One Young India
Math MagiciansCredits

Math MagiciansCredits

Picture, video and data credits

Every picture, video and dataset in this course:who made it, where it comes from and the licence that lets us show it.Thank you to everyone who shares their work freely.

The course home

A small cube-shaped die of fired clay, its numbers marked by round pits, on a dark museum shelf.A die from Mohenjo-daro, now in the Ashmolean Museum.Photo: Zunkir, CC BY-SA 4.0, via Wikimedia Commons.

Part 1: Chance: the mathematics of probability

Grey monsoon clouds sinking low over a green hillside and the blocks of flats below it.Monsoon clouds low over Anushaktinagar, in Mumbai.Photo: "Down come the clouds @ Anushaktinagar" by S.J.Saravanan, CC BY-SA 3.0, via Wikimedia Commons.
A black cricket scoreboard with white number cards for the total, the overs and the runs for the wickets fallen.A cricket scoreboard with number cards hung by hand, at a club in Essex, England.Photo: Acabashi, CC BY-SA 4.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
A painted oval portrait of Blaise Pascal with long brown hair and a wide white collar over a dark coat.Blaise Pascal, who wrote from Paris, in a portrait by Louis Devedeux.Photo: Romainbehar, CC0, via Wikimedia Commons.
A painted portrait of Pierre de Fermat with long dark hair, a white collar and a dark robe.Pierre de Fermat, who wrote from Toulouse, painted by Rolland Lefebvre.Painting: Rolland Lefebvre, public domain (author died more than 70 years ago), via Wikimedia Commons.
VideoThe last banana: A thought experiment in probability - Leonardo BarichelloFrom the channel TED-Ed. Watch the full video.
Roman-era dice carved from bone, their faces marked with ringed dots, against a dark grey background.Roman-era dice carved from bone, in the Musée Saint-Raymond, Toulouse's museum of antiquities.Photo: "Set of dice-Saint Raymond-IMG 0107-gradient" by Rama, CC BY-SA 3.0 fr, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
VideoHow many ways can you arrange a deck of cards? - Yannay KhaikinFrom the channel TED-Ed. Watch the full video.
A grey metal bicycle lock with four numbered code wheels, lying across a white cloth.A bicycle lock with four code wheels and six numbers on each.Photo: Arlo Barnes, CC0, via Wikimedia Commons. Cropped by One Young India.
VideoCheck your intuition: The birthday problem - David KnuffkeFrom the channel TED-Ed. Watch the full video.
Persi Diaconis, smiling, in a brown hat and dark jacket, standing outdoors in a garden.Persi Diaconis, a statistician at Stanford University, in 2010.Photo: "Persi Diaconis 2010" by Søren Fuglede Jørgensen, CC BY-SA 3.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
Salt Lake City in Kolkata seen from an aircraft: thousands of buildings and roads under scattered white clouds.Salt Lake City in Kolkata, seen from an aircraft.Photo: Sumita Roy Dutta, CC BY-SA 4.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
A lit Galton board: green balls piled in columns below rows of pins, tallest in the middle, under a drawn bell curve.A Galton board: balls drop through rows of pins into slots.Photo: "Planche de Galton" by Antoine Taveneaux, CC BY-SA 3.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
A small blue metal fire insurance plaque with three animal heads and the number 5266, fixed to a brick wall.A fire insurance plaque, number 5266, on the wall of a house.Photo: "Fire Insurance plaque - The Cottage" by Richard Law, CC BY-SA 2.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
An old printed lottery ticket with handwritten numbers and signatures and a coat of arms in one corner.A ticket from a lottery held in Geneva in 1773 for the city's General Hospital.Scan: Lottery of the General Hospital of Geneva, public domain (author died more than 70 years ago), via Wikimedia Commons. Cropped by One Young India.
A printed page from 1763: the heading of Bayes's essay on chances and the start of Price's letter, Dear Sir.The first page of Thomas Bayes's essay, as Richard Price sent it to the Royal Society, where it was read in December 1763.Scan: Thomas Bayes and Richard Price, public domain (author died in 1791), via Internet Archive. Cropped by One Young India.
David Spiegelhalter speaking, both hands raised as he explains a point.David Spiegelhalter, the statistician who advises stating a risk as how many out of 100 people like you would be affected.Photo: Paul Clarke, CC BY-SA 4.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
DataPeople killed in road accidents in India, year by yearData: Ministry of Road Transport and Highways, Road Accidents in India 2024, Table 1.6, figures from a Government of India report, credited. Drawn by One Young India.
DataPeople killed in road accidents in 2024, by state and union territoryData: Ministry of Road Transport and Highways, Road Accidents in India 2024, Table 5.6, figures from a Government of India report, credited. Drawn by One Young India.
Red and white streaks of light from traffic on a wide highway at night, seen from a footbridge, street lamps on both sides.Traffic on NH48 in Gurgaon at night, turned into streaks of light by a long exposure.Photo: Slyronit, CC BY-SA 4.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.

