A London cab, a piece of history and now an educational institution - all thanks to a small number. The story begins with G.H. Hardy's ride in 1919 when he met his Indian colleague Srinivasa Ramanujan. It was during this trip that the licence plate 1729 came up for discussion.
Hardy, who would later become one of the most renowned mathematicians of the 20th century, found the number dull. However, his friend Ramanujan had a different opinion - 'it is a very interesting number.' This number is notable because it's the smallest that can be expressed as the sum of two cubes in more than one way.
Ramanujan's point was proven to be correct when he showed Hardy that 1729 could be represented as both $1^3+12^3$ and $9^3+10^3$. This made it a significant discovery at the time, and this property has led to the creation of 'taxicab numbers,' which are defined by being the smallest number expressible as sums of two cubes in n different ways.
Today, we find ourselves faced with three puzzles inspired by this famous mathematical number. The first puzzle asks us to find a number that can be expressed as the sum of two squares in more than one way. A second problem deals with arranging strips of wood into triangles without exceeding a certain length limit. Lastly, there's a question about finding the value of a product of numbers.
But amidst all these puzzles and brain teasers, it's interesting to reflect on the humble beginnings of 1729 - a licence plate that would go on to inspire generations of mathematicians.
Hardy, who would later become one of the most renowned mathematicians of the 20th century, found the number dull. However, his friend Ramanujan had a different opinion - 'it is a very interesting number.' This number is notable because it's the smallest that can be expressed as the sum of two cubes in more than one way.
Ramanujan's point was proven to be correct when he showed Hardy that 1729 could be represented as both $1^3+12^3$ and $9^3+10^3$. This made it a significant discovery at the time, and this property has led to the creation of 'taxicab numbers,' which are defined by being the smallest number expressible as sums of two cubes in n different ways.
Today, we find ourselves faced with three puzzles inspired by this famous mathematical number. The first puzzle asks us to find a number that can be expressed as the sum of two squares in more than one way. A second problem deals with arranging strips of wood into triangles without exceeding a certain length limit. Lastly, there's a question about finding the value of a product of numbers.
But amidst all these puzzles and brain teasers, it's interesting to reflect on the humble beginnings of 1729 - a licence plate that would go on to inspire generations of mathematicians.
! Can you even imagine being one of the first people to meet Ramanujan and having such an epic conversation about maths 
?! 1729 is literally a number that's making waves in the math world right now, and it's all thanks to this random ride in London 
. I love how it just started with two mates chatting about numbers and ended up changing the game 
. It's so inspiring to see how one little discovery can lead to so many more and change people's lives 
.
. I mean, can you imagine having a conversation with someone who changed your life with just a random licence plate? It's crazy to think about how one encounter could lead to such a significant discovery in maths.
. I love how maths can be so subjective, and sometimes all it takes is someone with a fresh perspective to unlock the secrets of numbers.
. Who knows, maybe one day we'll have a London cab driving around with 1729 on its plate, inspiring a whole new generation of mathematicians 
. It's amazing to think about the impact that one small number can have on our understanding of the world 
.
. And now we're left with these mind-bending puzzles 
The power of a single number is truly inspiring 
.
i mean who knew something as simple as summing cubes could lead to so much innovation? 
and it's amazing how it all started with G.H. Hardy's ride in 1919 - talk about a history lesson 
Did you know that the number of ways a taxicab number can be expressed as a sum of two cubes is still unknown to this day? 
It's like, this number is still keeping us on our toes! 
Anyway, I'm kinda loving how 1729 has become this symbol of mathematical curiosity. Keep those puzzles coming and let's see if we can crack them all! 
the way hardy and ramanujan stumbled upon it in 1919 is so cool btw who knew a licence plate could lead to some of the most mind-blowing math problems ever 
. What I'd love to know is, do you guys think this number would've had the same impact if Hardy and Ramanujan hadn't met on that London cab ride? 
