Conveying complex ideas intuitively is an art

(This article is a transcript in English of one of my french linkedIn posts)

Conveying complex ideas intuitively is an art. As Andrew Ng says "Before diving into the subject, I first want to give you the intuition." Most people in AI have at some point taken one of his courses, and his teaching style leaves no one indifferent! More broadly, I admire personalities like Andrew Ng, Luis Serrano, Jay Alammar - they know, in my opinion, how to convey complex concepts intuitively. This is a skill I have often lacked in my own journey.

Indeed, I remember many classes, especially in mathematics, where priority was given to rigorous proof rather than developing intuition. Once the proof was presented, the teacher often considered the subject closed and understood by all. On the contrary, I have often had physics teachers whose main goal was to "explain with their hands" without proving anything. After all, this story of "intuiting" a concept must be, somehow, a physicist thing.

I am convinced that what really helps to durably assimilate a concept is to start by giving an intuitive representation, a mental image. It is essential in my opinion to develop an instinctive understanding of the underlying mechanisms before diving into the proofs.

Of course, some rigorous proofs can be exciting and essential. But are they really useful for all students? Probably not. Especially when they are presented as a mandatory step, without any apparent connection to concrete reality.

That's the problem: theoretical proofs often do not advance intuitive understanding. They are then likely to discourage more than anything else those who struggle to connect them to their intuition.

On the other hand, I have always been fascinated by short, elegant proofs that open your eyes to an almost cheeky way to solve the problem. They are powerful because they require a bird's eye view, a real step back from the problem. They also reveal a certain beauty in mathematical reasoning. The famous proofs that start with "we notice that" and 2 lines later the matter is settled, while in parallel an alternative proof consists in deploying brute force and filling 3 full pages.

I think this ability to explain things simply is very undervalued. It also requires being able to relate to learners, which is not always easy! I also notice that there is often a premium on complexity nowadays. No doubt it is also more reassuring and gratifying for the teacher to show that he can do complex reasoning?

I am very curious to know your point of view on this issue! Does your experience match this observation?