How important is mathematics to understand Artificial intelligence?

 On the first look, computer science has its root in mathematics and physics, therefor the assumption is, that AI is based on mathematics too. The precondition, according to the claim, to understand modern robotics is located in analysis, algebra, statistics and boolean algebra.

A closer look will show that mathematics isn't needed in AI research at all or to be more precise, mathematics didn't enable advanced AI in the past. What researchers from 1960 until around 2000s tried was to describe artifciial intelligence in terms of mathematics and logic and they failed. The problem is that none of the mentioned disciplines like statistics, algebra and so on contain a method how to enable artificial intelligence. Even if mathematics is a great science disciplines its complete useless to control a robot. Some attempts were made to solve robotics problems with mathematical description of trajectories including model predictive control, but even these advanced math subjects are not powerful enough to enable autonomous robots.

Artificial intelligence as a science discipline is working different than classic sciences like physics, math and computer science. From a pessimistic perspective there is no such thing like Artificial intelligence. Most research around thinking machines and autonomous robots comes to the conclusion that the promising new technique isn't working. That means, a large scale robot project with hundreds of man year effort isn't working at all, the applied techniques are useless and the researchers have no idea about the cause.

Such a kind of pessimistic situation is not an exception in AI research but it was the default situation from 1960 to 2000s. So the best analogy is to compare AI with a complex puzzle which is impossible to solve and no matter how well the researchers are familiar with mathematics, philosophy or psychology they had no idea how to make a machine intelligent.

AI research in the past was mostly a trial by error meta disciplines which wasn't able to solve any of the goals. It was impossible to build intelligent robots, it was hard to program AI agents for computer games, and speech recognition with a computer was another unsolved topic.

The good news is, that its possible to list techniques who are not leading to AI. These techniques are:
- neural networks
- maschine learning
- reinforcement learning
- mathematical optimiziation
- heuristics
- number crunching
- genetic algorithms
- state space search
- case based reasoning
- expert system

In other words, the entire AIMA book (Russle/Norvig: AI a modern approach) is an anti pattern. It doesn't contain recipes to program robots but it describes the struggle of AI researchers for doing so.

After listing all these techniques who are not leading to AI there is a need to find the shared bias. THis bias is the computational paradigm which means, to use a computer to provide intelligence. This shared bias hasn't worked in the past because its an anti pattern in AI research.

On the first look it makes sense to assume, that AI has to do with computation because the computer or the robot should calculate something which leads to intelligent decision making. Therefor AI has to do with number crunching, programming and mathematics. The problem is that in the reality this paradigm isn't able to control robots but it blocks the progress in technology.

It seems, that AI aka intelligence isn't located inside a robot but outside of the machine. On the first look, such an assumption sounds like blasphemy because outside of a computer there is nothing which can calculate or make decisions. At least until the 2000s such a claim would be rejected by mainstream AI research for sure. With more recent understanding of AI there are some new results available which show that AI might located indeed outside of a robot.

Suppose the source of intelligence is not located in the CPU and not inside of a robot hardware, then intelligence has nothing to do with mathematics or physics. This doesn't mean that intelligence is equal to a magic force but it implies that AI has to do with communication. Communication is the science of how to connect things, communication puts a focus on the air gap between two systems.

The transition from former computational paradigm which locates AI Inside of a robot, towards modern communication paradigm which locates AI between two systems is the major paradigm shift in AI research which took place after the year 2000. The revised understanding of intelligence is strongly connected with communication, linguistics and man to machine interaction. In contrast, former focus on computation, mathematics, algorithms and programming have been discarded.