Apr 1, 2002 … Every mathematician is trying to solve at least one of the seven notorious … since we mathematicians and theoretical computer scientists care very little … than a mundane `rigorous mathematical proof’ of PNP would have been. … hence it is safe for Mr. and Mrs. Clay to offer big prizes!, …

http://www.math.rutgers.edu/~zeilberg/Opinion45.html – 6k – Cached – Similar pages –

Somebody has to speak for those not able to…

]]>But then, a few of Freeman Dyson’s errors are also irreparable. Part of my real point is that sometimes we are a little too generous with mathematicians and scientists who win big awards.

]]>But let’s be generous with him just as we would be with a Nobel Laureate such as Freeman Dyson who sometimes says wrong things. The holographic bound does say that there is an upper limit of 400 qubits needed to **address** any qubit in the universe. A computer in the observable universe will never need more than a 400-bit address bus.

I love Wikipedia, and also math and physics books. They play a different role. In most of Physics and CS, you can work some problems, see how it goes, and move on to other aspects of the subject. In math (and complexity theory) a major role is played by delineating exactly what is proven. Thus some fraction of the books must start with the axioms and inch their way forward. Usually these don’t make light reading.

Classic examples in math are an analysis book by Landau (same guy who introduced/popularized the O and o symbols?) starting with some axioms (ZF set theory? I forgot) and proving and numbering each theorem through advanced calculus and into real analysis. Along the way, the first place the axiom of choice is truly needed is noted (existence of a non lebesgue measurable set?) I believe Titchmarsh followed up by carrying the numbering on through all the theorems of classical complex analysis (possibly in http://www.amazon.com/Theory-Functions-Edward-C-Titchmarsh/dp/0198533497, still in print).

I doubt if many are interested in reading these treatments, but it is nice knowing they are there in case you need them. Contrast this with Wikipedia: usually (for tech stuff) pretty good, often interesting, but you are never quite sure that it is right. Also, it might change in the next couple minutes, usually for the better. There is also the problem of topics that nuts and quacks take an interest in.

]]>*“Yeah,”* you’re thinking *“but what are some examples? Aside from pretty much everything by Grothendieck, I mean.”*

Well, the Clay Mathematical institute has two on-line proceedings *Strings and Geometry*, and *Mirror Symmetry* that (IMHO) are pretty good examples.

In aggregate, these two proceedings are 1,324 pages of cutting-edge mathematical excellence, in which dozens of mathematicians do their very best to explain to students (and to each other) what’s going on.

Do they succeed? Well … as the *Mirror Symmetry* introduction candidly describes it:

We are at a delicate point in the history of the interaction of [math and physics]: while both fields desperately need each other, the relationship seems at times to be a dysfunctional codependence rather than a happy marriage!

Why would a practical engineer be looking at these two proceedings? Well, we take a practical interest in the intersection of information theory and geometric quantum mechanics—that intersection being a working definition of the core mathematics of quantum simulation science.

So I was keyword-searching for informatic-type concepts like “decoherence, entanglement, simulation, tensor networks, Choi, Kraus, Stinespring”.

Zero, zip, nada. Which is (from one point of view) very *good* news for students … because it means that fundamental mathematical invariances remain to be explored … and plenty of work remains to be done! ðŸ™‚