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Last night I was about to close off my phone and saw the beginning of a very interesting lecture on how intuition is not always enough in Mathematics...

The lectures (so far unknown to me) started out showing that the regions of a circle cut-off by n-lines follow a rather non-intuitive pattern

1, 2, 4, 8, 16 ... 

and then continues unexpected with ... 31, 57, ... Wikipedia reference.

And then it looked like he was going to talk about another famous problem, the Borwein Integrals:

enter image description here

and I kinda could see it showing up in the slides, when I could not hold my jet-lag and fell asleep. Being such a privacy freak I had History turned off on the phone, it lost power, rebooted and this morning I was not able to locate it among my Android Discover cards.

I would love to be able to watch the entire lecture.

Does anyone here know the lecture/lecturer? He is skinny, has sort of a french accent and the video was recorded with the left half fixed on the slides and him moving on the right half of the screen. Do you know of any of the Math. institutes that records videos in this particular fashion?

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  • $\begingroup$ Do you have any kind of reference fo the problem with the integrals? I've never seen it before. $\endgroup$
    – saulspatz
    Jul 20, 2019 at 3:06
  • $\begingroup$ @saulspatz The integrals are called Borwein Integrals, introduced by the father-son Borweins. You can see a bit more detail here: en.wikipedia.org/wiki/Borwein_integral or johncarlosbaez.wordpress.com/2018/09/20/… The original reference for their article is: Borwein, David; Borwein, Jonathan M. (2001), "Some remarkable properties of sinc and related integrals", The Ramanujan Journal, 5 (1): 73–89, doi:10.1023/A:1011497229317 $\endgroup$
    – Paulo Ney
    Jul 20, 2019 at 3:38
  • $\begingroup$ This is amazing! Thank you. $\endgroup$
    – saulspatz
    Jul 20, 2019 at 4:04
  • $\begingroup$ Pure fun, isn't it? John Baez blog article (referenced above) is such a reading, specially the comment sections down below... $\endgroup$
    – Paulo Ney
    Jul 20, 2019 at 4:25

2 Answers 2

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The Most Misleading Patterns in Mathematics | This is Why We Need Proofs

This video doesn't match the description in the last paragraph of the question, but it does start with $1,2,4,8,16,31$ and the Borwein integrals, and it is about intuition not always being enough.

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    $\begingroup$ +1 vote but no cigar ... still someone else ... but it is definitely curious to find out that more than one person think these two are indeed thought as the "most misleading" patterns" of math ... $\endgroup$
    – Paulo Ney
    Jul 20, 2019 at 5:07
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Maybe E. Trizac - When random walkers help solve intriguing integrals?

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  • $\begingroup$ Yes!!!!! Thank you so much. $\endgroup$
    – Paulo Ney
    Jul 20, 2019 at 15:35
  • $\begingroup$ @PauloNey At first, I couldn't remember where I encountered the video. Now I remember--it was referenced in a physics.org news posting, "Illusive patterns in math explained by ideas in physics": phys.org/news/2019-07-illusive-patterns-math-ideas-physics.html $\endgroup$
    – awkward
    Jul 20, 2019 at 18:00
  • $\begingroup$ Yes! And being a physicist I did not recognize Emmanuel Trizac very easily or the place where the lecture was filmed. I recommend it to every one. $\endgroup$
    – Paulo Ney
    Jul 20, 2019 at 18:18
  • $\begingroup$ There's also a paper by Trizac and his coauthor, arxiv.org/abs/1906.04545 $\endgroup$ Jul 20, 2019 at 23:59

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