Many rely on the LLM also to perform mathematical operations. This approach does not work .

The issue is actually simple: large language models (LLMs) do not really know how to multiply. They can sometimes get the result right, just as I might know the value of pi by heart. But this does not mean that I am a mathematician, nor does it mean that LLMs really know how to do math.

Practical example

Example: 49858 *5994949 = 298896167242 This result is always the same, there is no middle ground. Either it is right or it is wrong.

Even with massive targeted training in mathematics, the best models can only solve a fraction of the operations correctly. A simple pocket calculator, on the other hand, gets 100% of the results correct, every time. And the bigger the numbers get, the worse the performance of LLMs.

Is it possible to solve this problem?

The basic problem is that these models learn by similarity, not understanding. They work best with problems similar to those on which they were trained, but they never develop a true understanding of what they claim.

For those who wish to learn more I suggest this article on "how an LLM works".

A calculator, in contrast, uses a precise algorithm programmed to perform the mathematical operation.

This is the reason why we should never rely completely on LLMs for mathematical calculations: even under the best conditions, with huge amounts of specific training data, they cannot guarantee reliability in even the most basic operations. A hybrid approach might work, but LLMs alone are not enough. Perhaps this approach will be followed for solving the so-called "strawberry problem."

Applications of LLMs in the study of mathematics

In the educational context, LLMs can act as personalized tutors, able to tailor explanations to the student's level of understanding. For example, when a student faces a differential calculus problem, the LLM can break down the reasoning into simpler steps, providing detailed explanations for each step in the solving process. This approach helps build a solid understanding of fundamental concepts.

One particularly interesting aspect is the ability of LLMs to generate relevant and varied examples. If a student is trying to understand the concept of a limit, the LLM can present different mathematical scenarios, starting with simple cases and progressing to more complex situations, thus enabling a progressive understanding of the concept.

One promising application is the use of LLMs to translate complex mathematical concepts into more accessible natural language. This facilitates the communication of mathematics to a wider audience and can help overcome the traditional barrier to access to this discipline.

LLMs can also assist in the preparation of teaching materials, generating exercises of varying difficulty and providing detailed feedback on students' proposed solutions. This allows teachers to better personalize their students' learning journey.

The real advantage

It is also to be considered, more generally, the extreme "patience" in helping in learning even the least "capable" student: in this case the absence of emotions helps. Despite this, even the ai sometimes "loses patience." See this "amusing" example.

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