But what is the Central Limit Theorem?

Please consider doing an entire series on probability theory and/or combinatorics.

I'm an engineering professor far more older than you and I must say whitout a doubt: you are the most skilled professor I have ever seen. The amount of work in this videos is outstandig. They are so flawless that can be considered as art. Congratulations!.

I have a PhD in applied mathematics, I work in numerical weather prediction as a research scientist. Gaussianity is this hardcore part of the basics of forecasting the weather (even though most atmospheric variables, and their errors, are actually non-Gaussian). This video did a great job at teaching the CLT. I have never seen it explained so well.

The actual rigorous no-jokes-this-time conclusion from watching 3Blue1Brown videos like this is that Grant deserves some new, yet-to-be invented prize that should be the equivalent of an Oscar for best computer generated imagery, an Emmy for outstanding narration / editing and a Nobel Prize in science for fostering interest in mathematics and science. Amazing, inspired work here.

Of all the years I've supported 3b1b, this video might be the one I was most excited to see pop up.

Next video, explaining the π and how the function e^(-x^2) arises: https://youtu.be/cy8r7WSuT1I As many helpful commenters have pointed out, at 6:37 and 7:15 the narration should say "skews left" instead of "right". In standard terminology, the skew direction refers to the direction of the longer tail.

the section unpacking the Gaussian formula is simply a work of art. Giving a graphical intuition about moving from e^(-x) to e^(-x^2), and then to a constant multiplier of the exponent... just absolutely pristine

This series of lectures must be incorporated into the math curriculum of all high schools in the world, I was trained in math and as a data scientist, but I have never seen the central limit theorem explained this way. It just made things so easy to understand and intuitive. Well done.

Hooray! A new 3Blue1Brown video!

Dealing with CLT pretty much every day here. Really impressed with how easily you explain it. By far the most intuitive and easily understood explanation of CLT. Salute!

Describing the mean of the weights as the center of mass of the distribution was just incredible. And the intuitive matrix multiplication without even mentioning it. You are a great teacher!

I can't tell you how insanely brilliant you are at taking a universal concept that is vaguely understood and illuminating all the nuance hidden in plain daylight to make this understood on a higher level!!! Genius

As someone who works with Kalman filtering on a regular basis, this is a very nice video to see. One of the core principles behind the Kalman filter is that all random variables involved must be Gaussian, which seems overly restrictive on the surface. I think this provides an excellent, succinct explanation for why that's actually a reasonable assumption for many systems, since every random process we can directly observe is really just a combination of many smaller processes. I look forward to the next one!

Grant, you are a lifesafer! My exams are in 2 weeks and I have not understood this yet. It's a miracle you are publishing this video online!

Thanks for producing such high-quality videos, i'm a maths student who love statistics. I would say this vid gives the clearest and neatest explanation to CLT ever, really inspiring, I sacrificed my sleep time watching it for 3 times!!! Amazed and shocked! Thank you Grant. <3

As I was watching this video, I wanted to say that videos from your channel inspire me to learn. Not just mathematics, but anything worth doing. Although I am an engineer and enjoy doing what I do, I have never been a huge fan of pure mathematics. But the way you explain concepts just makes it so easy to understand. Even though I might have to rewatch some videos to fully comprehend the meaning, I really enjoy it and it never feels like a chore. I have watched your videos more than my university lectures. I wish there are more teachers like you in this world. Thank you so much 3Blue1Brown!

This video is by far the best introduction to the CLT I've encountered. You are doing the world a great service by putting that much effort into this youtube channel. I adore your work and use your visualizations all the time in my classes (even though I teach in french).

I would absolutely love to see a series on probability/combinatorics/statistics on this channel. It's the subject I've struggled the most with in math by far. I think your ability to take the time to really think through and understand what the basic building blocks really mean will become a very valuable resource in my and many other people's math journeys.

I am constantly impressed by how Grant's videos extract the art that is inherent in certain mathematical concepts. What a great video!

As an actuary, I'd say this is perhaps the best descriptive video/lecture I've ever seen on the CLT. I wish I would have seen this when taking my classes for exam P because the visualizations are so useful in understanding what can be a very dense topic when it's spewed from a chalk board/overhead screen hastily.