Artificial Intelligence Mathematical Discovery: The Role of Human

Artificial intelligence explores new algorithms that are not only in the math world. Fast conversion experienced by solving problems at the Olympic level and integrating evidence processes, “Where is the role of man in mathematical discovery?” takes the question to the agenda. The necessity of balance between the technical capacity of artificial intelligence and human expertise is now the basis of discussions on mathematical research.

New Actor in mathematical discovery: Artificial Intelligence

In recent years, artificial intelligence imposes both academic and technological researches. DeepMind, OpenAI and Microsoft, the leading AI companies around the world, has been doing very comprehensive projects where AI-based systems are used in the fields of pockets, geometry, optimization, and especially evidence. Mathematical discovery is not only technological, if it is considered to be an area that has progressed with knowledge and theory accumulation throughout the history, it can also be said in a certain way that the transformation is interfering to a new era regarding human knowledge.

Algoritma Discovery: AlphaTensor Example

AlphaTensor study published in Nature in 2022 of DeepMindOnly one of the broken points in the field of mathematical exploration. The system discovered new algorithms that require lower processing in certain matrix sizes by converting matrix impact algorithms into a “game environment” and not only theoretical; hardware optimization has also created practical solutions. The study is a strong example of the contribution of artificial intelligence into the math world.

Problem Solving in the Olympic Level

AlphaGeometry and AlphaProof models Home In solving geometric problems at IMO (International Olympic) level, high performances were exhibited compared to human contestants. With these studies, artificial intelligence can produce high efficiency in well-defined problems, although in particular, the large part of solutions in open-end problems was proved to be human surveillance and verification.

Integration of Formal Ispat Processes

The most critical contribution to the mathematical research of artificial intelligence is to be integrated into formal evidence processes. Formal verification tools such as Lean, Metamath and HOL Light provide a layer of security that accurately validates evidence steps made by artificial intelligence. This plays a critical role especially when LLM-based systems are considered productive but unreliable structure. Especially solutions such as Lean4 enable researchers to carefully complete evidence by moving together with AI, automatic completion, error capture and faulty steps correction processes.

Human Resealable

It can lead to perception of technology to develop very quickly and disable people in research processes. However, mathematical research is not only about producing solutions, and in many areas, human control is important. We can place these fields as follows. :

Selecting and Formulating the problem

Not AI which mathematical problem should be solved, human researchers decide. Artificial Intelligence can only do some optimizations via the given problem but can not formulate the problem itself.

Verification

LLM-based models are often persuasive but can produce as faulty proof steps. These errors can lead unacceptable results in terms of mathematical accuracy. Therefore, the use of people and formal systems is a must.

Context Theorary Review

Understanding the actual value of a discovery is possible to place it into the math literature, generalize and theoretically interpret it. At this point, artificial intelligence is limited. Setting up the bond again falls to the human. a man again.

Ethics Responsibility

The biggest discussions on artificial intelligence are shaped around ethical problems. Therefore; mathematical accuracy is only possible with academic confidence beyond being a technical issue. Scientific journals still determine the arbitrator mechanisms and publishing principles of these journals, ethical standards.

Different Testimonials in Academic World

The formation of different perspectives on the role of artificial intelligence in the math glass is quite normal. For example Ken Ono from Virginia University, interviewed,AI; the math training of artificial intelligence expresses the concerns of particularly misleading information and basic control loss related to positive and negative possible effects. Ono, which states that the questions they asked to the systems are reviewing their responses, sees it as a situation where incorrect responses are not fully understood.

Limits with the common problem of other LLMs apply in mathematical research. Only large language models that specialize in data sets that they receive training can work problematic in new data. Also, HomeThe detailed information on how they reach results is not often shared directly with the user. This leaves a lot of questions behind.

On the other hand, it is a fact that artificial intelligence is a new discovery partner that completes human knowledge. In large-scale data, there is potential for people to explore situations where they may be overlooked, and the error share is reduced when combined with formal verification.

Artificial Intelligence in Mathematics Education

AI in math education has instant feedback and step-by-step solution capacity, which creates personalized learning environment for students. Also, the difficulty level can produce high quality problem pools set. However, these benefits bring potential risks. Students often resort to these vehicles in lessons and exams and cause the ability to solve the problem of the student. That’s why it’s important to use it as a tool that supports students as well as school in math education.

In the near future, mathematical discovery will be shaped in the framework with the joint work of three components:

• Artificial intelligence models will produce new algorithms and evidence.
• The evidence produced by AI with form correctors such as Lean will be stepped by step.
• Expert researchers will also evaluate and review results.

This structure will increase the nature of mathematical research but a scenario that will be completely disabled is not realistic for this moment. The problem selection, interpretation, verification responsibility and academic ethics are yet seen as stages to be met by no artificial intelligence tool. Proper operation of this structure has critical importance for reliable scientific discoveries.