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)