Infinitary Research Institute

Dear Fellow Mathematician,

I hope that you are doing well during these trying times of great change in the pandemic of 2020. My name is Nicolas Spoors and I am a logician who is deeply concerned because mathematicians are all assuming that ZF is bug-free without actually testing to see that it is. Because of this, I believe that we have an inefficiency in the development of mathematics. I am launching a nonprofit think tank to prove that ZF set theory, as we know it, is inconsistent. I believe that our "theory of everything" (ZF) is INEXACT. This is contrarian, but consider the fact that most computer programs must be debugged and given ongoing maintenance. Mathematics, through the lens of ZF set theory, is like a computer program that has NOT been tested for bugs, and yet it is assumed to work without any problem. We know that ZF cannot be proven true from logical axioms (Godel 1930)…but it could potentially be refuted, and nobody has tried (other than some skepticism about some individual axioms in ZF)! No one (but us) actually believes right now that ZF set theory (as we know it) is inconsistent, and this is why we are asking for your financial help to launch Infinitary Research Institute as a nonprofit mathematics think tank. Our first mission at Infinitary Research Institute is to prove the Spoors Inexactness Conjecture, which states that:

ZF set theory is inconsistent, and we should expect a degree of inexactness in our understanding of the axiomatic system of set theory. Thus, our understanding of set theory is not just incomplete, it is to some degree, inconsistent.

There is a long-standing bias in the world of mathematics to accept ZF as true/consistent without any reason, but we want to learn more about this inefficiency in mathematical knowledge. We do NOT suggest throwing away ZF, but we suggest instead enhancing it and thus protecting it from complacency and false confidence. We suggest that the axiomatic system of (true) set theory might be ENORMOUSLY more complicated than previously thought, and that we should expect to make ongoing maintenance to our understanding of ZF set theory as needed.
 
Why are we the team to turn this conjecture into a theorem?

FOCUSED:  We are building a think tank, not a school, and we are free from students and teaching responsibilities.
UNENCUMBERED:  We are NOT concerned with the status quo or risking our professional reputations within academia by supporting an unpopular conjecture.
STRATEGY:  Mathematicians use only a tiny portion of set-theoretic structures permitted by ZF. Inner and outer models of ZF through model theory are not enough. The key is to go to the outer limits of what is possible with ZF.
PERSPECTIVE:  We aim to be informed, but not entrenched by consensus opinion or bias (towards ZF consistency) while we conduct our research. We are conducting our research from the perspective of having a degree of doubt in mind about ZF, rather than acceptance.

Will you participate with us in history as we launch Infinitary Research Institute and prove the Spoors Inexactness Conjecture? Our long-term vision is to become the greatest think tank on the planet for answering the biggest questions in mathematical logic. Without your help, our research slows to a snail’s pace and novelty stops, but with your help we are changing the world like never before! This is about more than just a possible theorem; this is about a new program of inquiry into mathematics which looks not just for incompleteness but also for inconsistency as well. Our aim is to catalyze a major shift in mathematical research which produces more papers on the foundations of mathematics than ever before! Perhaps you see the value of stress-testing ZF for possible weaknesses, or perhaps you'd like to see the interesting knowledge that develops from our novel inquiries into ZF. In either case, we thank you for choosing to participate with us on this exciting journey of discovery.

Thank you,

Nicolas Benjamin Spoors
Founder of Infinitary Research Institute, a mathematics think tank dedicated to foundations
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