This post is for tomorrow’s page of Talmud to be studied, which is page 1,729 of the Babylonian Talmud. Print it up now and enjoy, and Shabbat Shalom from Talmudology.
The number of tomorrow’s daf, (Bava Basra) 95, has some special mathematical properties. For example, it is a Thabit number, (also called a 3-2-1 number) which is an integer that is of the form 3 · 2ⁿ - 1. But there is another mathematical curiosity about tomorrow’s page number. Starting from the beginning, it is page number 1,729 of the Babylonian Talmud. And 1,729 is the smallest Ramanujan Taxicab Number, a number that can be written as the sum of two cubes: (1³ + 12³=1729.) In two different ways: (9³ + 10³=1729).*
[*These numbers are also known as Hardy-Ramanujan numbers. Also, to be precise, they are numbers that can be can be written as the sum of two cubes using positive integers. Let’s keep going.]
Here is one version of the story of how these numbers were discovered:
Curious properties sometimes lurk within seemingly undistinguished numbers. 1729 sparked one of maths most famous anecdotes: a young Indian, Srinivasa Ramanujan, lay dying of TB in a London hospital. G.H. Hardy, the leading mathematician in England, visited him there. 'I came over in cab number 1729,' Hardy told Ramanujan. 'That seems a rather dull number to me.'
'Oh, no!' Ramanujan exclaimed. '1729 is the smallest number you can write as the sum of two cubes, in two different ways.' Most of us would use a computer to figure out that 1³ + 12³ = 9³ + 10³ = 1729. Ramanujan did it from his sickbed without blinking.
Mathematicians have mined his theorems ever since. ..Far more than just another number theory, 1729 is the first of the 'Ramanujan numbers' or taxicab numbers. Mathematicians are competing to search for more of them (with higher powers) and testing the strength of new computing technology. The search is seen as mathematics' current greatest challenge. Only recently, a lost bundle of Ramanujan's notebooks turned up in a Cambridge library setting maths off on a new voyage of discovery.
“Ramanujan, a largely self-taught mathematician, seemed to solve problems instinctively and said his formulas came to him in the form of visions from a Hindu goddess. During the height of British colonialism, he left his native India to become a protégé of mathematician G.H. Hardy at Cambridge University in England.”
In case you are wondering, this is the only page of the Talmud that is a taxi-cab number. (There is a machloket achronim [debate] as to whether 2 is a taxicab number. Some lists include it. Others don’t. Personally, I don’t think it counts, but my opinion on the matter is of zero mathematical importance.) The next one is 87,539,319.
