I Have Found Inspiration!

Dearest Journal, June 22, 1922

Here is a piece that I created after being inspired by the palace.

Who would have thought that I would be sitting here today in love with the place where I am living? My elation has come from the Alhambra palace you see, for I have traveled here to Spain after my schooling in Haarlem. Oh how frustrating and experimental those years were! It has been four years since I was re-taking those miserable, torturous classes in the Higher Technical School. It baffles me that during those years I was willing to comply to father's dream for me to become an architect. I know now that I have made, with the help of Samuel Jesserum de Mesquita one of my most inspirational teachers, the best decision of my professional life so far. I find it quizzical to call it my professional life, for my days have only consisted of countless hours re-sketching and re-working these tireless pieces of art. If not for the guidance of Samuel, I cannot fathom where I might be today. Regardless, I can say that although I have steered my life away from architecture, for it only took one week in the School for Architecture and Decorative Arts to decide that, I have not, and will not shake my intense pessimistic view of my work. I have created more rubbish that art, and for that I am ashamed, but I will continue to work, for this is my destiny.
                I am sitting now in a section of this magnificent palace. The majolica tiles line the rooms from the floor to the ceiling, and are truly a spectacle. I would take this place over any club with a flapper show in the evening. I am discovering that the more time I stay here in this magical setting, the more strange looks I encounter from tourists. They are puzzled to see me so intent in deciphering these great artistic feats that cover the walls. I have also noticed that this palace is filled with mathematical complexities; there are shapes everywhere, and I when I sit outside and stare into the heavens, I see these same shapes mirrored in the clouds. As I sit here I am content, not with my work but with my life. Through my many years of traveling I have fallen in love with Italy, and even though I was just in Florence in April, I have decided that I shall return promptly. I have desires to paint the breathtaking landscapes that fill the countryside but due to my new found interest in the geometry which I am discovering all around me, I believe that I do not want to paint typical landscapes. My ideas including bringing the land into the center of the plane, as if it were merging into a pit, or possibly skewing the perspective to play a trick on the viewer. Whatever I decide I am completely inspired by this palace and plan on returning some day. I hope that Italy holds good artwork in my future.

Maurits Cornelis Escher

Journal Entry 278

Journal Entry 278
December 13, 1900

I have not written in a long while, due to the fact that my last year has been very full. Firstly, I finally finished my formal list of geometric axioms. I became very frustrated with the mathematic community accepting something as vague as Euclid’s geometric axioms. He made too many assumptions and provided concepts with no formal definition! So I set out to fix the ambiguity and completely reinvent concepts which haven’t been touched in over two centuries! I started by specifying the three terms I would use, along with three concepts.
    Terms:

• Point
• Line
• Plane

    Concepts:

• Congruence - “Two binary relations, one linking line segments, and one linking angles, each denoted by an infix ≅ ”
• Betweenness - a ternary relation linking points
• Containment - three binary relations, one linking points and straight lines, one linking points and planes, and one linking straight lines and planes

Next I proceeded to rewrite all of Euclid’s axioms with only these very rudimentary laws, leaving nothing up to assumption. I made it a point to outline which axioms allowed each of the proofs to be valid, along with taking painstakingly detailed notes. By the time I published my work last year, I managed to finish twenty-one axioms to govern the field of geometry.

    Secondly, I prepared for and attended the International Congress of Mathematics, held in Paris, France. My major focus in preparing for this event was the future of mathematics. Recently, progress in the field of mathematics has been slow and sporadic (mostly fueled by my contributions). My goal was to present either a concept or a problem to fuel the next one hundred years of mathematics, and hopefully lead to many astounding discoveries in the field. On the eighth of August, I presented my twenty-three problems, endearingly called the “Century Problems”, to the conference of my peers. I also formally published them for the greater world to see. Currently none of the problems have been solved and my fellow mathematicians are very intrigued and contemplative about them. When preparing my list, I originally had a twenty-fourth problem, however I decided not to include it on the published list. I felt as though it’s contribution was unnecessary and the phrasing of the problem was weak. After my very detailed work on Euclid’s axioms, I had no interest in publishing a weak problem only to have it rejected or revised by the mathematic community, claiming it’s “too vague to solve”. My problems do range in precision, with some needing a specific answer, and others the introduction of a new mathematical concept to solve. A few of my problems (the 11th and 16th, for example), focus on furthering current disciplines of certain less noticed, yet drastically important fields of mathematics.
    Now I’m late for a meeting with a colleague of mine. We will be discussing my favorite of my twenty-three problems: the first. I hope this conversation will be both interesting and mentally stimulating!

Cover of My Twenty-Three Questions Presented in France In 1900 (Translated into French)