  The existence of incompatible observables constitutes one of the most
prominent characteristics of quantum mechanics (QM) and can be revealed and
formalized through uncertainty relations. The
Heisenberg-Robertson-Schr\"odinger uncertainty relation (HRSUR) was proved at
the dawn of quantum formalism and is ever-present in the teaching and research
on QM. Notwithstanding, the HRSUR possess the so called triviality problem.
That is to say, the HRSUR yields no information about the possible
incompatibility between two observables if the system was prepared in a state
which is an eigenvector of one of them. After about 85 years of existence of
the HRSUR, this problem was solved recently by Lorenzo Maccone and Arun K.
Pati. In this article, we start doing a brief discussion of general aspects of
the uncertainty principle in QM and recapitulating the proof of HRSUR.
Afterwards we present in simple terms the proof of the Maccone-Pati uncertainty
relation, which can be obtained basically via the application of the
parallelogram law and Cauchy-Schwarz inequality.
