Mental calculation

Mental calculation, also known as mental computation, is when people do arithmetic in their minds without using pencils, paper, or calculators. This skill is useful when tools are not available, when it is quicker than other methods, or even in fun competitions. Mental calculation often uses special tricks for solving different kinds of problems, many of which are based on the decimal number system.

How well someone can do mental calculation depends on their short-term memory, especially a part called the phonological loop, which helps with adding numbers. Being flexible in thinking also helps a person succeed in mental calculations. This means knowing how numbers relate to each other and spotting patterns.

During the 1700s, researchers noticed that children who were very good at mental calculations often grew up to be successful scientists or mathematicians. Sometimes, however, these very skilled calculators struggled in other areas of life. People who could do incredibly fast and accurate mental math were called prodigies or savants. In the past, they might have been called lightning calculators or geniuses.

Studies with children in England showed that mental imagery—the ability to picture things in the mind—plays a role in mental calculation. Using special brain scans, scientists found that certain parts of the brain, called the parietal lobes, become active when people use mental imagery for calculations. Learning mental calculation is sometimes part of school lessons, where teachers focus on teaching useful mental strategies.

Exceptional calculational ability

Some people have an amazing ability to do math in their heads, like adding, subtracting, multiplying, or dividing big numbers without any tools. Before we had electronic calculators and computers, skilled people who could do mental math were very important in places like research centers, such as CERN. You can read more about this in books like Steven B. Smith's The Great Mental Calculators from 1983, or in the book Hidden Figures and the film adapted from it.

Competitions

World Cup

The Mental Calculation World Cup is a big international contest where people compete to be the best at doing math in their heads. It started in 2004 and happens every two years in Germany. Contestants solve four main types of problems: adding ten big numbers, multiplying two very large numbers, finding square roots, and figuring out weekdays for specific dates. There are also surprise tasks. The most recent event was in September 2024, and Aaryan Nitin Shukla won, becoming a two-time World Champion.

Mental Calculation & Speed Reading Olympiad

The Mind Sports Olympiad has held yearly world championships since 1998.

Memoriad – World Memory

The first international Memoriad happened in Istanbul, Turkey, in 2008. The second was in Antalya, Turkey, in November 2012, with 89 competitors from 20 countries. Awards were given for ten different skills, including five types of mental calculation. The third Memoriad was held in Las Vegas, USA, in November 2016.

Mind Sports Organisation

The Mind Sports Organisation has recognized six grandmasters of mental calculation and one international master. In 2021, Aaryan Nitin Shukla became the youngest champion ever at just 11 years old.

World records

Shakuntala Devi from India has been featured in the Guinness World Records. Aaryan Nitin Shukla from India currently holds seven Guinness World Records in mental calculation. Neelakantha Bhanu Prakash from India has been noted for being faster than a calculator in addition. A performer from Sri Lanka and Malaysia was a runner-up in 2019 on Asia's Got Talent.

13th root

Doing the 13th root of a number is a famous mental calculation challenge. It means finding a number that, when multiplied by itself 13 times, gives the original number. For example, the 13th root of 8,192 is 2.

Doing the 13th root of a 100-digit number has been a record challenge. The first record was set in 1970, and the best time was 13.55 seconds in 2002. For 200-digit numbers, the first record was set in 2005, with times improving over the years.

Media

Literary

Frank Herbert's novel Dune, has special characters called Mentats who use their minds to remember lots of information instead of using computers. In Roald Dahl's novel Matilda, the main character can do big math problems in her head very quickly.

Film

Fiction

Twentieth century

1980s

In the 1988 movie Rain Man, a character can do large math calculations in his head.

1990s

In the 1991 movie Little Man Tate, a boy answers a math question suddenly. In the 1997 movie Cube, a prisoner uses his mind to find special numbers. In 1998, a film shows a character doing big math problems in his head. Also in 1998, a movie features a 9-year-old who can solve a very difficult secret code.

Twenty-first century

2000s

In the 2006 film Stranger than Fiction, a man can do fast math when asked.

2010s

In the 2012 film Safe, a child with great math skills is taken. In the 2016 film The Accountant, a man uses his mind to find mistakes in money matters. In the 2017 film Gifted, a very smart young girl becomes part of a family disagreement.

Bio

In 2020, a film called Shakuntala Devi tells the story of a real person known for doing math in her head.

Television

In the show Suits, a character multiplies big numbers in his head to impress others. In Malcolm in the Middle, a boy does amazing math in his head. In NewsRadio, a character easily does math problems. In The Big Bang Theory, a main character does math for his science work. In Breaking Bad, the main character figures out numbers for his work just using his mind. In Fringe, characters meet someone who can solve many math problems at once after taking special medicine. In Scorpion, a very smart man is called a “human calculator”.

Animation

In the 2009 animated film Summer Wars, a math expert can break security codes with his mind and find out what day someone was born by their birthday.