Mathematical models can yield certainty, as can probabilistic models where the probabilities degenerate. The field of formal methods emphasizes developing such certainty about engineering designs. In safety-critical systems, such certainty is highly valued and, in some cases, even required by regulatory bodies. But achieving reasonable performance for sufficiently complex environments appears to require the use of AI technologies, which resist such certainty. This paper suggests that certainty and intelligence may be fundamentally incompatible. First, Bayes Theorem shows, rather trivially, that certainty implies an inability to learn when presented with new data. A more subtle issue, however, is that logic and mathematics, necessary for certainty, may be a result of intelligence rather than the foundations of intelligence. This paper makes the case that intelligence is an evolved form of prediction, that logic and mathematics were not discovered but rather were invented because of their predictive value, and that the certainty they can give us cannot be about systems that exhibit intelligence.