What are the mathematical prerequisites to be able to study artificial general intelligence?

Question

What are the mathematical prerequisites to be able to study artificial general intelligence (AGI) or strong AI?

Answer 1

I always recommend starting with game theory, combinatorial game theory, and algorithmic combinatorial game theory, (but I'm potentially biased;)

Combinatorics is a given--discrete mathematics is heavily utilized in computer science, and, with the advent of Combinatorial Game Theory (CGT), ability to determine if a given choice can be deemed optimal ("perfect play"). CGT arises out of traditional Game Theory, which we sometimes term "economic game theory" to make the distinction. Out of Game Theory also arises subfields such as Evolutionary Game Theory, which is important in AI.

These fields relate to rationality, which is the basis for optimized decision making. Decision making algorithms seems to be the fundamental distinction of what constitutes an Artificial Intelligence.

From minimax to gametrees, it's probably a good idea to have a basic grounding in these fields, even if the problem you're AI is trying to solve isn't formally defined as a game.

All problems, from a fundamental standpoint, can be regarded either as puzzles--non-competitive context--or games--competitive context. This distinction is based on whether there is a single agent (puzzles) or multiple agents (games.)

Answer 2

Most of the answers are oriented towards statistical/probabilistic models. For more 'classic' AI I would say you would need some knowledge of predicate calculus. This is the more symbolic planning approach to AI problem solving.

You could argue it's a bit 'old school', but still relevant for certain aspects of AI.

Answer 3

Before proceeding and answering the actual question, it's worth noting that AI and AGI are not the same thing, as was the case at the beginning in 1956, as suggested in the official proposal for the Dartmouth workshop.

Nowadays, people that consider themselves "AI researchers" or "AI practitioners" (e.g. myself) typically are not trying to directly build an AGI, but are focusing on a specific AI approach, such as reinforcement learning, which could, one day, be used to build an AGI. The reason is that we have noticed that directly tackling the "AGI problem" (i.e. creating an AGI) is a lot more complex than was originally thought and some do not think that this is even possible. AGI is a sub-branch of AI that studies how to create an AGI (or human-like AI). Only a few people are still working on AGI.

Ben Goertzel, who's one of the people that is still interested in and attempting to directly create an AGI, wrote a blog post about this topic: AGI Curriculum. If he had to design a curriculum, it would be divided into 6 courses

1. History of AI
2. AI Algorithms, Structures and Methods
3. Neuroscience & Cognitive Psychology
4. Philosophy of Mind
5. AGI Theories & Architectures
6. Future of AGI

He then suggests multiple readings (books) for each of these courses/topics. Below, I will list one book for each of the courses (also based on their free availability online as pdfs). You can find more books in the blog post.

1. The book What Computers Still Can't Do (1992) by Hubert Dreyfus
2. The book Artificial Intelligence A Modern Approach (AIMA) by Russell and Norvig, but Goertzel notes that this is not an AGI book, but gives an introduction to multiple AI topics that have been used in many cognitive architectures for AGI
3. The book Neuroscience: Exploring the Brain by Bear, Connors and Paradiso
4. The book Being No One: The Self-model Theory of Subjectivity (2003) by Thomas Metzinger
5. The paper Artificial General Intelligence: Concept, State of the Art, and Future Prospects (2014) by Ben Goertzel
6. The book Singularity is Near (2005) by Kurzweil

So, to conclude, if you want to study artificial general intelligence, it's not sufficient to just read the typical machine learning or deep learning books, but you also need to have a more solid understanding of other aspects of artificial intelligence and even neuroscience in order to study and do research on AGI. Moreover, it's probably a good idea to also have a good background in all the traditional approaches, what they can or not do, the history of AI (why some approaches have failed or not), and understand the philosophical problems and, last but of course not least, read about the current approaches to AGI, such as universalist (e.g. AIXI) or symbolic ones (all the cognitive architectures such as OpenCog).

To answer your question more directly, if you can read and understand the AIMA book, then you probably have if not all most of the mathematical prerequisites, which will probably include

• logic
• discrete mathematics
• calculus
• optimization
• linear algebra
• probability theory
• theory of computation (this will definitely be needed if e.g. you want to learn about AIXI, but you will also need a nice dose of measure theory and algorithmic information theory to understand all the mathematical details of the theory)

Note that, although these subjects (logic, probability theory, or theory of computation) are necessary to understand the current approaches to AGI, they may not be sufficient to develop a full AGI, but this is a different story. Moreover, note that these mathematical subjects are not just required to understand the current approaches to AGI, but they would also be useful to understand any other AI sub-branch, such as machine learning (and that's probably why people may think that this answer is misleading, but it's not: if you have ever tried to learn something about AIXI, you will know that all the subjects above are more than required!)

In the future, if you also want to do serious research on AGI, having a degree in Computer Science, Cognitive Science, Neuroscience, Mathematics, and/or, of course, Artificial Intelligence, may be a good thing. By the way, Ben Goertzel has a Ph.D. in math. Marcus Hutter, the inventor of AIXI, did his bachelor's and master's in CS with minors in mathematics, and one Ph.D. in theoretical particle physics and another Ph.D. in CS during basically the time that he developed AIXI.