In the current year 2016, we are celebrating the third centennial of Leibniz's death. This is a good occasion to present some highlights in the immense mathematical work of the great universal genius under a modern point of view, and to add some surprising interpretations that might have elapsed the Big Master of Science - or consciously hidden by himself in order to prevent plagiarism.

Here are some problems we shall discuss and solve by surprising methods:

(1) How to compare Leibniz's harmonic triangle with Pascal's triangle?

(2) How to compute infinite sums of reciprocal hypergeometric numbers?

(3) How to visualize the Leibniz series with a pizza?

(4) How to understand that a hanging chain cannot be a parabola, and
how to find its real shape?

(5) How to determine logarithms by using a file?

(6) How to compute the area of a Portuguese windmill wing by rotating
the wheel?

Our approach will be supported by the modern slogan: "A picture is worth
a thousand words".