The Large Hideous Collatzer

Mathematics is still full of surprises. The solution to simple to state problems may elude mathematicians for centuries. One example is the celebrated Fermat’s Last Theorem (stating that equations of the form have no integer-only solutions for ) that was finally solved by Andrew Wiles with tools Fermat couldn’t possibly know nor understand¹.

Another one of those problems is the Collatz Conjecture. Proposed by Lothar Collatz in 1937, the conjecture is that a simple recurrence function—that we will discuss in detail in just a moment—terminates for all natural numbers. This one, however, isn’t solved yet.

Suggested Reading: The Trouble With Physics

Lee Smolin — The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next — Mariner Books, 2006, 392 pp. ISBN 978-0-618-91868-3

(Buy at Amazon.com)

In this book, the physicist Lee Smolin tries to explains us in what kind of predicament modern physics is today. He starts by enumerating the five great questions that modern physics must answer:

• Unify general relativity and quantum mechanics; that is, formulate the theory of quantum gravity
• Solve a number of problems within quantum mechanics
• Unify forces, that is, explain all of them within a coherent theory
• Explain the numerous natural constants, that is, explain why they have their specific values and not some other
• Explain weird cosmological phenomena such as “dark matter” and “dark energy”