Richard Feynman on Artificial General Intelligence

In a lecture held by 1965 Nobel Laureate in Physics Richard Feynman (1918–1988) on September 26th, 1985, the question of artificial general intelligence (also known as “strong-AI”) comes up.

Audience Question

Do you think there will ever be a machine that will think like human beings and be more intelligent than human beings?

Below is a structured transcript of Feynman’s verbatim response. With the advent of machine learning via artificial neural nets, it’s fascinating to hear Feynman’s thoughts on the subject and just how close he gets to the solution, even 35 years ago.

Continue reading

The Golden Age of Quantum Physics

The Fifth Solvay International Conference on Electrons and Photons (1927)

“The Most Intelligent Photograph Ever Taken”, as it is sometimes known, was captured during the Fifth Solvay International Conference on Electrons and Photons held in 1927 in Brussels, Belgium. The photograph is famous because it was captured in the middle what would later become known as the “debate of the century” over the non-deterministic nature of quantum physics. Present at the conference, famously, were many of the men instrumental in devising the theories which are now considered to be at the heart of modern physics.

Among those present, on one side of the debate were the originators of the newly introduced quantum mechanics -paradigm, including Werner Heisenberg himself, in addition to his collaborators Wolfgang Pauli, Max Born, Hendrik Kramers, Émile de Broglie, Niels Bohr and Paul Dirac. On the other side, also present, were supporters of the classical, deterministic paradigm, represented most prominently by Albert Einstein himself, but also Max Planck, Paul Ehrenfest and Erwin Schrödinger. Of the 29 attendees at the meeting, 17 had or would go onto win the Nobel Prize in physics or chemistry. Among them was also Marie Curie who had already won both. Continue reading

A Computability Proof of Gödel's First Incompleteness Theorem

“Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e. there are statements of the language of F which can neither be proved nor disproved in F.”

Gödel’s 1931 paper containing the proof of his first incompleteness theorem is difficult. It is 26 pages long, contains 46 preliminary definitions and several important propositions which are presented in a highly formal way (Nagel & Newman, 2001). Gödel’s proof had to be this long, because it was formulated before the establishment of the general theory of computability (Turing, 1936; Church, 1936) and so the general concept of a formal system had indeed yet to be formulated (Franzen, 2005).

Gödel hence instead proved his incompleteness theorem for a formal system of his own making, P, and argued that it contained properties shared by a wide class of systems. Utilizing Turing and Church’s invention of computability, with the help of the late, great Torkel Franzén (2005) we can devise the sketch for a computability proof of Gödel’s incompleteness theorem that is equally as strong as Gödel’s version, but much easier to deduce. Continue reading

The Envy-Free Cake-Cutting Procedure

How to Ensure Fairness as a Mechanistic Outcome

In the context of economics and game theory, envy-freeness is a criterion of fair division where every person feels that in the division of some resource, their share is at least as good as the share of any other person — thus they feel no envy. For n=2 people, the protocol proceeds by the so-called divide and choose procedure:

The Envy-Free Cake-Cutting procedure states that if two people are to share a cake in way in which each person feels that their share is at least as good as any other person, one person ("the cutter") cuts the cake into two pieces; the other person ("the chooser") chooses one of the pieces; the cutter receives the remaining piece.

For cases where the number of people sharing is larger than two, n > 2, the complexity of the protocol grows considerably. The procedure has a variety of applications, including (quite obviously) in resource allocation, but also in conflict resolution and artificial intelligence, among other areas. Continue reading


This essay is part of a series of stories on math-related topics, published in Cantor’s Paradise, a weekly Medium publication. Thank you for reading!

The Unparalleled Genius of John von Neumann

“Most mathematicians prove what they can, von Neumann proves what he wants”

It is indeed supremely difficult to effectively refute the claim that John von Neumann is likely the most intelligent person who has ever lived. By the time of his death in 1957 at the modest age of 53, the Hungarian polymath had not only revolutionized several subfields of mathematics and physics but also made foundational contributions to pure economics and statistics and taken key parts in the invention of the atomic bomb, nuclear energy and digital computing.

Known now as “the last representative of the great mathematicians”, von Neumann’s genius was legendary even in his own lifetime. The shear breadth of stories and anecdotes about his brilliance, from Nobel Prize-winning physicists to world-class mathematicians abound:

”You know, Herb, Johnny can do calculations in his head ten times as fast as I can. And I can do them ten times as fast as you can, so you can see how impressive Johnny is” — Enrico Fermi (Nobel Prize in Physics, 1938)

“One had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch.” — Eugene Wigner (Nobel Prize in Physics, 1963)

“I have sometimes wondered whether a brain like von Neumann’s does not indicate a species superior to that of man” — Hans Bethe (Nobel Prize in Physics, 1967)

And indeed, von Neumann both worked alongside and collaborated with some of the foremost figures of twentieth century science. He went to high school with Eugene Wigner, collaborated with Hermann Weyl at ETH, attended lectures by Albert Einstein in Berlin, worked under David Hilbert at Göttingen, with Alan Turing and Oskar Morgenstern in Princeton, with Niels Bohr in Copenhagen and was close with both Richard Feynman and J. Robert Oppenheimer at Los Alamos.

Continue reading

Loading more posts…