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The Questions

Ten questions, each asked because the one before it had been answered, or had not.

  1. Socrates, as written by Plato

    Theaetetus · c. 369 BCE

    What is knowledge?

  2. Euclid

    Elements · c. 300 BCE

    What can be known from what we already know?

  3. Isaac Newton

    Philosophiæ Naturalis Principia Mathematica · 1687

    Can the motion of the heavens and the motion of the earth be described by the same laws?

  4. Michael Faraday

    Experimental Researches in Electricity · 1831

    What connects electricity and magnetism?

  5. James Clerk Maxwell

    A Dynamical Theory of the Electromagnetic Field · 1865

    What if mathematics can reveal something that experiment has not yet shown us?

  6. Albert Einstein

    On the Electrodynamics of Moving Bodies · 1905

    What happens to time when the speed of light does not change?

  7. Georg Cantor

    Über eine elementare Frage der Mannigfaltigkeitslehre · 1891

    How large is infinity?

  8. Kurt Gödel

    On Formally Undecidable Propositions of Principia Mathematica and Related Systems · 1931

    Can a formal system prove everything that is true about itself?

  9. Alan Turing

    On Computable Numbers (1936); Computing Machinery and Intelligence (1950) · 1936 · 1950

    What does it mean for something to be computable?

    “Can machines think?”

  10. John Keats

    Letter to George and Tom Keats · 1817

    What if not knowing is not failure?

    “uncertainties, Mysteries, doubts”

The emblems draw each person’s work rather than their face. Questions without quotation marks are paraphrases of what the work pursued; words in quotation marks are the person’s own, checked against the sources below.

Sources, and how each question led to the next

  1. Socrates, as written by Plato: Plato, Theaetetus 145e–146c (Socrates asks what knowledge is; wording varies by translation).

    → Knowledge that cannot be doubted: Euclid builds certainty from definitions and postulates.

  2. Euclid: Euclid, Elements, Book I (definitions, postulates, Proposition 1: the equilateral triangle by compass and straightedge).

    → Geometry applied to motion: conic sections become orbits in Newton's Principia.

  3. Isaac Newton: Newton, Principia (1687), Book III: universal gravitation unites terrestrial and celestial motion.

    → Action at a distance left open: Faraday pictures the space between as lines of force.

  4. Michael Faraday: Faraday, Experimental Researches in Electricity, First Series (1831): electromagnetic induction; lines of force.

    → Maxwell translates Faraday's lines of force into mathematics.

  5. James Clerk Maxwell: Maxwell, A Dynamical Theory of the Electromagnetic Field (1865). The four equations are shown in the later vector form due to Heaviside.

    → The equations predict waves travelling at the speed of light: light is electromagnetic.

  6. Albert Einstein: Einstein, Zur Elektrodynamik bewegter Körper, Annalen der Physik 17 (1905); general relativity 1915 (Riemannian geometry).

    → Physics rests on mathematics; mathematics now asks about its own foundations and infinities.

  7. Georg Cantor: Cantor (1891): the diagonal argument; some infinities are larger than others.

    → The diagonal method returns as self-reference in Gödel.

  8. Kurt Gödel: Gödel, Monatshefte für Mathematik und Physik 38 (1931): incompleteness via a self-referential sentence.

    → Turing turns formal procedure into a machine and meets the same limit.

  9. Alan Turing: Turing, Computing Machinery and Intelligence, Mind 59 (1950), opening line: “I propose to consider the question, ‘Can machines think?’”

    → From what machines can do back to what it is like to be the one asking.

  10. John Keats: Keats, letter to George and Tom Keats, December 1817: “…when man is capable of being in uncertainties, Mysteries, doubts, without any irritable reaching after fact & reason”.

    → Every road returns: the questions converge.