# 3X+1 is an unexpectedly weird math problem

The Collatz Conjecture is the simplest math problem no one can solve — it is easy enough for almost anyone to understand but notoriously difficult to solve.

Toward the end: “If anything it shows that all the things we can solve are miracles.”

More on the Collatz Conjecture.

Hat tip: Heather Zeiger

See also: Things exist that are unknowable: A tutorial on Chaitin’s number

and

Yes, you can manipulate infinity in math. The hyperreals are bigger (and smaller) than your average number — and better! (Jonathan Bartlett)

## 10 Replies to “3X+1 is an unexpectedly weird math problem”

1. 1
kairosfocus says:

Yes, indeed, this is an interesting problem, as was noted here earlier. Your linked case, for 3 illustrates how the process looks for the ladder of powers of 2 and once this hits, goes to the 421 loop: 3, 10, 5, 16, 8, 4, 2, 1,… KF

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Barry Arrington says:

Fascinating!

3. 3
hoosfoos says:

At collatz.com, Franz Ziegler offers a proof of the Collatz Conjecture (3n+1). Is this proof valid? Why or why not?

4. 4
kairosfocus says:

H, there are as yet no generally accepted proofs. KF

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jerry says:

Fell apart at the end by promoting Brilliant. We can all waste time in various ways and maybe Brilliant is one.

But another way is The Great Courses. I recently purchased a course for less than a dollar a lecture, called Great Thinkers, Great Theorems. If you are interested in mathematics, this is the best one I’ve seen.

Three lectures just on Euclid. He did not use any numbers. Question- how does one define a right angle with no numbers.

https://www.thegreatcourses.com/courses/great-thinkers-great-theorems

6. 6
Silver Asiatic says:

But another way is The Great Courses. I recently purchased a course for less than a dollar a lecture

I am waiting for the price to drop on the History of Science, ancient to 1700. That one was highly recommended to me.
A very excellent Great Courses I completed was Daniel Robinson on the nature of Consciousness. I was shocked to discover he is a Thomist-realist with tremendous knowledge of contemporary ideas on consciousness. Dr. Robinson recently passed away – R.I.P.

7. 7
jerry says:

I am waiting for the price to drop on the History of Science, ancient to 1700

All the history of science courses are good. I like the more modern era ones better since more has happened since 1700. They go on sale every 4-6 weeks. Some times at very low prices.

They also have a program where you can stream hundreds of video courses for a yearly fee. I have that but will get those courses that show up at about \$20/\$30 per 24/36 lectures when they are on sale. Normal prices are 70% off list but have seen them occasionally at 90% off list.

The History Science prior to 1700 is only on audio so not on their yearly streaming. It is probably available on Audible. But doesn’t come with a course book. They recently on The Great Courses, last week, had all audio courses on sale.

8. 8
Silver Asiatic says:

I wish they would notify me when those go on sale. I’m digging into the roots and origins of science. That course shows that science emerged from theism and Christianity specifically.
I saw it listed for around \$99, which seems too much for just audio.
I look on EBay for Great Courses also and there are hundreds. But a used copy of that one is still \$60 which is probably a very good deal but it seems a lot for audio and no book. A few people have old VHS versions for around \$30 and that just seems crazy.
Especially because as you say they offer brand new DVD sets for \$20 to 30.
The one on Quantum Theory you posted looks good also.

9. 9
jerry says:

The Amazon audible version was \$35.

I think I have the VHS version someplace. If I see the audio one on sale, I will post it but you have to be around that day.

Another good one by same author is Science and Religion.

10. 10
Silver Asiatic says:

Thanks. I’ll check their site also for sale pricing.