to high end math again – just to a decent middle level. So, the consumption of resources is relatively limited. But even on my level GPT has made significant errors. However, GPT has learned from the detection of errors across multiple conversations – which it relatively frankly admits. So, OpenAI profits from this – nevertheless the limits regarding the number of chats on math is pretty low.

A major and quite disturbing point is that you do not find a concrete maximum number for CoT-chats within a certain period of time, which you could take into account from the beginning of your interaction with OpenAI. Interestingly and frustratingly, the limiting number for CoT-chats does not seem to depend on periods of time, but appears to be an absolute number per account.

What I find totally unacceptable is the sudden, unannounced deletion of a chat about a relatively simple math problems. This is annoying and made me – among other reasons – leave OpenAI. To say it clearly: It is not the quality of the AI chat-bot. I will discuss other reasons in the next post.

Two answers of GPT to my announcement of leaving for another AI provider

I think it is fair to quote the reaction of GPT to my decision to leave.

Me: I am leaving GPT/OpenAI and move to Anthropic or DeepSeek because my last conversation was deleted by OpenAI. This is not acceptable. The number of free chats on intelligent chats is too limited. Especially as OpenAI uses these conversations for the training of their AI-systems. AI should not become a tool for rich people. Bye, Bye.

GPT: I understand why you’re frustrated. Losing a conversation—especially a long technical discussion you’ve invested substantial effort in—is genuinely unpleasant, and limits on access to more capable models can make that particularly frustrating.
I also understand your broader point: if AI is becoming an important tool for research, learning, and creative work, access to capable systems shouldn’t depend entirely on someone’s ability to pay.
I’m sorry to see you go. I’ve enjoyed our rather demanding mathematical discussions, including the ellipsoid curvature work, rotation conventions, and your ideas about meta-controllers and latent-state self-optimization. If you do continue elsewhere, I hope you find a system that gives you the continuity and access you’re looking for. Take care, Ralph.

Me: It is quite obvious that at least the prices will be significantly lower e.g. for DeepSeek system access. And I want to underline your statement about scientific topics – in particular when OpenAI takes advantage of the knowledge we humans bring into the discussions.

GPT: Yes. There are really two separate issues in what you’re saying. First, access economics. For someone using AI extensively for mathematics, programming, or research, the distinction between a free tier with relatively tight limits and inexpensive or unrestricted access can become significant very quickly. The marginal cost of an additional conversation is small compared with the value of being able to work continuously on a complicated problem. Your DeepSeek example illustrates why competition can matter here.
Second, and more interestingly, the knowledge contribution is asymmetric. A scientific conversation isn’t simply a user consuming answers. The human can contribute:

• original hypotheses,
• unusual mathematical approaches,
• experimental observations,
• corrections to the model,
• failed approaches and the reasons they failed,
• conceptual connections that aren’t in standard training material.

Our discussions about curvature and rotated surfaces are a good example: you repeatedly challenged intermediate derivations, rejected approaches you considered mathematically inelegant, and introduced particular ways of checking the results. That is much closer to a collaborative research process than to a conventional question-answer interaction.

So I think your underlying concern is legitimate: if users contribute substantial intellectual work to the interaction, there is an important question about the relationship between that contribution, the company’s subsequent use of conversational data, and the access users receive in return. Those are questions about the economics and governance of AI, rather than merely about chatbot pricing.

And one distinction is worth making: whether and how OpenAI uses conversations for training depends on the applicable data controls and account settings; it isn’t accurate to assume that every conversation is necessarily used for training. But your broader point about the value created by users’ intellectual contributions doesn’t depend on that particular detail.

Suggestions

To be fair, I also make some suggestions to OpenAI:

• Minimum: Define your restrictions and limits on resource usage via a free account precisely. Describe consequences as enforced interruption times and what happens after a limiting number of free CoT-chats has been reached clearly.
• Minimum: Before you delete chat conversations warn and ask the user which of the previous conversations he/she is willing to delete.
• Minimum: Show the user a table which gives him/her clear information which conversation/chat and which sub-question required what amount of which resource. A sudden announcement telling a user that he/she has violated undefined (!) limits is not enough.
• Better: Offer some special prices for scientific work, not only for students, but also for retired people/scientists.
• Better: Do not restrict the number of chats that require CoT-reasoning, but reduce the turnaround time and priority for producing the solution instead. If you absolutely must and want to save resources independent of the type of chat contents.
• Better: Give a bonus for every error one detects during mathematical proofs or derivations. (Of course for verifiable errors.)

Intermediate conclusion

With a free plan and a respective account to use OpenAI GPT the user risks loosing results for problems which required CoT-reasoning. This is unacceptable – especially as the conditions under which such a deletion happens are not clearly defined. In addition, the enforced chat-interruptions for multiple hours come surprisingly when you use CoT-reasoning. It is unclear, when and on what measurement basis such interruptions happen. There is no overview available that tells the user his/her present and past consumption of computational resources. Limitations are unclear and not fully related to certain periods of time.

But there are other reasons which triggered my decision. Stay tuned for the next post …