Every number is interesting
Give it any whole number up to a trillion and it will find something worth saying.
1 + 2 + 3 + 4 + ⋯ = −1/12wait, what?!
For the love of numbers.
An unofficial ode to Numberphile, and a growing library of the ideas it made us fall for: primes, infinities, impossible shapes, and sums that shouldn't work.
Why brown paper?
Since 2011, filmmaker Brady Haran has been pointing a camera at mathematicians and asking them about the thing they can't stop thinking about. There are no slides. Someone uncaps a marker, pulls over a sheet of brown paper, and starts drawing.
What comes out is a corner of the internet where adding up every whole number can start an argument that lasts for years, a magic square that doesn't quite work becomes a beloved in-joke, and a single number can hold your attention for twenty minutes.
On the paper over the years: Matt Parker, James Grime, Hannah Fry, Holly Krieger, Tony Padilla, Tadashi Tokieda, Neil Sloane, Cliff Stoll, Ben Sparks and many more.
This site is a thank-you note. It collects those ideas, explains them in plain words, lets you poke at a few of them, and sends you back to the videos.
A few greatest hits
The episode guide
Numberphile's back catalogue as one list you can sort and filter. Tap a column heading to sort, or tap a guest or topic to see everything that shares it. Tap a title to watch it right here; watch it to the end and it's ticked off for you. Tick the box by a title once you've watched it.
By the numbers
The whole back catalogue, counted up. These charts are drawn straight from the episode guide above, so they move with it as new videos arrive.
Episodes each year
What they're about
Topics are our rough labels, so take them lightly. Tap one to see those episodes.
Who turns up most
Odds and ends
Links from the episodes
Everything the episodes point to: the guests' interactive files and apps, code, papers, OEIS entries, books and extra footage, gathered from each video's description on YouTube and kept up to date. Numberphile's own links, like Patreon, merch and sponsors, are left out.
The library
A shelf of big ideas from across mathematics, each explained on a single scrap of paper. Open one to read more, then follow it down the rabbit hole.
Not on brown paper yet
Constants and open problems we couldn't find a Numberphile video about. With hundreds of videos, some may have come up in passing, so treat this as a wish list rather than a verdict. Every card can search the episode guide, so you can check for yourself.
Constants
Problems and puzzles
Recently filmed, so no longer on the list: Khinchin's constant, Apéry's constant, Mills' constant, the Euler–Mascheroni constant, the plastic ratio, random Fibonacci numbers and colouring the plane.
How math works
Science gathers evidence and stays open to being wrong. Mathematics asks for proof, and once a proof is found it is final. Here is how that machine runs.
A short history of numbers
From notches on a bone to proofs checked by computer: some of the moments that made mathematics what it is.
The number lab
Small experiments you can run yourself. Type a number, drag a slider, see what happens.
Collatz: does it always reach 1?
If the number is even, halve it. If it's odd, triple it and add one. Repeat. Every number ever tried falls to 1 eventually. Nobody can prove they all do.
The 6174 machine
Take four digits that aren't all the same. Arrange them largest-first and smallest-first, subtract, and repeat. You will land on 6174 within seven steps.
The Ulam spiral
Write the counting numbers in a square spiral and mark the primes. They shouldn't line up. They do.
The golden angle
A sunflower adds each new seed at a fixed turn from the last. Turn by the golden angle, about 137.5°, and the seeds pack with no gaps. Nudge it and watch spokes appear.
The chaos game
Pick a random corner, jump part of the way toward it, leave a dot, and repeat. Pure chance, and yet a perfect fractal appears.
Recamán's sequence
Start at 0. On step n, jump back n if you land on a new positive number, otherwise jump forward n. Draw every jump as an arc.
Zoom into the Mandelbrot set
Each point is a number c. Start at 0, then square and add c, over and over. The dark points stay bounded forever. Tap the picture to zoom in three times closer; the edge never runs out of detail.
Sandpiles
Pour grains of sand onto the middle square. Any square holding four grains topples, passing one grain to each neighbour, and that can set them off too. Nobody draws this pattern. It builds itself. Tap the pile to drop one more grain and see what it sets off.
The birthday paradox
How many people do you need before two of them probably share a birthday? Pick a party size, then throw a party and see.
Buffon's needle
Drop needles on a floor of boards exactly one needle wide. The share that land across a crack is 2/π, so counting them estimates π.
The times-table circle
Put points around a circle and join each point n to point 2 × n, wrapping round when you pass the end. A heart-shaped cardioid appears. Change the multiplier and watch it morph.
Games
Five games with mathematics hiding inside: one where your instincts lie to you, one you can always win once you know the secret, one that tests your eye for patterns, one where binary decides who survives, and an ancient puzzle with a modern twist.
Three doors
A car is behind one door and goats are behind the other two. Pick a door, and I'll open a different one with a goat behind it. Then you choose: stick or switch?
Pick a door.
Nim
Take turns removing as many counters as you like from a single row. Whoever takes the last counter wins. I never make a mistake, but every game starts in a position you can win.
The secret
Write each row's size in binary and add the columns without carrying, so 1 + 1 = 0. That total is the nim-sum. If it isn't zero, some move makes it zero, so make that move. Keep handing me a zero and I can't win.
What comes next?
Each puzzle is a famous sequence. Type the next number.
Survive the circle
People stand in a circle. Going round, every second person is out, until one is left. Tap the seat you think survives, then watch.
Tap the seat you think will survive.
The trick
Write the number of people in binary, move the leading 1 to the end, and read it back. With 41 people, 101001 becomes 010011, which is seat 19.
Make it magic
Swap tiles until every row, column and diagonal adds up to 15. Tap one tile, then another, to swap them.
The Parker square
Could you build a 3 × 3 magic square from nine different square numbers? Nobody knows. In 2016 Matt Parker tried, and his near miss, which repeats numbers and has one diagonal that doesn't add up, became the Parker square.