The Oldest Unsolved Problem in Math [31:32]

YouTube ^ | March 7, 2024 | Veritasium (Derek Alexander Muller)

[SunkenCiv]

Do odd perfect numbers exist?

...A massive thank you to Prof. Pace Nielsen for all his time and help with this video.

A big thank you to Dr. Asaf Karagila, Pascal Ochem, Prof. Tianxin Cai, and Prof. William Dunham for their expertise and help.

The Oldest Unsolved Problem in Math | 31:32
Veritasium | 15.2M subscribers | 6,120,035 views | March 7, 2024

[Redcitizen]

“How do you like them apples?”

Freshly baked as in apple pie with a side of ice cream.

[EEGator]

It takes time for neuroplasticity to form new synaptic connections.

[Sicon]

“I guess it took longer for the math molecule in my brain to develope.”

And the spelling molecule is evidently still a work in progress. 🤣

[Peter ODonnell]

The author says “the solution could be as simple as finding one odd perfect number” but that should surely read

“the solution is as simple as finding one odd perfect number” since any other solution would be very complex, a theoretical reasoning of why no odd number can be perfect.

I wonder how any larger even perfect numbers have been found in the search? Or if any theory exists to predict them, or if they just find the by trial and error?

I find prime numbers very interesting too, (numbers that have no factors other than themselves and 1), I understand there is a theory to prove there cannot be a largest prime number, but the frequency of them keeps dropping off very slowly. In ranges of odd numbers like 1,001 to 2,001 about 35% of the odd numbers are primes (no even numbers above 2 can be primes), by 1,000,000 to 1,001,000 it is down to about 20%, but it stays well above 10% a long, long way up into a realm where “largest known prime numbers” are found by very complicated computer programs. I believe the largest known prime number has 10^24 digits. The progress made in this computer age is considerable, in the medieval period the largest known prime number was only in the low million range. Once again, there is no universal theory predicting a progression of prime numbers, they tend to be more frequent in certain equation generators like 2^n - 1, but there is nothing like a series predictor. So every so often a person with access to a very large computer and time to waste comes up with the newest largest known prime. We know from the theory that this search can never end, but I suppose you could say, any number (prime or not) that is greater than the number of particles in the universe cannot be used to count anything that exists, so it is an irrelevant number.

[Bonemaker]

"The short answer is that both of these words are correct.
Develope is an old British spelling of the word. Develop is a more modern, American way of spelling the word.
You can use both spellings, just like "colour" and "color".
The short answer is that both of these words are correct. Develope is an old British spelling of the word. Develop is a more modern, American way of spelling the word. You can use both spellings, just like "colour" and "color".
😝

[Bonemaker]

But I repeat myself ...at 2:40 am CDT.

[Sicon]

“The short answer is that both of these words are correct. Develope is an old British spelling of the word.”

Interesting. Learn something new every day.

[nwrep]

The narrator is very bad at pronouncing names. He says “Dee-Carts” for instance. Very off-putting.

[SunkenCiv]

Hey, at least you didn’t complain about the transcript.

[SunkenCiv]

:^)

Perhaps we shouldn’t even be using base 10, it’s probably rooted and mired in white supremacism, just as the term white supremacy is. /rimshot

[Organic Panic]

Soon to be followed up by the media breathlessly claiming a couple young black girls in public school have solved this and never following up when they didn’t.

[Bonemaker]

There are a lot of little quaint things in the King’s English vs Americanese!😊 i screw it up half the time!

[zeugma]

my favorite math oddity is the Collatz Conjecture

I wrote a bash script for it:

$ collatz 27
27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1
Starting with the initial value of 27, it takes 111 steps to reach unity.

$ collatz 26
26 13 40 20 10 5 16 8 4 2 1
Starting with the initial value of 26, it takes 10 steps to reach unity.

$ collatz 25
25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
Starting with the initial value of 25, it takes 23 steps to reach unity.

[Sicon]

Yes, as someone said (paraphrased, and of uncertain origin), “Britain and the U.S. are two countries separated by a common language.”

[Tymesup]

Thanks for the hour of rabbit hole.

[zeugma]

Thanks for the hour of rabbit hole.

LOL! You're quite welcome! one of the great things about the Collatz conjecture is that it is so incredibly simple. Any child with basic math skills can do it. I have found some serious oddities within it, like how often certain numbers show up. For instance, if you run the first 1000 numbers through it, 354 of the numbers will reach 9232 as the highest number. Out of the first 10,000, you will see 9232 pop up 1579 times.

as a shortcut you could identify numbers that show up often like that, and stop work when you hit it, because you already know:
9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1
Starting with the initial value of 9232, it takes 34 steps to reach unity.

Another shortcut is that if you are testing numbers in sequence, once you hit a number than is smaller than your initial number you can stop, because you know you've already tested that number

Consider yourself lucky you only lost an hour. I independently discovered most of the weird fractal charts on the wikipedia when I started scripting and graphing the results.

[thecodont]

Develope is an old British spelling of the word. Develop is a more modern, American way of spelling the word.

This isn't like envelope and envelop, is it?

[Tymesup]

Aarrghh, refreshed page at the wrong time.

There must be a whole of different coefficients, exponents and number of alternatives.

I tried divide by 2 or 3, otherwise multiply by 7 and add 1. 19 took 35 terms to circle back to 19.