@thomasrinschler6783
13:25 "But Euler wasn't finished yet." I think this sentence appears in most histories of mathematical concepts.
@deanrinehart
Watching a math related video strictly out of curiosity and having your general math professor Bill Dunham from 25 years ago pop up is a surprise…and finding out he’s now a well respected mathematics historian and not just some guy who endlessly suffered non-math students struggles with train problems is absolutely fantastic. Go Mules!
@janviersechan9670
Factorizing 2^67-1 without using calculator or any mechanical computing device is insane 😮
@jonahmishaga1995
As a physics undergrad. I’ve come to realize that Euler is a Titan alongside Einstein and Newton. Every single bit of modern physics has Euler to thank for providing the mathematical Tools to construct a vivid picture of the universe and its underlying principles. Absolute legend.
@lifthras11r
One big application of Mersenne primes, that came from studying perfect numbers, is a good random number generator. RNGs had been historically very bad, until the introduction of Mersenne Twister in 1997, which uses a property of Mersenne primes to prove a good randomness. The most popular version uses a Mersenne prime 2^19937 - 1 for example, hence the name MT19937. There exist much more performant RNGs than Mersenne Twister now, but Mersenne Twister is still widely used thanks to its initial impact.
@VintageBlacklist
I have a research project due tomorrow and I was really looking for something distracting. My procrastination thanks you.
@Oodle-ox2vf
I am an old, retired scientist/engineer/educator, who refuses to quit. I enjoy the interesting discussion that comes from many of your videos. They are also on my list of insomniac pastimes. Thank you. Keep them coming. 🙂
@nathanaelhahn
4:03 "Euclid was actually thinking along similar lines" Euclid: calculates perfect numbers with actual lines
@madjson1429
When Euler says "it's most difficult", it's gotta be impossible.
@Color_Splsh
Wow, this topic throws me back. I remember in middle school, one of my friends was a big math nerd and he told me that his one goal in life was to find the odd perfect number. I had completely forgotten about that until i saw this video, thank you veritasium.
@logician1234
There is something so bizarre about Euclid and Euler having a collaboration. If the history of mathematics was a book of fiction, I would call this a fan service 😂
@haleyroe2647
I love consistently understanding the first 25% of veritasium maths videos.
@BronsonMWhite
WOAH! Dr. Pace Nielsen was my professor for intro to proofs. I was NOT expecting him to show up in the video. He's a fantastic guy, exceptional professor, and brilliant number theorist.
@johnseo5525
Well done. I admire your work. Thank you.
@concrete401
I took a class from Dr. Nielsen in 2009. He was a very engaging, dynamic teacher, to the point that when he wrote an answer on the board, followed by an exclamation point, someone asked, "Is that factorial or excitement?" and he responded, "EXCITEMENT!"
@martafixarcoolt5993
I love when people have made up their mind on something, like there is a heuristic argument for that there is no odd perfect numbers, and then faced with a reasonable counter argument, imidiately recognize that their original argument is flawed. Just listening to reason and take that logic in, it is beautiful
@seanshepherd1071
28:00 "Useless" problems are never really useless, because in the pursuit of attempting to solve them, something useful almost invariably gets created along the way. Entire fields of mathematics have been formalized because the tools that existed before them were insufficient to solve some problem with no practical application.
@AA-100
21:15 As of Oct 2024, largest known prime is now 2^136,279,841 - 1
@Tritone_b5
As a computer and math enthusiast I'm so disappointed I didn't know what Prime 95 was for, other than a OC stress test tool.
@cupostuff9929