Part 2: Statistics, and how to spot a lie

A hand-coloured chart of England's imports and exports over the years, two lines with the gap between them shaded.William Playfair's chart of England's imports and exports, from his Commercial and Political Atlas of 1786.Scan: William Playfair, public domain (author died more than 70 years ago), via Wikimedia Commons.
DataIndia: the mean and the median, in dollars a dayData: World Bank Poverty and Inequality Platform (2026), processed by Our World in Data, CC BY 4.0. Drawn by One Young India.
DataIndia's average temperature, month by month, in 2025Data: Copernicus Climate Change Service, ERA5 monthly averages, processed by Our World in Data, Contains modified Copernicus Climate Change Service information (2026). Drawn by One Young India.
Two water depth gauges marked in feet and metres stand in a river beside an old brick wall and green trees.Depth gauges at a ford on the Blackwater river, between Hampshire and Berkshire in England.Photo: Martinvl, CC BY-SA 4.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
VideoPros and cons of public opinion polls - Jason Robert JaffeFrom the channel TED-Ed. Watch the full video.
Four red fire engines parked in the sunny yard of a fire station in Jajpur, Odisha.Fire engines at the fire station in Jajpur, Odisha.Photo: "Andola, Odisha 755007, India" by Deepak das, CC BY 3.0, via Wikimedia Commons. Cropped by One Young India.
A painted portrait of James Lind in a white wig and grey coat, one hand resting on a book.James Lind, painted by George Chalmers in 1783.Painting: George Chalmers, public domain (author died more than 70 years ago), via Wikimedia Commons.
VideoEsther Duflo: Social experiments to fight povertyFrom the channel TED. Watch the full video.
The title page of A Treatise of the Scurvy, in three parts, printed in old type on yellowed paper.The title page of James Lind's A Treatise of the Scurvy, printed in Edinburgh in 1753.Scan: James Lind, public domain (author died in 1794), via Internet Archive. Cropped by One Young India.
VideoHow to spot a misleading graph - Lea GaslowitzFrom the channel TED-Ed. Watch the full video.
Florence Nightingale's chart of army deaths: two wheels of coloured wedges, one wedge for each month, larger wedges for more deaths.Florence Nightingale's 1858 diagram of the causes of death in the army in the East, drawn to make a case.Diagram: Florence Nightingale, public domain (author died more than 70 years ago), via Wikimedia Commons.
VideoHow statistics can be misleading - Mark LiddellFrom the channel TED-Ed. Watch the full video.
Sather Tower, a pointed clock tower on the Berkeley campus, against the bay and the Golden Gate Bridge at dusk.Sather Tower on the campus of the University of California, Berkeley, whose graduate admissions figures for autumn 1973 are a famous real case of Simpson's paradox.Photo: "Bay Blue" by Joe Parks from Berkeley, CA, CC BY 2.0, via Wikimedia Commons. Cropped by One Young India.

