Abide By Reason

Hope you enjoyed the latest Hilbert Space video! I've seen many comments about Banach Spaces and wondering how they differ. Should I make a video about Metric Spaces/Banach Spaces first and then do a video on Lagrangian and Hamiltonian Mechanics?

1 week ago | [YT] | 46

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STORY TIME

If you don’t know what a Hilbert Space is, you’re in good company. As the story goes, the great mathematician David Hilbert, once entered a lecture hall. The speaker that day was fellow math giant, John von Neumann. The topic, Hilbert Spaces. At the end of the lecture, a confused Hilbert raised his hand to ask just one question:

"Dr. von Neumann, I would very much like to know: What is a Hilbert Space?"

While the story is likely just a legend, it amusingly captures the importance that both of these figures played in the development of Hilbert Spaces. Hilbert did much of the groundwork and von Neumann finished it off by giving the first complete definition of them.

3 weeks ago | [YT] | 66

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I'm currently working on a video about Hilbert Spaces. What would you like to see a video on after? (Feel free to comment other suggestions too)

3 weeks ago | [YT] | 21

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HISTORICAL TIDBIT

Once when Henri Lebesgue entered the Scottish Cafe (a coffee shop in Poland), he was given a menu written in Polish. After staring at it for a while, Lebesgue handed the menu back to the waiter and said, "No, thank you. I only eat well defined objects."

Interestingly, this cafe was a common place many of the legends of 20th century Mathematics loved to work in. Frequent visitors included Stefan Banach, Hugo Steinhaus, John von Neumann, and many others.

A typical day would involve someone proposing an unsolved math problem, writing it on the marble top in the cafe, and offering a prize to whoever solved it. One of the more interesting was "a bottle of whiskey of measure > 0" offered by von Neumann.

1 month ago (edited) | [YT] | 76

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A SET WITH NO SIZE

My latest video is on the Vitali Set, a truly interesting, non-intuitive set. It is uncountably infinite, yet has no size (i.e. it is non-measurable). It's not that it's size is 0 or infinity, it can't possibly have any size whatsoever.

You can learn exactly why here: https://youtu.be/hs3eDa3_DzU

Best,
Dan

2 months ago | [YT] | 40

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TOPOLOGY OF THE CANTOR SET

I just posted my latest video where I explain what it means for the Cantor Set to be a compact, totally disconnected, perfect set.

You can check it out here: https://youtu.be/c4oKdtUtJOk

Hope you have a good week ahead!

Best,
Dan

2 months ago | [YT] | 19

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It's easy to refer to the nth item in a list but how do you refer to the (n-1) item in a list?

2 months ago | [YT] | 1

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GREAT NEWS!

YouTube has finally fixed my AdSense account. The issue with "invalid traffic" was resolved. Thank you so much to all of you, especially to anyone who retweeted me on Twitter/X. Essentially, getting a real person to finally look into it was the key.

Currently finishing up the next video and will hopefully post it by the end of this week.

I appreciate you all. Hope you are doing well!

Best,
Dan

3 months ago | [YT] | 34

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HELP! Channel is BANNED! (this is serious, not a joke)

Hey all, the last week has been rough. My google AdSense account has been banned for "invalid traffic." Essentially, their system has detected bots viewing some of my videos. Despite the fact that I have not done anything wrong and have not violated any community guidelines, every single appeal I have filled out has been rejected. I've done all that I could to remove this "invalid traffic."

So the only thing I can think of now is to try to get as much attention as possible to TeamYouTube on twitter. Here's where I can use your help:

GO TO TWITTER/X and REPOST my recent tweet directed at TeamYouTube. ALSO, share this with anyone you know (especially other YouTubers).

Thank you for taking the time to read this and especially for any of you who take the time to help spread the word.

Best,
Dan

3 months ago | [YT] | 64

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FORD CIRCLES and FAREY SEQUENCES

Latest video shows how this cool structure of Ford Circles arises from Farey Sequences. If you haven't had a chance yet, check it out here: https://youtu.be/wE1iJkXs1Xg

Hope you have a good weekend!

Best,
Dan

3 months ago | [YT] | 9