After much hesitation, I decided to share with you the videos of my lecture: Open collaborative mathematics over the internet – three examples, that I gave last January in Doron Zeilberger’s seminar at Rutgers on experimental mathematics. Parts of the 47-minutes talk is mathematical, while other parts are about mathematics on the Internet, blogs, the polymath projects, MathOverflow, etc.
I tried to give some homage to Doron’s own lecture style, but when I saw the video, I could not ignore some aspects of my own style – complete indifference between plus and a minus, between and , between multiplying by something and dividing by the same thing, between subscripts and superscripts, between what are “rows: and what are “columns”, etc., and, in addition, randomly ending English words with an ‘s’ regardless of what English grammar dictates. Apologies. This was a rare occasion of giving a talk about “meta” matters of doing mathematics.
My first (and main) example was Erdős discrepancy’s problem, and I mentioned some experimental aspects, and heuristic arguments. The second example was Möbius randomness, continued with some comments on MathOverflow, some of the “goodies” one can earn participating in MathOverflow, and some comments on a debate regarding polymath projects organized by I.A.S a few years ago. The third example was about mathematically oriented skepticism. This time not about my debate with Aram Harrow and quantum computing skepticism (that I briefly mentioned), but about my “Angry Birds” skepticism. The lecture was a mixture of a blackboard talk and presentation of various Internet site.
Summary and links
Here are the links to the Internet pages I presented with an outline of the lecture:
Video I (Erdős discrepancy problem)
00:00-00:43 Doron’s introduction; 00:43-4:00 On the screen: Erdős discrepancy problems: showing this post (EDP22) from Gowers’s blog. I talked about the chaotic nature of mathematics on the Internet. Then I explained what are polymath projects, mentioned polymath1 and density Hales-Jewett, other polymath projects, and polymath5.
4:00-12:00 Polymath5, discrepancy of hypergraphs, and The Erdős Discrepancy problem. [6:06 “There is nothing more satisfying in a lecture than seeing attempts by the speaker to move an unmovable blackboard”]; Some basic observations, random signs, Mobius functions, the log n example.
12:00-16:00 Plan for the next fifteen minutes: a) Greedy methods, b)Heuristic approaches, c) Hereditary discrepancy
17:00 – 18:40 Alex Nokolov and Kinal Talwar’s work on hereditary discrepancy. On the screen: Talwar’s post discrepancy to privacy and back on Windows on Theory
18:40 -23:00 Greedy approaches. On the screen: My question on MathOverflow – on a certain greedy algorithm for Erdős discrepancy problem; The MO answer by ‘rlo'; a follow up question
23:00 – 27:00 What is MathOverflow. On the screen: my old MO page. (Here is the new one.) What is “MO- reputation,” which “badges” you can earn and for what; Earning “hats” in more advanced site: On the screen: hat champions from TCS-Stackexchange, winter 2012. (This webpage is no longer available.)
27:00 – 30:00 My heuristic approach for EDP
Video II (Möbius randomness, and angry birds)
On the screen: My MO question on Möbius randomness of the Walsh functions
00:00-02:00 Diversion: The IAS debate on polymath projects between Gowers and Sarnak, and comments by me and by Noga Alon.
02:00-05:40 Möbius randomness and computational complexity. What is Mõbius randomness (MR); Peter Sarnak’s Jerusalem talk on MR, his belief regarding the hardness of factoring, and my opinion; The prime number conjectures and Walsh functions. My MO question; Ben Green’s MO-answer to one problem and Bourgain’s result answering a second question.
05:40-7:50 A remaining question on MR of Rudin-Shapiro sequences. On the screen – my MO question Mobius randomness of the Rudin-Shapiro sequence; What is a bounty in MathOverflow; Diversion: The power that comes with high reputation on MO. Who won my bounty.
09:30-14:30 Example 3: Another mathematically related skepticism – Angry Birds. On the screen this page from Arqade : Most voted questions (a few are very amusing); Introduction to the game “Angry Birds”; My skeptical theory: “Angry Birds” is becoming easier with new versions, and the statistical argument for it. I mentioned the Arqade’s question “Is angry Birds deterministic” that got (then) 143 upvotes, and was a role-model for me.
14:30-17:00 My Arqade question, my hopes, and how it was accepted by the computer-games community; On the screen: my Arqade question: