The Mosaic Problem - How and Why to do Math for Fun

Comments · 183

• JO

  @JohnDoe-ti2np · 3 years ago

  According to combinatorialist Gian-Carlo Rota, Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your 12 problems to see whether it helps. Every once in a while there will be a hit, and people will say: "How did he do it? He must be a genius!"

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• YA

  @yaitz3313 · 2 years ago

  You should submit the (n,2) and (n,3) cases to the Online Encyclopedia of Integer Sequences. They're two interesting sequences of integers, which is exactly what the OEIS tries to collect.

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• PA

  @PaulMurrayCanberra · 3 years ago

  My back-burner problem for a while was the question "What does it mean to double a probability?" It led me eventually to find the logistical function.

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• MA

  @matthew6666 · 3 years ago

  Nice video! I think I've always had some of these "back burner problems", which might explain a lot. I hope some students see this and get inspired with their own back burner problems.

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• DA

  @darkkupo5162 · 3 years ago

  I&apos;ve had a back burner problem throughout most of my post secondary education.<br>The problem started because one day my dad made a joke about how the square root of 99 should be 33. This made me wonder if there were any numbers consisting of just a single repeating digit (greater than 10) that is the square of an integer. It&apos;s pretty easy to just check and see no such number exists; however, it gets interesting if you ask for which numerical bases can you find a repeating number that is the square of an integer in that base. for example 11 (4) in base 3 is a square of the integer 2<br>more formally you&apos;re asking for what integer b does there exist n such that: sqrt((b^n - 1)/(b-1)) is an integer.

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• JA

  @jackhanke343 · 3 years ago (edited)

  Thank you all for watching! There is a small correction at <a href="https://www.youtube.com/watch?v=D3dp5RBmPcs&amp;t=682">11:22</a>, as the notation t_{i, 2} should be t_{5-i, 2}.

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• YE

  @yellowthegreat691 · 3 years ago

  Very inspirational video, top tier content

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• JA

  @jackdinsmore4326 · 2 years ago

  Great video! Problems like the mosaic problem are actually very useful in physics. Counting all the mosaics with loops allows you to find the temperature at which a liquid evaporates into a gas in some simple models (we would call the generating function a cluster expansion, and the liquid gas model I was thinking of is called the Ising model). Just goes to show that sometimes your back burner problem might not be as esoteric as it seems at first!

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• HO

  @hobbified · 3 years ago (edited)

  As a computer programmer I very often run into people online asking questions like &quot;I&apos;m learning &lt;some language&gt;, what should I write?&quot; Or &quot;I want to contribute to open-source, what project should I contribute to?&quot; As a participant in various nerdy hobbies I run into people asking &quot;okay, I&apos;m new to this hobby and I just bought all the equipment they say I need to get started [ouch!]... now what do I do?&quot;<br><br>My answer to all of those people is very much related to this video: explore what interests <b>you*. Have something *you</b> want to accomplish. Wanting to learn a language, or partake in a hobby, or absorb a mathematical concept, aren&apos;t really the kind of goals that you can get invested in for their own sake. They&apos;re means to an end. You need to go into the game with an end in mind, something that drives you personally, and then you&apos;ll have a reason to knock down everything that stands in your way — and to discover something new that you didn&apos;t know you cared about in the beginning.<br><br>Ordinary people can probably sustain one or two such interests. Really <b>interesting</b> people cultivate several and find ways to synthesize them.

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• 78

  @78Mathius · 3 years ago

  Your voice is good for YouTube and the animation was as visually stimulating as your voice over. &nbsp;On top of that, the content was interesting and the script well written. &nbsp;I hope you make regular math videos.

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• SQ

  @squidwithcheese · 2 years ago

  I finally got around to watching this video, and I can say that I’m glad I did!

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• OR

  @OrçunYalçın-p3z · 2 years ago

  I was doing this without realising the benefits, now when i think, they really helped me

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