The Key to Solving these Two Problems „Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.” (David Hilbert, „Mathematical problems”) Contents Hilbert's 1st problem, continuum hypothesis (CH) and its current status Quantified version of CH and its alternatives About infinity in other way – by the helps of positional numeral system About infinity in other way – by the methods of projective geometry Extensions of number lines and the lessons of CH’s alternatives Hilbert's 6th problem, the axiomatization of mathematical physics and its current status The basic concepts of the probability theory and the spacetime character of events The two-element numbers and the probability theory The two-element numbers…