Contrarian Research

At any given time, we are always interested in the biggest questions about mathematical logic that we can ask. Currently we are focused on disproving the Continuum Hypothesis (abbreviated: CH) by using our ZF Inexactness Conjecture. The Inexactness Conjecture states that: “Our fundamental understanding of mathematics is not just incomplete, it is inexact. Thus we should expect a degree of inexactness in our understanding of mathematics as we already do in science.”

ZF Set Theory

Although there are other foundational theories of mathematics, “ZF set theory” is the most basic and “ad hoc” understanding of mathematics, and it is part of every other foundational theory. Thus it is considered to be the LEAST controversial part of mathematics. We intend to show however that although the fundamental principles of ZF set theory (called “ZF axioms”) have been effective where they have been needed in the past, they are still harboring a contradiction. To put it more simply: We believe that ZF is FALSE and that this is essential to disproving CH. However, we also think that ZF set theory is just inexact instead of simply inconsistent (that it has value still).

The Continuum Hypothesis

The “Continuum Hypothesis” (or CH) in ZF set theory has remained intractable for over a century, and we believe that it is FALSE. CH states roughly that: “There is no size of infinity between the two most popular sizes of infinity that are used in mathematics today (the size of the real numbers, vs the whole numbers).” It says that the quantity of real numbers is just the NEXT level of infinity above that of the whole numbers. In other words, there is actually more than one size of infinity and mathematicians don’t yet know if the real numbers are in the 2nd, or maybe the 10,000th…or maybe even the ∞th. It’s just not known yet. We really believe though that with the right focus, funding and teamwork (in other words, in an absence of grading homework, and in an ABUNDANCE of financial power and collaboration), we can solve this problem. Some challenges require a new and robust approach.

Infinitary Research Institute (IRI)

We are a private research firm located in Lowell, MA and are a subsidiary of Infinitary Fund, LP which is an investment firm in Yorktown Heights, NY. Unfortunately, we are NOT hiring at this time. Except for Infinitary Fund, LP, we do NOT contract with any businesses or individual customers to do any work related to industry or finance. We do NOT accept any investments because we are NOT an investment advisor and do not offer grants.