Abstract
In 1998, Fields medallist Stephen Smale [Smale (1998) [1]] proposed his famous eighteen problems to the mathematicians of this century. The statement of his eighteenth problem is simple but very important. The statement of his problem is, "What are the limits of intelligence, both artificial and human?". To answer the limit of human intelligence, in this paper, we introduce cognitive-consequence space and cognitive-consequence topology, and mainly prove that deductive and non-deductive parts of a human mind will never be empty. It proves a human being will continue to think and solve problems using both deductive and non-deductive inferences as long as they are alive. Hence, we conclude that human intelligence is limitless. We also introduce cognitive closure, cognitive similarity distance, cognitive limit point, cognitive-continuous function, consequence ideal, consequence filter, Gödel's incompleteness black hole, and study related properties. We also provide suitable justifications to show that cognitive consequence topological space is not similar to that of any existing topological space because it connects cognitive space and consequence operator in one frame to find the limit of human intelligence. Moreover, we also provide justifications to state that artificial intelligence has limitations. Thus, we conclude that human intelligence will always remain superior to artificial intelligence.