It was a natural thing for Beethoven to compose for the piano. Not that it came to him easily. We have proof in the form of his sketchbooks how he would mull things over on paper and in his mind until the composition was as he wanted it, polishing and perfecting. The thirty two piano sonatas he wrote are part of the core piano repertoire and music in general. They hold a vast mount of musical ideas, challenges for playing and interpretation, and the sheer variety and range of emotion contained within them dictate that they will remain part of the core repertoire. If Beethoven had written nothing but these 32 sonatas, chances are he would still be regarded as a great composer.
The last sonata sees a Beethoven that has weathered much, learned much, and progressed much. The work is in two movements, the first being written in raw-sinewed, sprawling sonata form that has a short introduction that Chopin paid tribute to in the opening of his 2nd piano sonata (Beethoven's 32nd piano sonata was a favorite of Chopin's). it also has a first theme that is deep and ominous that is given a fugal treatment in the middle of the movement. The second movement is an Arrietta and variations that take piano writing to new heights and sounds. From the jazz-sounding section to the cosmic trills near the end of the work, Beethoven transcends the instrument and writes music of a purity that is rare and beautiful.
It is all outside my comprehension how such things are possible, but it is a treasure that we have music of such power, beauty and emotion, music offered up as Beethoven himself said, "from the heart to the heart".