The presenter introduces the significance of the number 2,084.

• The number 2,084 arises from a story involving a chessboard.

An infinite chessboard is described, and a square spiral numbering system is established.

• The chessboard in the story is infinite, and the squares are numbered in a spiral starting with the number 1.

The knight's movement creates a unique sequence on the infinite chessboard that ends unexpectedly.

• A knight starts at square 1 and moves to the smallest numbered square it can reach, creating a sequence.
• The sequence generated by the knight ends after 2,016 moves when no new square is available to move to, with the last square being number 2,084.

A visual representation of the knight's journey is shown.

• A notebook contains a color-coded illustration of the knight's path on the square spiral.

The presenter expresses surprise and delight at the knight's journey and the unexpected end of the sequence.

• The presenter is surprised and fascinated by the strange and unexpected termination of the knight's sequence.

Discussion on different sequences, shapes of chessboards, and other chess pieces.

• The presenter suggests exploring sequences with other chess pieces and alternate chessboard shapes.

A quadrant chessboard is introduced and a new knight's sequence is explored.

• On a quadrant chessboard, squares are numbered along antidiagonals and the knight's sequence is tracked similarly to the infinite board.
• This sequence also ends unexpectedly, at step 2,402 with the square number 1,378.

The presenter shares a personal anecdote about chess and introduces the video's sponsor.

• The presenter shares that they retired from playing chess at 14 because it was too time-consuming.
• A transition is made to a sponsorship segment for Brilliant.org.

Brilliant.org is promoted as a sponsor of the episode.

• Brilliant.org offers quizzes, puzzles, and courses designed to improve critical thinking in science and math.
• Numberphile viewers are offered a 20% discount on a premium membership.