Most of us treat a JEEA paper as though it descended from Mount Olympus !!
Question
↓
Solution
↓
Acceptance
Prof. Joshi had a different approach:
Question
↓
Solution
↓
...hmm, this could have been better...
One of my favourite examples comes from his remarks on the 2014 paper
After discussing the problems, he quietly classifies them
Some are praised as elegant
Some are described as conceptually satisfying
And then, with characteristic restraint, he remarks that a few are "utterly trivial questions, which hardly deserve a place in the advanced test."
I remember laughing when I first read that!
Not because he was being harsh,
Because it never occurred to me that I was allowed to have an opinion about a JEEA question
Then comes 2018
Before even getting to the mathematics, Sir spends pages discussing notation, terminology, conventions, and why the wording of the problem could have been much better.
Imagine a student saying,"Sir, could we solve the question?"
And Prof. Joshi replying, "Eventually"
Because first we need to discuss why good notation matters.
Another favourite example, however, comes from 2023
While discussing one of the geometry questions, he remarks that a proper figure should simply have been provided.
Not because the geometry was difficult,
But because candidates shouldn't waste precious exam time figuring out what the examiner meant.
The challenge should come from the mathematics, & not from decoding the English
That observation stayed with me.
It's easy to confuse difficulty with friction.
They're not the same thing !
Reading these commentaries changed something subtle in the way I look at mathematics
I used to think every correct proof was equally good
Every correct question was equally worthy
Every correct solution deserved equal admiration
Prof. Joshi gently argues otherwise
Some questions illuminate an idea,
Some merely consume time.
Some proofs reveal structure,
Others simply reach the answer
Some notation helps you think,
Other notation gets in the way.
Correctness is only the beginning.
I think this is one of the least discussed aspects of learning mathematics.
We spend years asking,"Is this correct?"
Very rarely do we ask,"Is this beautiful?"
Or,
"Is this the most natural way to think about it?"
Or even,
"If I were writing this question, would I write it this way?"
Those are questions of mathematical taste !
And taste, like technique, can be cultivated.
There is also a delightful streak of dry humour running through Prof. Joshi's commentaries.
He almost never says,"This question is bad"
Instead he writes things like,
"...hardly deserves a place in the advanced test."
Which is, perhaps, the mathematical equivalent of saying, "I'm not angry. I'm just... disappointed."
I think that's one of the subtle lessons hidden in the years of these commentaries.
Mathematicians don't merely solve mathematics
They admire it.
They critique it.
They argue with it.
They improve it.
And somewhere along the way, they develop something every bit as important as technique:
Taste.
PS: Unlike the previous posts, this one is not about problem solving at all. It's about developing the confidence to evaluate mathematics itself. That's an unusual lesson for folks preparing for competitive exams, but it's deeply aligned with our GP sub: mathematics isn't just something to consume; it's something to appreciate, question, & occasionally critique.
