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From Terry Tao's Blog, Vaughan Jones, who made fundamental contributions in operator algebras and knot theory (in particular developing a surprising connection between the two), died this week, aged 67.

Vaughan Jones was a very creative mathematician and he was arguably an extreme point in the convex hull of all mathematicians. He will very much be missed. And as a scientific family from MO we extend our sincere condolences to his family, friends and students.

And here is my big list/simple question to know more about this creative mathematician is:

Question: What do you like in the mathematics of Vaughan Jones? and how Vaughan Jones liked mathematics to be ?

Addendum: This part is directed to his students and his colleagues. As Jon Bannon suggested and pointed out in the comments, since Vaughan Jones was a very creative mathematician we may get from Vaughan Jones' students or by his colleagues the state of the art of his vision? And how Vaughan Jones saw what the applications of planar algebra in Quantum theory should be? The best example is the reformulation of Riemann hypothesis using planar algebra. More than that, how Vaughan Jones saw the connection between planar algebra and number theory should be used to solve biggest open problems in pure mathematics like Riemann hypothesis and irrationality measure of pi? Also from the point of view of Vaughan Jones does the expedition growth of mathematics need more development of knot theory and its connection with other area of mathematics and physics?

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    $\begingroup$ In my last year of high school (12th grade), I took a couple of classes at UC Berkeley, including discrete math and proofs (mostly for computer science students) taught by Vaughan Jones. That was a great class! $\endgroup$ – Zach Teitler Sep 9 at 19:57
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    $\begingroup$ This is asking about Jones’s lesser results, Jones’s known results, Jones’s vision for quantum theory and Jones’s vision for number theory — so I have voted to close for lack of focus. I would prefer a simpler big-list question, “what do you like in the mathematics of Vaughan Jones?” $\endgroup$ – Matt F. Sep 10 at 5:47
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    $\begingroup$ I agree with Matt F. "Lesser-known results" worked very well for John H. Conway but I don't think it works equally well for all mathematicians, and I don't think that every time a famous mathematician dies, there should automatically be an MO question asking for lesser-known results. $\endgroup$ – Timothy Chow Sep 10 at 12:19
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    $\begingroup$ This question feels...premature. There will come a day when it's time to write about Jones' mathematical contributions, but for most of his students and colleagues, he was a friend and news of his death was a shock. (It's possible that some of them learned about his death from this MO post.) Most of the people who could answer this question well are busy processing grief right now, and it feels a bit ghoulish to request that they amuse us by filling in answers to a big list question. Right now, I think this question falls afoul of Paul Siegel's 'tasteful' criterion. $\endgroup$ – user1504 Sep 11 at 2:37
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    $\begingroup$ I have to agree in a sense that this is a bit jarring to see such a question so quickly. I'm even still mourning another mathematician's passing and never found it fitting to compose a memorial question for him. I tried to write a reflective piece to deal with it, but stalled and hope one day to do so well. There is, though, a desire/impulse to immediately pay one's respects or deal with the grief by posting or writing something...even right away. It may feel as if one can hold onto the experience of hearing a mathematician's ideas one final time as a farewell. $\endgroup$ – Jon Bannon Sep 11 at 17:14