“The most common instance of beauty in mathematics is a brilliant step in an otherwise undistinguished proof.”
— Gian-Carlo Rota
The number 1729 has an interesting story in mathematics involving the extraordinary Indian mathematician Srinivasa Ramanujan. G. H. Hardy accounts:
“I remember once going to see him (Ramanujan) when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. ‘No’, he replied, ‘it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways.’”
Ramanujan had a knack for numbers. Growing up in India at the turn of the 20th century, Ramanujan was largely self-taught. Over his short life time (aged 32), he independently developed nearly 4,000 results in mathematics. He kept his results (without proofs) in notebooks that modern mathematicians are still looking into this day. Nearly all of his results have been proven to be true and have driven research in number theory for the past century. Recently, one of Rumanujan’s results, previously unknown to mathematicians, was an important piece to a 2006 publication.
Their methods… 😂😂😂
Pythagoras and Einstein 🤭😂😂
An astonishing rendering of algebraic numbers.
As described by the source, “[This is a v]isualisation of the (countable) field of algebraic numbers in the complex plane. Colours indicate degree of the polynomial the number is a root of (red = linear, i.e. the rationals, green = quadratic, blue = cubic, yellow = quartic…). Points becomes smaller as the integer polynomial coefficients become larger. View shows integers 0,1 and 2 at bottom right, +i near top.”
Mathematics is beautiful. <3