Taxicab Numbers

 

The most famous taxicab number with mathematicians is 1729. The origin of this number is when Godfrey Hardy went to visit Srinivasa Ramanujan in the hospital. Both are famous mathematicians. Hardy, recognizing the genius of Ramanujan, sponsored him at Cambridge 1914-1919. Hardy told Ramanujan during his visit that his taxicab had the uninteresting number of 1729. Ramanujan replied that it isn’t an uninteresting number as it is the lowest number that can be expressed as the sum of two cubes (of positive numbers), two different ways: 1³+ 12³ = 1729 and 10³ + 9³ = 1729 (note; if one allows cubes of negative numbers 91 can be expressed as the sum of 6³ + (-5)³ or 4³+ 3³.

Additional taxicab numbers are those smallest numbers that can be expressed as the sum of more than two cubes or only the sum of two cubes.

So far, the following six taxicab numbers are known (sequence A011541 in the OEIS) - see prior post on the OEIS:

From Wikipedia: Taxicab number - Simple English Wikipedia, the free encyclopedia

Note: OIES sequences were reviewed in the post - Math Vacation: What is the next number in the sequence...? (jamesmacmath.blogspot.com)

 

Related Posts:

Math Vacation: The Ramanujan Machine (jamesmacmath.blogspot.com)

 

Hardy’s Book: Math Vacation: Book Review: A Mathematician's Apology (jamesmacmath.blogspot.com)