Heya! Appreciate the discourse, its awesome!

As a starting point, I've shared the rough description from wikipedia on the t-SNE algorithm:

> The t-SNE algorithm comprises two main stages. First, t-SNE constructs a probability distribution over pairs of high-dimensional objects in such a way that similar objects are assigned a higher probability while dissimilar points are assigned a lower probability. Second, t-SNE defines a similar probability distribution over the points in the low-dimensional map, and it minimizes the Kullback–Leibler divergence (KL divergence) between the two distributions with respect to the locations of the points in the map. While the original algorithm uses the Euclidean distance between objects as the base of its similarity metric, this can be changed as appropriate.

So the algorithm is definitely trying to minimise the KL divergence. In trying to minimise the KLD between the two distributions it is trying to find a mapping such that dissimilar points are further apart in the embedding space.