Intelligence is mathematically intractable
Google "intelligence is mathematically intractable". Nothing comes up, why?
For "is intelligence is mathematically tractable" you get the same result.
Its not often you can put such a short sensible phrase about an important topic into Google and get no results.
[Edited: The reason for my post now follows]
It is quite clear from research into AI that it has been assumed that advanced mathematics, statistical techniques and algorithms can be used to generate intelligence. However anyone who sees the results of these efforts will see software and algorithms that will run under a very specific environment, but are very fragile and fail completely as soon as the environment is changed.
Someone who has actually tried to program a computer to demonstrate intelligent behavior relating to a data set will often look at the data, immediately see what is going on an then assume it is an easy task to program the computer to see that also. However that is not the case! Any simple algorithm developed to use it correctly will fail in a simple but unexpected way, complex algorithms fail in complex ways and any change in the environment in which the data is collected will very often cause it to fail completely. Whether it is an Artificial Neural Network, Support Vector Machine, or Adaptive Gaussian Filtering etc that is used the result is often the same: The human understands the data ever better, while the machine makes only slow halting progress.
So why is it the case that mathematical tractability is sought so much by the AI field? One senior academic I know even called neural nets "black magic" and wanted to have nothing to do with them. However I would quite happily use some "black magic" in my work if it gave the results I wanted. A reason perhaps is because if a method cannot be analysed mathematically then it is harder to communicate and publish the results. That leads researches always towards methods that can be analysed in this way, even if they give inferior results.
But why should intelligence be amenable to mathematical analysis? After all, if there was a formula for intelligence then such a formula could then be used to generate other formulas and mathematical proofs. It would be a formula to rule all other formulas and mathematics would generate itself just by blindly following it. I don't think this is the case. Fields of mathematics such as topology are created as a result of sensory experience (knots etc) of the people creating them. There is no mathematical formula that provides the inspiration for mathematical proofs themselves.
Perhaps mathematical tractability always leads away from intelligent behavior, not towards it. Perhaps researchers should seek systems that become mathematically intractable as quickly as possible in the search for intelligence. It is a bit surprising to me that while maths/logic works so well for the physical sciences, algorithms to deal with real world data developed with it appear brittle, inflexible and unable to cope with changing circumstances. Given progress or lack thereof in the AI field I expect that intelligence in a machine will come from simulating biological neurons/synapses, and we will the stumble upon the mechanism because it will be right in front of us rather than us figuring it out.