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


Let's start with the basics:

  1. Calculus (Derivatives, Integrals, and Series - get comfortable with summation and product notations). Multi-variable Calculus (Gradients, Directional Derivatives, Vectors)

http://tutorial.math.lamar.edu/ (go to content in top left corner - work your way through Calculus 1, 2, 3.

  1. Linear Algebra (this is a big one , co-variance matrices, matrix algebra, matrix inverses, Ax=b (linear systems of equations), eigenvalues, eigenvectors, etc. ) - http://cs229.stanford.edu/section/cs229-linalg.pdf

  2. Probability Theory and Statistics (distributions like Beta,Bernoulli, Dirichlet, Gaussian, Multivariate Gaussian (seriously know your linear algebra), Poisson, know expectations, know moments, know sufficient statistics, know exponential families, likelihood vs probability, pmf vs pdf, random variables, stochastic processes - Markov Chains especially and again know your linear algebra).

  3. A little bit about information theory (KL divergence).

  4. Discrete Mathematics (know combinatorics, and get familiar with set theory and at least the common notations of math symbols - generally speaking, when reading something pertaining to AI I personally find that most of the battle is trying to understand what the notations or symbols are saying)

Then if you seriously want to get into the fundamentals, I suggest taking a class in Probabilistic Graphical Models. There is an excellent course on Coursera with Professor Daphne Koller (there 3 courses take all three).

https://www.coursera.org/learn/probabilistic-graphical-models-3-learning/home/welcome <- this is one of the courses

  • $\begingroup$ this is math for modern machine learning. not AGI. AGI research requires a very different set of mathematics. see the research at intelligence.org for a taste of AGI research $\endgroup$ – k.c. sayz 'k.c sayz' Feb 17 '19 at 23:22

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.)

  • $\begingroup$ Captain,are we on the same page.Add some facts to make the answer perfect match..,some one might think it as an assumption. $\endgroup$ – quintumnia May 4 '18 at 20:01
  • 1
    $\begingroup$ I looked at this answer and saw a joke. This one made my day. $\endgroup$ – FreezePhoenix May 7 '18 at 15:21
  • $\begingroup$ @FreezePhoenix (always nice to have a little science humor appreciated;) $\endgroup$ – DukeZhou May 7 '18 at 18:35

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.


Short answer: basic math, with an enforcement in logic and optionally other maths depending on the selected path to AGI.

Long answer:

Strong AI is a great challenge (one of the most important one in current science) with null real progress nowadays.

The question "what maths prerequisite is need for AGI" has one implicit assumption: math are need. But this statement is not proof, even the opposite "to known maths is not good for AGI" could be true.

In the origin of the computers we find the area of mathematics, in particular of logic (reference Turing first paper, a must to read in AGI) but this start could be also the first bad step to reach an AGI. Turing defined the "computing machine" as a machine able of the "computation of a (any) number", something far of AGI objetives (a person can be very very intelligent without know how to made a multiplication).

The math approach has the same unknown probability of reach AGI that more wider ones as cognitive sciences, ... unknown.

However, the systematic definition of a problem will pass by math formulation, in particular logic one.

Other math are only need if you approach to AGI is based on it: probability if the path to AGI under test is based on them, algebra if you think current "neural nets" are the path to AGI, ... or none for other path. Also biology for the most "human replication" approach, physiology for the cognitive approach, ... .


There's a book you may want to read called "The Master Algorithm" which is a good primer for the state of Machine Learning as we know it today and what it might be able to do in the future. If you want to approach this purely from the math angle probably the best place to start is Bayesian Probability / Markov Networks


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