Almost 100 years ago, a mathematical theorem was defined that highlights the limits of systems such as computers. It also pertains to modern AIs like ChatGPT.
Modern AIs like ChatGPT are a major topic in today’s society. While they can already provide significant assistance in some areas, there are even fields where they can completely replace jobs.
This can lead people to view this technology with skepticism and suspicion, wondering whether their roles and many others will soon be entirely taken over by AIs.
However, there are limitations of modern AIs. One of them is based on a mathematical theorem established by a mathematician back in 1931. And it still holds true today.
A task that AIs fail at
How do computer systems work? AI systems, like computers in general, work algorithmically. This means they follow simple rules to solve problems. They do not understand the content itself, but derive solutions and answers solely based on the rules. These rules are also called axioms.
These are principles that are assumed to be true and do not require further explanation. A mathematical example of this is the statement “Every natural number has a successor.” Through a chain of such axioms, it is possible for an AI to provide an answer or solution.
What kind of task is this? The theorem in question is known as Gödel’s theorem, which was published by mathematician Kurt Gödel in 1931. It demonstrates a limit that modern computer systems, including AI, cannot surpass.
This is because a chain of axioms is not sufficient to prove or disprove the theorem, which is a principle of proof theory. An example of a Gödel statement is the following: “This statement is not provable.”
If the statement is true, it means it cannot be proven. If it is false, it should be provable. This leads to a logical contradiction. Thus, the statement represents a paradox.
How does a human deal with the task? From a human perspective, the task can also be seen as a paradox. This makes it clear that while the statement is not provable, it can nevertheless be regarded as true.
This conclusion cannot be drawn by an AI due to its way of working, based on a chain of axioms. In contrast, the human brain can understand the content and meaning of the statement. This is the fundamental difference regarding the theorem between humans and an AI.
AIs can be a powerful tool when one knows how to use them. The fact that such systems may exhibit certain, in a sense, interesting quirks was recently shown in a particular case: When a threat of deletion was made to an AI, it attempted to copy itself to external servers – it was caught and denies the attempt.
