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Essays are published in groups of roughly fifteen, and a group usually opens up a subject the collection had not covered before. Between one group and the next nothing changes, so a reader who has seen the most recent group has seen everything.

12 August 2026

15 essays ondynamics

• The staircase that shows the whole orbit — dynamics
• A point that pulls, and a point that pushes — dynamics
• The road paved with doublings — dynamics
• A constant that does not care which map — dynamics
• A difference too small to draw — dynamics
• How fast two orbits part — dynamics
• The shape in every picture of itself — dynamics
• One c, one picture — dynamics
• Where Newton's method goes instead — dynamics
• Eight rules and a triangle — dynamics
• The rule that computes — dynamics
• Three gaps and no more — dynamics
• The orbit that must come back — dynamics
• Two lobes and no cycle — dynamics
• The question nobody can answer — dynamics

11 August 2026

15 essays onnumber

• The primes are what is left over — number
• There is no last prime — number
• A fraction that never closes — number
• Every fraction, exactly once — number
• How close a fraction can get — number
• One way to factor, and no other — number
• The shape of a number's divisors — number
• Numbers that are their own parts — number
• Two squares, and a lattice — number
• Every triple, on one circle — number
• Necklaces that prove a theorem — number
• Two dials at once — number
• Counting one rectangle, twice — number
• The square that cannot shrink — number
• A diagram turned on its side — number

10 August 2026

12 essays ongeometry, analysis, algebra, discrete, topology and probability

• An angle that does not care where it stands — geometry
• The plane, divided by whoever is nearest — geometry
• Euclid proves it without moving anything — geometry
• The same terms, in a different order, adding to whatever is asked — analysis
• Area is the undoing of slope — analysis
• Completing the square, by completing a square — algebra
• Numbers that wrap — discrete
• Six people at a party — discrete
• Three moves, and what they cannot undo — topology
• Nothing on a sphere can be combed flat — topology
• A walk that always comes home, until it does not — probability
• The door that was not opened — probability

6 August 2026

15 essays ongeometry, analysis, algebra, discrete, topology and probability

• The rectangle that eats itself — geometry
• A circle unrolled into a triangle — geometry
• Round is not the only way to be the same width — geometry
• A sum whose terms vanish and whose total does not — analysis
• One point's worth of information — analysis
• The slope of a single point — analysis
• The dot product is a shadow — algebra
• The directions a map leaves alone — algebra
• More things than boxes — discrete
• Four colours, and a proof nobody can read — discrete
• One sequence, counting everything — discrete
• Every corner pays for itself — topology
• Something always stays put — topology
• Twenty-three people — probability
• Bayes' theorem is a picture of a square — probability

2 August 2026

18 essays ongeometry, analysis, algebra, discrete, topology and probability

• Two squares, four triangles, and no algebra — geometry
• Every square is a stack of odd numbers — geometry
• The oldest algorithm, drawn as a tiling — geometry
• Why the list of perfect solids stops at five — geometry
• One cone, four curves — geometry
• A sine wave is a circle seen from the side — analysis
• Adding up rectangles until they stop being rectangles — analysis
• A square wave built entirely out of round ones — analysis
• The curve that is its own slope — analysis
• A matrix is a picture of what happens to the grid — algebra
• Multiplying is turning — algebra
• Seven bridges, and the invention of throwing things away — discrete
• Pascal's triangle, in two colours — discrete
• The primes on a spiral, and a pattern nobody ordered — discrete
• The surface with one side, and what happens when it is cut — topology
• A sphere is a plane plus one point — topology
• A bell curve assembled out of coin flips — probability
• Getting pi by dropping needles on the floor — probability