Foundations of Mathematics

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Humanity, at this point in human history, desperately needs a renaissance in science, specifically math and physics. We will address mathematics here. The core of science is math; the core of mathematics is set theory. Near that is the theory of numbers.

For years, I have dabbled in and reflected on both. That does not make me an expert nor authority. But I Care and that fact alone impels me to express what needs to be said at this desperate time.

We need to encourage and nurture our youth to explore and develop their own ideas. Of course, we should do our best to educate them on the history and previous developments. But we cannot squash their curiosities with dogma; we cannot give preference to regurgitation over creativity. This is our fundamental mistake in conventional academia regarding physics and mathematics. This article is a first step in Vixrapedia toward correcting that.

I never use the word “fundamental” lightly. It has precise meaning in mathematics. The title of this article is apt because it deals with set and number theory but explicitly from a fresh and invigorating perspective elucidated above.

Try a vixra search on my full name: Salvatore Gerard Micheal. Skim the article on Set Theory. It is precise; it is authoritative; it is ignored by convention. Let us not waste time talking about why; let us rather discuss why it should NOT be.

I believe it could be a cornerstone of a renaissance in mathematics mentioned above. It could be used as an example for our youth to see what can be done when we are NOT forced to regurgitate conventional dogma or when their curiosities are NOT squashed. It could be used as a metaphorical flag for them to wave to inspire other curious minds we so desperately need to nurture.

Finally, skim the article titled Counting the ‘uncountable’. It’s a set of essays about number theory. I wrote and published it six years ago. I reread it yesterday. In all humility, I’m somewhat flabbergasted and astonished by the article. Thinking of the author in the third-person, I thought “This guy is either a Genius or an Idiot.” Looking at the number of downloads, I realized likely nobody with any authority and wisdom read it. I assume this will be the case for several hundred years. But what if, on the slim chance, this guy is NOT an Idiot? And so we present this article.