Who was the first woman mathematician in India?

As per ancient Mathematical records, the first woman Mathematician is Hypatia who was also a Greek Philosopher .She was a famous teacher and a public speaker, who also taught her students to make astrolabes and hydrometers.

Her own accounts are recorded on Apollonius work conics (geometry) and Diophantus Arithmetica (number theory) are really amazing at that time

Now the first woman Indian Mathematician is Shakuntala Devi.

Also known as the ‘Human Calculator’ or ‘Human Computer’ , she demonstrated the multiplication of two 13 digit number which are 7,686,369,774,870 and 2,465,099,745,779 on an event held on 18th June 1980. These numbers were picked randomly by the computer department of Imperial Collage London where she answered the question in 28 seconds and that is 18,947,668,177,995,426,462,773,730.

She also earns a place in 1982 edition of the prestigious Guinness Book of World Records 2 year later based on the above mentioned event. Shakuntala Devi wrote a number of books which includes novels as well as texts about Mathematics, puzzles and astrology.

The 23rd root of a 201 digit number was given by her in 50 seconds which is 546,372,891. This answer was proven correct by the UNIVAC 1101 computer at US Bureau of Standards. They had to write a special program in order to incorporate such large calculation.

Who is/was the most mysterious mathematician?

Well I think it may be Srinivasa Ramanujan. Indian mathematician whose contributions to the theory of numbers include pioneering discoveries of the properties of the partition function.He was the youngest fellow of royal society and the only second Indian member and the first Indian to be elected a fellow of Trinity college Cambridge.

He lived for only 32 years but in those years of his life he discovered 3900 results. He achieved many highly mathematical and innovative results , which includes Ramanujan Prime, Ramanujan Conjecture , Ramanujan Theta Function, Partition formulae,Ramanujan’s Master Theorem and Mock Theta Function. These results has not only motivated and encouraged many mathematicians to research on these fields but also provided a new vision of work on the mentioned results.These research works opened a pathway to a number of segments of research which includes the intriguing concepts of the infinite series of π

\(\frac{1}{π} = \sum_{k=0}^{\infty} \frac{(4k!)(1103+26390k)}{({k!}^4)(396^4)}\)

Another research includes his vivid work on composite numbers which gave birth to a distinct number of researchers in the filed of those numbers.Ramanujan is believed to be a man of remarkable rapid problem solving techniques. We are all quite familiar with the famous Hardy-Ramanujan number 1729 which was described as the smallest number that can be expressed as sum of two cubes in two different ways which are

1729 = \(10^3\)+\(9^3\)

1729 = \(1^3\)+\(12^3\)

Ramanujan discovered a wide range of formulas to be worked in later in detail. As per G.H Hardy’s view the discoveries made by Ramanujan have a more impactful insight than what one could usually see. Also Ramanujan’s original letter are enough to show his extreme high calibre that can be compared to mathematical legends like Euler and Jacobi.

Also some of his collaborative works are like

Brocard-Ramanujan Diophantine Equation

Dougall-Ramanujan Identity

Ramanujan-Negell Equation

Ramanujan-Peterssen Conjucture

Ramanujan-Soklem’s Constant

Landau-Ramanujan Constant

Ramanujan-Soldner Constant

Rogers-Ramanujan Identities

Ramanujan-Sato Seris

He published 37 papers in total. B.C Berndt said that "A huge part of his work was not taken in sight which is spread in three notebooks and a lost notebook. These notebooks contain approximately 4000 claims, all without proofs. Most of these claims have now been proved”. It is believed even on his last years he accounted certain functions that approached to him in his dreams.

But research is still going on , on his works.

What's the speciality of the number '5040'?

In mathematics there are many interesting number like  π,  The golden ratio φ , 1729 , and many others

In such interesting numbers 5040 is also in the list of them. So this number 5040 looks normal like without any special characteristics but it do posses some of the very eye catching characteristics.

So if we start from just looking at the number we can say that it is  7! that is 5040 and if we closely look at this in the view of permutation then we can see that it is the number of permutation of 4 items out of 10 choices that is \(^{10}C_4\)=10*9*8*7

Now if we look at this number in a mathematical and analytical way

  1. We can see that 5040 has exactly 60 factors including 1 and 60 itself which are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040.
  2. Again this number 5040 is unique in another way that is , this number is the sum of 42 primes that is 42 consecutive primes and that is 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 +163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229.
  3. 5040 this number is just one less than a square, making (7, 71) a Brown number pair that is 7!+1=5041 which is 1 less than 5040. Now in mathematics a brown number are pairs of the numbers taken like (n,m)  that solve the Brocard's Problem {Brocard’s problem in mathematics is where we have to find an integer values of m and n mentioned above for which n!+1=\(m^2\) } values of  and that solve Brocard’s problem are called Brown Numbers . Until 2019, we found the existence of three brown number pairs which are (4,5) , (5,11) and (7,71)
  4. Our number 5040 is also a superior highly composite number. Now in mathematics a highly composite number is a number which has more divisors than any other number which is smaller than the number itself and also there prime factorisation should be the multiplication of consecutive primes.

5040=\(2^4\)*\(3^2\)*5*7 

So it is a highly composite number.

5. This number 5040 is also a colossally abundant number. The first 15 colossally abundant numbers are 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800.

Some small but interesting facts about 5040

  1. 5040 can be divided by every number from 1 to 12 only exception to this is 11.
  2. However 5038, the closest number to 5040 can be divided by 11.
  3. The 12th part of the number 5040 is divisible by 12.

5040 in our daily life

Okay now if we look into history and I will say some philosophy we can see that.