*we*I mean the community, not

*Harry and I*or

*Harry and I and Alexandra*,

The one larger point I would suggest adding is to add my operational definition of progress: Progress is being made on a problem if, when the solution is published, it will cite work being published today. Of course that is “operational” only after the fact. Demillo Lipton Perlis at the end have a nice riff on this. The alchemists thought they were making progress on turning lead to gold but they weren’t, even though we know that was actually a solvable problem. Likewise jumping off of higher and higher buildings was not making progress toward heavier than air flight.

*not*tell them that my PhD thesis was about that sort of thing (oracles). I could say

*Once you know what's not going to work you can concentrate one what is going to work.*

*Counterargument*: 50 years of 20th and 21st century mathematics is A LOT.

*Counterargumen*t: there are some (1) mavericks who buck the system, and (2) people like Carl's son-of-a-party-member who are allowed to think deeply for years.

*Mathematics may not be ready for such problems.*

*posed*means in this context. Did the ask for a construction OR did they ask for EITHER a construction OR a proof that there wasn't one?

*MATHEMATICS WAS NOT READY FOR SUCH PROBLEMS.*

*MATHEMATICS WAS NOT READY FOR SUCH PROBLEMS*,

*MATHEMATICS WAS READY FOR SUCH PROBLEMS*

*MATHEMATICS WAS NOT QUITE READY FOR SUCH PROBLEMS.*

*MATHEMATICS WAS ALMOST READY FOR SUCH PROBLEMS.*

*MATHEMATICS IS NOT READY FOR SUCH PROBLEMS.*

*COMPUTER SCIENCE WAS NOT READY FOR SUCH PROBLEMS.*

*the hard one*though probably they were all hard. This one is harder for me to speculate on. When it was solved and Darling wanted to know why it was worth $1,000,000 I told her that it says

*if something*

*tastes and smells and feels like a sphere, its a sphere*. She was unimpressed. But back to our story: in hindsight,

*MATH WAS READY FOR SUCH PROBLEMS*

*MATH WAS READY FOR SUCH PROBLEMS*

*Steady progress*: see the Wikipedia entry here. What's of interest to us is that there was a barrier result of Omega(n^{8/9}) by Ruzsa (apparently unpublished) that said the techniques being used could not do better-- so people, in short order, found new techniques. Here is hoping that happens with P vs NP.

*Is it true? When will it be resolved?*He said

*Yes*and

*Never*.

*Collatz*is not a word?

*What is R(5)? When will we know?*He said

*43*and

*Never*.

*law*

*of small numbers*: patterns that hold for small numbers stop holding when the numbers get too big. (I've seen other things called

*the law of small numbers*as well.)

*MATH MAY NEVER BE READY FOR SUCH PROBLEMS*

*Note:*The conversations about Collatz and R(5) were within 10 minutes of each other. Depressing day!

*DO NOT KNOW IF MATH IS READY FOR SUCH PROBLEMS*.

*Note*: I found that information here which seems to be an Encyclopedia Britannica website. I would have thought that, with the web and Wikipedia, they would be out of business. Good for them to still be in business!

*MATH IS NOT READY FOR SUCH PROBLEMS*

*I do not recommend spending half your life on the Riemann Hypothesis.*

*surely,*he didn't mean ALL metrics. Probably right, but stop calling me

*Shirley*!) For a byte more about Hilbert's problems, including a few paragraphs on H4, see my reviews of two books on them, here. Same as the last item- if you have an opinion (informed or not) about, for which of them that are though to be sort-of open, is math ready for them, leave a comment.