Part 3: Growth and strategy

An ivory chess set with red and white pieces on a raised, inlaid board in a museum case, more pieces beside it.An ivory chess set made in Maharashtra in the 18th century, now in the Raja Dinkar Kelkar Museum, Pune.Photo: Alexkom000, CC BY 4.0, via Wikimedia Commons. Cropped by One Young India.
DataTransistors on one microprocessor, 1971 to 2021Data: Karl Rupp, Microprocessor Trend Data (2022), processed by Our World in Data, CC BY 4.0. Drawn by One Young India.
VideoExponential growth: How folding paper can get you to the MoonFrom the channel TED-Ed. Watch the full video.
A round silicon wafer covered in a grid of hundreds of tiny square chips, lying on a red cloth.A silicon wafer of microprocessor chips, a couple hundred of them on one disc.Photo: "486 Wafer" by Bill Smith, CC BY 2.0, via Wikimedia Commons.
DataIndia's population, 1950 to 2023Data: UN World Population Prospects (2024), with HYDE and Gapminder, processed by Our World in Data, CC BY 4.0. Drawn by One Young India.
The decorated title page of Luca Pacioli's Summa de arithmetica, its title printed in red inside a black knotwork border.The title page of Luca Pacioli's Summa de arithmetica, in its 1523 edition.Scan: "Titelbladet till "Summa de arithmetica ..."" by Stockholms Universitetsbibliotek from Stockholm, Sweden, CC BY 2.0, via Wikimedia Commons. Cropped by One Young India.
An influenza virus particle under an electron microscope, coloured orange and purple to show its coat and the strands inside.An influenza virus seen through an electron microscope, coloured to show its parts.Photo: Cynthia Goldsmith, CDC, public domain (US government work), via Wikimedia Commons. Cropped by One Young India.
John Nash in a jacket and patterned tie, looking at the camera, in black and white.John Nash in 2006.Photo: "John f nash 20061102 3" by Elke Wetzig (Elya), CC BY-SA 3.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
VideoGame theory challenge: Can you predict human behavior? - Lucas HustedFrom the channel TED-Ed. Watch the full video.
A Keep left, pass right sign beside a straight road through dry grassland, one car far ahead.A Keep left sign on the B2 road in Namibia, which drives on the left, as India does.Photo: Olga Ernst, CC BY-SA 4.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
VideoHow to outsmart the Prisoner’s Dilemma - Lucas HustedFrom the channel TED-Ed. Watch the full video.
A long queue of white jeeps stuck nose to tail on a mountain road, snowy peaks above the valley.Jeeps queued nose to tail on a mountain road at Saribal.Photo: "Traffic Jam at Saribal" by Mike Prince from Bangalore, India, CC BY 2.0, via Wikimedia Commons. Cropped by One Young India.
Elinor Ostrom in glasses and a white polo neck, the red and white embroidered edge of her jacket showing, at a press conference.Elinor Ostrom in 2009, the year she shared the economics prize given in memory of Alfred Nobel.Photo: "Elinor Ostrom close-up (cropped)" by © Holger Motzkau 2010, Wikipedia/Wikimedia Commons (cc-by-sa-3.0), CC BY-SA 3.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
VideoWhat is the tragedy of the commons? - Nicholas AmendolareFrom the channel TED-Ed. Watch the full video.
A fisher steers a long wooden boat across the still, grey water of Chilika Lake, past rows of bamboo fishing stakes.A fishing boat on Chilika Lake at Satpada, among the stakes of fish traps.Photo: Phadke09, CC BY-SA 4.0, via Wikimedia Commons.
VideoWhich voting system is the best? - Alex GendlerFrom the channel TED-Ed. Watch the full video.
The title page of Condorcet's Essai sur l'application de l'analyse, printed in Paris by the royal press.The title page of Condorcet's essay of 1785, where he showed that majority votes can go round in a circle.Scan: Nicolas de Condorcet, public domain (author died more than 70 years ago), via Wikimedia Commons.
The empty Lok Sabha chamber in the new Parliament building: curved rows of benches facing the Speaker's chair.The Lok Sabha chamber in the new Parliament building, New Delhi, where the members chosen in India's 543 constituencies sit.Photo: Ministry of Parliamentary Affairs, GODL-India, via Wikimedia Commons. Cropped by One Young India.
A sealed ballot box, painted white and red, standing on the floor of an empty polling room.A sealed ballot box at a polling station in Poland, for the 2010 election.Photo: "2010 Poland elections round 2 ballot box" by Piotrus, CC BY-SA 3.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.

