[saeranv]

His mathoverflow responses are surprisingly intuitive and elegant.

Intuition for visualizing/imagining high-dimensional geometry: https://mathoverflow.net/questions/25983/intuitive-crutches-...

Intuition for convolution: https://mathoverflow.net/questions/5892/what-is-convolution-...

This is much more satisfying way to think of these concepts. The idea of thinking of convolution as a 'fuzzy' optical phenomena, the idea of thinking of n-dimensional space as a probability distribution.

It's interesting the way he grounds his intuition in practical applications. For convolution for example, a common application is to convolve a 2d image with a gaussian kernel to fuzz the image. I know that, but always still had a not-very intuitive, but very dry and technical understanding of convolution as a sort of dot product of two vectors representing the underlying image and the kernel. Terence Tao in contrast exploits the practical intuition of 'fuzziness' in this process to suggest thinking of convolution as a fuzzy (probablistic) addition of functions. It's a subtle step, but giving some sort of physical, or visual intuition for mathethematics like this is so helpful.

[cambalache]

Yep being a lowly engineer who loves math I always wanted to learn a more rigorous approach, but then again I am lazy, so for example I started with Rudin, but gave up as soon as I couldnt grasp something, same with other analysis books and lecture notes. Then comes Terry with his 2 jewels of books on Analysis, but I thought to myself, no way I am going to understand anything from arguably the best mathematician in the last decades. But not only the prose is clear and unpretentious the motivation of why analysis is "needed" is presented perfectly, the books are self-contained and the progression is very smooth,no pun intended. Highly, highly recommended.