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The Pencil Room

Questions nobody can answer yet, written in pencil. Each links to a source that says it is still open. When one is settled, it is inked with the year. We re-check every source once a year (last checked 2026-10-13).

Still in pencil

• Why do we dream?

  How dreaming happens in the brain is fairly well mapped. What it is for, if anything, is not; the leading theories each explain only part of it.

  Still open, says Mota-Rolim, Holzinger, Nadorff & De Gennaro, "In the Arms of Morpheus", Brain Sciences (2024): we still do not know why we dream

• What is dark matter?

  It outweighs ordinary matter about five to one by its pull on galaxies. Every candidate particle proposed so far is still unconfirmed.

  Still open, says NASA Science, "Dark Matter": scientists have not yet found evidence which would confirm any candidate

• Is chess a draw?

  With perfect play, does White win, or does the game end level? Every position with seven or fewer pieces is solved. The starting position, with thirty-two, is not.

  Still open, says Wikipedia, "Solving chess": No complete solution for chess in either of the two senses is known

• Is every problem that is quick to check also quick to solve?

  This is P versus NP. Most people who work on it think the answer is no; nobody has proved it either way, and a million-dollar prize is still waiting.

  Still open, says Clay Mathematics Institute, Millennium Prize Problems

• Is there a pattern to where the primes fall?

  The Riemann hypothesis says their irregular spacing follows one precise rule. Computers have checked trillions of cases and found no exception; there is still no proof.

  Still open, says Clay Mathematics Institute, Millennium Prize Problems

• What did the Minoans write?

  Their script, Linear A, survives on clay tablets from Crete. Its sister script, Linear B, was read in 1952. Linear A has no bilingual text to start from and is still unread.

  Still open, says Smithsonian Associates, "Linear A and B: Keys to Mycenaean Greece": This 'Minoan' writing system remains undeciphered

Inked

Once open, now settled.

• What did the Mycenaeans write? inked 1952

  Linear B was read in 1952 by Michael Ventris, an architect, building on Alice Kober's work. It is an early form of Greek.

  Settled in University of Cambridge, Faculty of Classics, "The Decipherment of Linear B"

• Can two cubes ever add up to a cube? inked 1995

  No, nor any higher power. Fermat claimed a proof in a margin around 1637; Andrew Wiles published one in 1995.

  Settled in Wiles, "Modular elliptic curves and Fermat's Last Theorem", Annals of Mathematics 141 (1995)

• Is every closed three-dimensional space with no holes a sphere? inked 2003

  Poincaré asked it in 1904: if every loop in such a space can shrink to a point, must it be a three-sphere? Grigori Perelman proved yes in preprints of 2002 and 2003, and declined the prize.

  Settled in Clay Mathematics Institute, "Poincaré Conjecture"

• Is checkers a draw? inked 2007

  Yes. After eighteen years of computer search, perfect play by both sides leads to a draw.

  Settled in Schaeffer et al., "Checkers Is Solved", Science 317 (2007)

• Is the greengrocer's stack the densest packing of spheres? inked 2017

  Kepler's 1611 guess. Hales's 1998 proof was too long for referees to certify; a computer-checked formal proof completed in 2017 settled it.

  Settled in Hales et al., "A Formal Proof of the Kepler Conjecture", Forum of Mathematics, Pi (2017)

Know of one that has been answered? Tell us through How we work. There is a children's room at Spark & Anvil. Bring one question to the table: Nine in Ten is a game about how sure to be when you do not know.