About the Author

Why I Question the Foundations of Science and Mathematics

It began while I was watching a television program featuring several world-renowned scientists. During the broadcast, they asserted something that immediately caught my attention: they claimed that it is perfectly acceptable for paradoxes to exist in science, physics, and mathematics.

I found those comments deeply disturbing.

By definition, a paradox is a statement or conclusion that contains a logical contradiction. Science is knowledge built strictly on reason, empirical logic, and sound principles. If we accept that paradoxes belong in science, we implicitly accept that science can be built on illogicality and nonsense.

This raises fundamental questions:

• What is the current ratio of logic to absurdity in modern science?

• Is there a limit to how many paradoxes a scientific framework can tolerate before it breaks?

• Who decides which paradoxes are elevated to foundational truth?

Today, famous paradoxes are often glorified rather than resolved. Entire fields of modern theoretical science are built upon these idolized contradictions. But when a proposed theory fails to make logical sense, we should re-examine its underlying axioms—not obediently bow to authority simply because a famous name proposed it.

Driven by a background in mechanical engineering, I decided to examine these famous paradoxes myself. I assumed I would merely form a personal opinion on a few edge cases in physics. Little did I know that this decision would ignite years of deep research into the very foundations of mathematics.

The result of that journey is the Polarized Number System. Whether my findings offer a logical resolution or merely add to the debate, I invite you to read the proofs and decide for yourself.

— Peter Kosc