After a late night Christmas party and the usual early
morning presents by the tree, this Christmas was slightly different.

My wife’s cousin, who just came to US a couple of days ago,
is with us for the weekend before heading to Florida on Sunday for his Masters
in Aeronautics. I happened to notice his book on “Flight Stability and
Automatic Control” and was drawn to the calculus - derivatives and integration used in the
text book. And, it soon lead to reminiscing about some math problems.

I am usually intrigued by Math problems that younger students
ask as it allows me an opportunity to indulge in a common language despite the
age difference! He posed the following.

- Is it possible for velocity of an object to be 0 and acceleration to be non-zero ?
- What is larger - x or 1/x ?
- A vehicle moves 1Km at 30 Kmph from A to B. What velocity would it have to move from B to C (another 1km distance) so the average velocity from A to C is 60 Kmph ?
- What is the derivative of Sqrt(2+sqrt(2+sqrt(2+sqrt(2+..… infinite series
- And then, once he assessed me with that, he got on to the real one.. derivative of Sqrt(x+sqrt(x+sqrt(x+sqrt(x+..… infinite series

I don’t consider myself a math whiz, but take pride in my interest in basic math and like solving problems like these from time to time. After answering all of them, I must have gained the right to ask and it was my turn.

^{th}grade – almost a quarter century ago!

I asked him - which of the following, if any, is/are integrable ? And, if they are, solve them.

- 1/(1+x^4)
- x/(1+x^4)
- x^2/(1+x^4)
- x^3/(1+x^4)
- x^4/(1+x^4)
- x^5/(1+x^4)

As soon as I said that, my 7 year old daughter who is still
struggling in getting her 2 digit additions right – accidentally blurted out
the correct answer – “All of them”. She probably figured the pattern in how I quiz
her already J.
I told her she was the first one who ever answered that question correctly.
(and definitely the one to answer without even solving them !)

And, after a good discussion in solving all of them with the 21
year old student, he told me – “You created this problem even before I was born”.
That was a profound observation. And, one of the reasons why I love Math
problems – the timeless nature of the problems and more importantly – their
solutions. Strangely, the solutions provide a sense of stability in this day
and age where everything changes at a frantic pace. I cannot say how many other
solutions remain the same over such a long period of time!

I look forward to asking the same question in about a decade
when my daughter learns calculus. I am sure I will remind her she got it right
her first time :)

After writing this article, I prod her – “how did she answer it correctly when I asked her about the “integrable” question?. She says - All of those are “Incredible” – the word she heard ! Math problems and solutions are incredible indeed– with their unvarying answers in this ever-changing world!

After writing this article, I prod her – “how did she answer it correctly when I asked her about the “integrable” question?. She says - All of those are “Incredible” – the word she heard ! Math problems and solutions are incredible indeed– with their unvarying answers in this ever-changing world!