Even 8 quadrillion years wouldn't be enough: Scientists say safe AI is impossible
AI will never be perfect (photo: Magnific)
Artificial intelligence cannot be made 100% predictable and safe — fundamental mathematical limitations stand in the way. Scientists have identified at least two boundaries that cannot be overcome even with unlimited computing power, according to the Transactions of the American Mathematical Society.
What does mathematics say?
The first obstacle is a lack of time.
Mathematics has a classic combinatorial problem: imagine a program that has to find the shortest route for a courier who needs to visit several cities and return to the starting point.
If there are only 10 cities, a conventional computer can find a solution in a fraction of a second.
But when there are 20 cities, the number of possible combinations rises to 2.4 quintillion, and the calculation time increases to 77 years. With 30 cities, the number of possible combinations reaches an astronomical figure with 32 zeros — more than 260 nonillion.
To simply go through all these possible routes, the fastest computer would need 8.4 quadrillion years. That is roughly 600,000 times longer than the age of the universe.
No increase in processor speed can fix this, because the number of possible combinations will always grow faster than any technological advances.
The second obstacle involves questions for which no algorithmic answer exists in principle.
Back in 1953, Rice’s theorem was proven. It states that no program can automatically analyze arbitrary code and guarantee that it will always behave exactly as its author intended.
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Why does this make safe AI impossible?
The AI alignment problem — ensuring that a system acts solely for human benefit and does not cause harm — runs into both of these barriers at the same time.
Not enough time for testing: to test just six safety parameters, with 10 possible settings for each, a computer would have to analyze one million combinations.
Real-world safety systems have far more parameters.
The impossibility of an exact proof: mathematically guaranteeing that AI will behave safely under every possible situation and command is impossible precisely because of Rice’s theorem.
As a result, scientists have moved away from the idea of "mathematically proving safety" and instead rely on limited testing.
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Quantum computers and the practical compromise
Quantum computing is often seen as a potential solution. Scientists emphasize that it only pushes the wall back rather than removing it.
The well-known Grover’s algorithm, introduced in 1996, can significantly speed up searches. With it, the calculation for 20 cities could theoretically be reduced from 77 years to about two seconds, while the 30-city case could drop from 8.4 quadrillion years to around six months.
However, as the number of cities or parameters continues to grow, the explosive increase in possible combinations will once again outpace even quantum computing power.
In real life, such complex problems are solved by changing what we mean by a solution.
How?
Logistics companies build detailed routes for thousands of trucks every day using simplified rules. They produce routes that may be only a few percent worse than the theoretical optimum, but do so in a matter of seconds.
Applied AI works in much the same way: developers build systems that perform highly effectively without providing absolute mathematical guarantees.
A more advanced AI model does not change the laws of mathematics — it simply makes its approximate guesses much more accurate.
