-1/12

Mathologer examines how identities like 1+2+3+... = -1/12 arise in Ramanujan's work, starting from his 1913 letter to Hardy. The video explains the rules for summing infinite series and why such results are meaningful but not naive sums.

A Numberphile video in which physicists Tony Padilla and Ed Copeland show a seemingly astounding result that 1+2+3+4+... equals -1/12. The argument is informal and has drawn criticism for glossing over what the result actually means.

Mathologer examines the infamous Numberphile claim that 1+2+3+... equals -1/12, explaining what is wrong with the calculation and how it connects to real math like the zeta function and analytic continuation.

Numberphile's James Grime makes the case for base 12 (dozenal) over base 10, showing how twelve's many divisors make arithmetic and everyday fractions easier.

Engineering Explained examines BMW's Hydrogen 7, a V12 that burns liquid hydrogen or gasoline. He covers cryogenic storage at -253C and why the approach is impractical.

Hugh Jeffreys tears down the iPhone 12 and assesses its repairability, focusing on how parts are serialized and tied to the device so swapping components between phones does not work.

Pannenkoek2012's commentated tool-assisted Super Mario 64 run collecting the Watch for Rolling Rocks star with half an A press, using parallel universes and QPU movement. The video is marked outdated in favor of a newer version.

Technology Connections explains that US household power is split-phase, with two 120V legs that combine to 240V for large appliances. It covers the breaker panel and how the system works.

Technology Connections explains why electric kettles are uncommon in the US, centering on 120V circuits limiting power. He tests ways of boiling water on gas, electric ranges and kettles.

12tone tells the story of pitch inflation and how concert A came to be standardized at 440 Hz, including attempts at legal standards. It is a short music history explainer.

Hans Rosling uses augmented-reality animation to show 200 countries over 200 years in four minutes, built from 120,000 data points. It tracks life expectancy and income to show the world's development.

3Blue1Brown visualizes the Riemann zeta function and the analytic continuation that extends it beyond where its series converges, building toward the Riemann hypothesis.

jan Misali presents an humorous but earnest case for counting in base 6 (seximal) instead of base 10 or 12, comparing the arithmetic advantages of each.

A minutephysics explainer showing that the Moon's path around the Sun is not a spiral but closer to a 12-sided polygon with curved corners. It argues the Moon arguably orbits the Sun rather than the Earth.

NASA's animated explanation of the Curiosity rover's Mars landing, which relied on a complex automated sequence taking about seven minutes. It features NASA engineers discussing the risks before the 2012 landing.

Aaron Francis walks through how PHP has changed from 2012 to 2023, covering traits, array destructuring, generators, typed properties and more. It is a quick chaptered tour of modern PHP features.

ScienceClic explains why nothing can go faster than light by treating motion through space and time together, so everything moves at the speed of light through spacetime. It uses animated visuals to cover relativity basics in 12 minutes.

Andreas Antonopoulos answers a question about how to secure your Bitcoin. He covers holding your own keys, backing up the 12 to 24 word seed phrase, and the tradeoffs of custodial accounts, phone wallets and hardware wallets.

Numberphile's James Grime discusses highly composite numbers, nicknamed anti-primes, which have more factors than any smaller number, using 5040 as the central example. It touches on Plato and Ramanujan.

Numberphile explains the long and short scales for naming large numbers, covering millions, billions, trillions, milliards and the Greek myriad, with James Grime and Tony Padilla.

Tom Scott visits the Strid at Bolton Abbey in Yorkshire, a deceptively narrow stretch of river with dangerous currents. He covers its reputation and the 12th-century legend of the Boy of Egremont.