Via the
n-category cafe (and just now also the
Arcadian functor ) I learned that Benjamin Mann of DARPA has constructed a list of 23 challenges for mathematics for this century.
DARPA is the “Defense Advanced Research Projects Agency” and is an agency of the United States Department of Defense ‘responsible for the development of new technology for use by the military’.
Bejamin Mann is someone in their subdivision DSO, that is, the “Defense Sciences Office” that ‘vigorously pursues the most promising technologies within a broad spectrum of the science and engineering research communities and develops those technologies into important, radically new military capabilities’.
I’m not the greatest fan of the US military, but the proposed list of 23 mathematical challenges is actually quite original and interesting.
What follows is my personal selection of what I consider the top 5 challenges from the list (please disagree) :
1. The Mathematics of Quantum Computing, Algorithms, and Entanglement (DARPA 15) : “In the last century we learned how quantum phenomena shape our world. In the coming century we need to develop the mathematics required to control the quantum world.”
2. Settle the Riemann Hypothesis (DARPA 19) : “The Holy Grail of number theory.”
3. Geometric Langlands and Quantum Physics (DARPA 17) : “How does the Langlands program, which originated in number theory and representation theory, explain the fundamental symmetries of physics? And vice versa?”
4. The Geometry of Genome Space (DARPA 15) : “What notion of distance is needed to incorporate biological utility?”
5. Algorithmic Origami and Biology (DARPA 10) : “Build a stronger mathematical theory for isometric and rigid embedding that can give insight into protein folding.”
All of this will have to wait a bit, for now
HAPPY & HEALTHY 2008
braid group, geometry, quantum, Riemann
5 comments
Posted in general, modular
Written on Sun, 30 December 2007 at 9:10 pm
Tags: braid group, geometry, quantum, Riemann
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December 30th, 2007 at 11:25 pm
To “1. The Mathematics of Quantum Computing, Algorithms, and Entanglement”: I always had the impression that the biggest challenges in quantum computing we are facing now are physical engineering challenges. We already have a couple of quantum algorithms, like Shor’s and Grover’s and Kitaev’s. But at this moment we have not one usable implementation of a quantum computer.
Of course we will find and need more quantum algorithms, but actually we have “the mathematics required to control the quantum world”. What we lack is the engineering to control the quantum world.
December 31st, 2007 at 12:42 pm
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December 31st, 2007 at 9:43 pm
Thanks again for the link. The first three on your list are the ones most obviously related to quantum gravity. I’m going to put in a proposal for the Riemann hypothesis (just for fun) although I’m better qualified to comment on 1.
January 1st, 2008 at 2:28 am
Hi Lieven,
Although I am personally most interested in your #4 and #5 relating to biology, #1 is also of interest due to research in DNA computing.
I do think engineering is presently in the lead due to their use of mathematical game theory, with electrical perhaps in a better position than mechanical.
Because of the prominence of the helix in many aspects of information such as ballisyics [rifling], biology, statistics and control theory, I suspect that the next decade will have a great deal of progress.
The wiki Polarization section Basics: plane waves, shows how linear, circular an elliptical variants are related to the helix. The ideal unit circle with a radius (1/2PI) can modulate statistically from 0 to 1 for each single cycle.
January 5th, 2008 at 11:10 am
Koen, I agree we have wonderful quantum-algorithms and an excellent knowledge of quantum physics and that the major obstacle against building a quantum computer is decoherence. My point (if any) is that we need to understand the geometry at the quantum level better before we can solve the engineering problem. Suppose medieval engineers were asked to build a GPS system at a time the earth was considered to be flat. Probably they would have come up with another and less efficient method…