@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 😮
@nathanaelhahn
4:03 "Euclid was actually thinking along similar lines" Euclid: calculates perfect numbers with actual lines
@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!"
@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.
@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. 🙂
@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.
@johnseo5525
Well done. I admire your work. Thank you.
@haleyroe2647
I love consistently understanding the first 25% of veritasium maths videos.
@Art_Vandelay_Industries
As someone that was never good at math it blows my mind how people could and can think in ways that can actually make sense of math so abstract. And without having computers to do the crunch for them back in the days.
@AA-100
21:15 As of Oct 2024, largest known prime is now 2^136,279,841 - 1
@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.
@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
@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.
@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.
@jcccm3303
17:48 Something about this quote just hit me hard, we are in the age of computers that started just a few decades ago and we often ignore how seriously revolutionary computer advancements are, something that could take years can now be done by a child with an iPad.
@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 😂
@cupostuff9929