Part 4: Secrets, data and your question

An Enigma cipher machine in its open wooden case: rows of lettered keys, a lampboard and the rotor wheels on top.An Enigma cipher machine from the cryptography collection of the Swiss Army.Photo: "Enigma-IMG 0487-black" by Photograph by Rama, Wikimedia Commons, Cc-by-sa-2.0-fr, CC BY-SA 2.0 fr, via Wikimedia Commons.
A worn silver coin with Julius Caesar's head in a wreath and the words CAESAR IMP around the edge.A silver coin of Julius Caesar, struck in 44 BC, with his portrait and the words CAESAR IMP.Photo: American Numismatic Society, CC0, via Wikimedia Commons.
Part of a handwritten page in Arabic script, crowded with columns of letters and marks.Part of a page of al-Kindi's treatise on deciphering messages, in a manuscript kept in the Süleymaniye Library, Istanbul.Scan: Al-Kindi, public domain (author died more than 70 years ago), via Wikimedia Commons. Cropped by One Young India.
A metal cipher wheel: an inner ring of letters turns against an outer ring of letters, with a crank handle beside it.A cipher wheel from the Swiss Army's collection: turn the inner ring and every letter shifts at once, as in Caesar's cipher.Photo: "Cryptographic wheel-IMG 0530 cropped" by Rama, CC BY-SA 2.0 fr, via Wikimedia Commons.
Whitfield Diffie, with long white hair and a white beard, smiling, in a dark suit.Whitfield Diffie, who set out public-key cryptography with Martin Hellman in 1976.Photo: Duncan.Hull, CC BY-SA 4.0, via Wikimedia Commons.
Clifford Cocks, smiling, in a dark suit and a blue checked tie, against a plain grey background.Clifford Cocks, who found an equivalent method at GCHQ in 1973, kept secret until 1997.Photo: The Royal Society, CC BY-SA 4.0, via Wikimedia Commons.
VideoPublic Key Cryptography - ComputerphileFrom the channel Computerphile. Watch the full video.
Part of a printed page packed with small numbers in columns: a table of factors from a book printed long before computers.Part of a page of J. W. L. Glaisher's Factor table for the fifth million, printed in 1880, long before computers could find factors for us.Scan: James Whitbread Lee Glaisher, public domain (author died in 1928), via Internet Archive. Cropped by One Young India.
Part of a page of US password guidelines: the section on password verifiers, with numbered rules on length and characters.From NIST's guidelines of July 2025: a password used on its own must be at least 15 characters long.Scan: National Institute of Standards and Technology, public domain (US government work, NIST), via NIST. Cropped by One Young India.
Rows of black server racks, full of computers and cables, in a room with a pale tiled floor.Server racks in a data centre.Photo: "Datacenter Server Racks" by Carl Lender from Sunrise, USA, CC BY 2.0, via Wikimedia Commons. Cropped by One Young India.
Part of a printed page: a column of numbers written only in 0s and 1s, beside worked sums and French text.Part of Leibniz's paper on binary arithmetic, published in 1703, with numbers written in 0s and 1s only.Scan: Gottfried Wilhelm Leibniz, public domain (author died more than 70 years ago), via Wikimedia Commons. Cropped by One Young India.
VideoHow exactly does binary code work? - José Américo N L F de FreitasFrom the channel TED-Ed. Watch the full video.
Close up of magnetic-core memory: tiny black rings threaded on a grid of thin copper wires.Magnetic-core memory close up.Photo: Bubba73 (Jud McCranie), CC BY-SA 4.0, via Wikimedia Commons.
A form filled in by hand: rows of written digits in printed boxes, from a US government collection of handwriting samples.Part of a form filled in by hand for a US government collection of handwritten digits and letters.Scan: NIST, public domain (US government work), via Wikimedia Commons. Cropped by One Young India.

The free preview

Grey monsoon clouds sinking low over a green hillside and the blocks of flats below it.Monsoon clouds low over Anushaktinagar, in Mumbai.Photo: "Down come the clouds @ Anushaktinagar" by S.J.Saravanan, CC BY-SA 3.0, via Wikimedia Commons.
A black cricket scoreboard with white number cards for the total, the overs and the runs for the wickets fallen.A cricket scoreboard with number cards hung by hand, at a club in Essex, England.Photo: Acabashi, CC BY-SA 4.0, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.
A painted oval portrait of Blaise Pascal with long brown hair and a wide white collar over a dark coat.Blaise Pascal, who wrote from Paris, in a portrait by Louis Devedeux.Photo: Romainbehar, CC0, via Wikimedia Commons.
A painted portrait of Pierre de Fermat with long dark hair, a white collar and a dark robe.Pierre de Fermat, who wrote from Toulouse, painted by Rolland Lefebvre.Painting: Rolland Lefebvre, public domain (author died more than 70 years ago), via Wikimedia Commons.
VideoThe last banana: A thought experiment in probability - Leonardo BarichelloFrom the channel TED-Ed. Watch the full video.
Roman-era dice carved from bone, their faces marked with ringed dots, against a dark grey background.Roman-era dice carved from bone, in the Musée Saint-Raymond, Toulouse's museum of antiquities.Photo: "Set of dice-Saint Raymond-IMG 0107-gradient" by Rama, CC BY-SA 3.0 fr, via Wikimedia Commons. Cropped by One Young India. The crop is shared under the same licence.

Pictures are public domain or under a Creative Commons licence that allows reuse with credit; each one links to its licence and its source. Charts are drawn by One Young India from the data named under them. Videos play from their own channels.

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