In an earlier write up we had dealt with Ramanujan’s all consuming love for maths and the famous Ramanujan number:1729.
Prime numbers, which are the building blocks of the number system, had Ramanujan’s attention early in his career and he made extraordinary contributions to the prime number theorem that had kept many mathematicians busy for decades.
It is one of the first things we learn about in primary math : numbers that are only divisible by themselves and one are primes. Numbers such as 2, 3, 5, 7, 11…. In the first ten numbers, there are 4 primes.
In the next group 11 to 20 – there are four (11, 13, 17and 19);
But in the 21 to 30 group there are only two (23, 29)……
Mathematicians try looking for patterns. It helps them generalize or predict – in this case, when the next prime number will turn up, or the rate at which you will encounter them. For instance, in the first 100 numbers, there are 25 primes, in the second hundred there are 21 of them……The surprising thing is that there is no last prime number! As long as there are numbers, there will be primes – even in the billions!
Here’s a math work out for you:
Q) Identify prime numbers and create your own prime number table:
201 -500: and so on. See how far you can go!
It will prove useful in solving your school math problems!
Of even greater value would be a table or chart worked out by you containing the factors of composite numbers – i.e. numbers that are not primes – 4,6,8,10,…………20,22,24 etc
One of Ramanujan’s big contributions was on the properties of highly composite numbers (numbers like 24 which have many factors – 1, 2, 3, 4, 6, 8, 12, 24). A 52 page paper authored by him on this topic appeared in the London mathematical society in 1915, in which he provided many elegant proofs about the properties of such numbers!
Your own chart of such factors can serve as a ‘ready reckoner’, when you are computing L.C.Ms and H.C.Fs for your homework problems! You could even tackle various ways to ‘partition’ a number- the many ways you can add up numbers to get a particular number. Ramanujan had made significant contributions in this area.
For example: you can get the number 4 by:
2+2; 1+3; 1+1+2; 1+1+1+1, or 4+0; this means that there are 5 different ways to add up numbers to get the number 4. In mathematical terms, the number of partitions of 4 is 5. This seems a very easy thing to do. But, as you start partitioning the numbers, you notice the number of partitions increases very rapidly as you work your way up the number scale. Number 3 has only 3 partitions, number 10 has 42 and you can partition number 50 in 204,226 ways!
Working out the partitions of numbers, at least for the first 20 numbers can be a reasonably interesting way to spend one’s free time!
For Ramanujan, his interest in math was egged on not so much by arriving at a correct answer; it came from ‘messing about’ with numbers, equations, even solutions to problems. In the words of one of his biographers, Robert Kanigel, it came from “turning them upside down, inside out, seeing in them new possibilities, playing with them as a poet does with words and images, the artist color and line, the philosopher ideas.”
ssYou too can devote some time to ‘messing around’ with numbers and see where it leads you. If nothing else, it will remove the fear that math seems to hold over most of the human race!