Mathematicians Use Numbers Differently From The Rest of Us

These are literally scientific documentaries of the highest quality at this point. It's amazing that I'm able to watch this stuff for no cost at all. Thank you so much Veritasium

I don't normally think of Veritasium as a math youtuber, but with videos on Newton's calculation of pi, Godel's incompleteness theorem, discrete Fourier transform, logistic map, Penrose tiling, Hilbert's hotel paradox, and various probability puzzles, he definitely should be. I mean, this video alone (p-adic numbers, Fermat's last theorem, Hensel lifting) would be an extremely ambitious topic even for a math-focused channel, and he and Alex Kontorovich did a great job with it!

0:24 "so, does this pattern continue?" me immediatelly: "patterns fool ya, paterns fool ya, ..."

The level of quality in these videos is sublime. You never insult the audiences, by not going as deep as is required. Excellent work as always

I’m a geologist so my maths is questionable at best. I find it utterly fascinating how well I can follow along with this, yet still be completely bewildered and confused.

I took a graduate course on p-adics in university and it felt like all I did was manipulating symbols on paper without understanding what is happening. This video finally made me understand what is going on.

Bravo! You covered in 30 minutes what took me semesters to master in my youth. I am totally inspired.

I'd heard of p-adic numbers and was vaguely familiar with their definition, but didn't know much about their motivation or applications. After watching your excellent video, I'm motivated to learn more about them.

As an engineer and video editor, I am absolutely mind-blown by the production quality of this video. I can't even imagine the number of hours put into the editing alone. It's amazing that content like this is available for free. Not that your other videos aren't great as well, but this was something else.

Thanks for bringing this amazing topic to us

The quality of these videos is insanely high. Thank you very much!

Derek, you have literally been the person teaching me the most since I found YouTube. Shortly after is Destin at SmarterEveryDay, but you two give me more knowledge than I've ever wanted in so many fields. I HAAAAATE most of the subjects you cover on the surface, but when you break them down into applicable and project-oriented and realistic applications, it makes me realize my disdain for things like Mathematics and Science, is because of the academic application, versus what it means in real life. You two are truly those who have expanded my mind to forget my hatred for the academia part, and realize that it can directly apply to the "fun stuff" as well. I guess it proves the difference between "AP" and "GT" students... Same intelligence, just different applications. Regardless, this video was amazing, and thank you for the visual and practical applications.

As someone who does computer science, it was extremely cool to suddenly make the connection to how we represent negative numbers using two's complement.

My Granddad used to play P-adics numbers game with me. He started by asking me to write any random numbers before decimals and he used to write his random numbers below them, And sum of them always comes Zero. His techniques and methodology amazed me and fascinated to learn More Math. Miss you Granddad ! And Thank you Veritasium for this Video

This is the kind of clarity and explanation we need in university maths classes. So much of the time we are left to our own devices to interpret the logic of abstract claims like the "size" of a number. Textbooks usually state the mathematical relation. I fully get how hard it is to describe these things conceptually to a general population but it's so useful and it makes these things appreciated more. Looking at p-adics still freaks me out and I don't quite see them as stars but I can at least see how viewing a series as a different category of number altogether makes sense for why series are used in proofs so often to break down some what simple rational number or variable. (I'm not explaining myself properly because I know the convergence of infinite sums is useful. It's more understanding how the parts inside work and what those mean, or just another way to visualise infinite series.)

It's been a while since a topic in mathematics captured my imagination so much. There is something about the p-adics that feels wrong, but also something that feels so compelling and so deep. What a wonderful introduction and brilliantly done.

This video is the perfect example of encouraging the audience to rise to the level of the content (the exact opposite of talking down to the audience.) Very inspiring.

I couldn't imagine someone could do a youtube video on this topic. Complete with graphics and engaging commentary. It takes a very special level of film making skill plus top notch scientific knowledge to do such a thing. I am a phd in maths. At one time sixteen years back, i was entranced by p-adics. Used to organize student level lectures on it. Slowly my interest wore off and i moved on. Thanks for reminding those days again.

I majored in math as an undergrad at a top engineering school. I recently found my notebooks from the classes and it’s a whole new language

A better trick for converting decimal to any other base is by doing this Divide 17 by 3, the remainder is 2 and the divisor is 5, now divide the divisor by 3, the remainder is 2 and the new divisor is 1. The process should be repeated till the newest divisor is less than the new base. Now arrange the remainders in the order of the first remainder in one's place, the second in the tens place and so on. Here the number becomes 122.