Hi everyone,

While I wait for things to change, I have been playing a lot of chess against bots. I decided to give myself a break tomorrow, since I've been playing a little bit too much and my focus and endurance have been affected.

Thus, tomorrow, I am going to read the following paper and try to prove three unproved conjectures that I saw proposed in this paper authored in part by a Harvard math professor that seems to be related to topology:

"Coincidences between homological densities, predicted by arithmetic"

I haven't really started looking at the paper yet, but as usual, I'll go through the paper, identify the key sections that I need to pay attention to, and make a few passes through it to write down any difficult-to-remember defined terms or terms that I do not understand the meaning of and need to clarify. It shouldn't take too long to understand the problem...maybe I'll get the three conjectures proved within a week while I re-include chess into my daily routine.

I'm sharing a little about this partly for the sake of continuing to characterize my professional brand (in case I can sell IP, have to get a job as a programmer, or start a startup), partly because I feel like discussing my recent mathematics activities, and partly because I think some readers interested in familiarizing themselves with open problems might benefit from my thoughts above on how to get into understanding a new mathematics research problem when such readers might have a solid undergraduate-level understanding of math but no experience with a particular field or subfield.

Thanks for reading my post...Happy Almost New Year!

-Philip White (philipjwhite@yahoo.com)

On Thursday, December 30, 2021 at 6:48:22 PM UTC-5, B.H. wrote:
> Hi everyone,
>
> While I wait for things to change, I have been playing a lot of chess against bots. I decided to give myself a break tomorrow, since I've been playing a little bit too much and my focus and endurance have been affected.
>
> Thus, tomorrow, I am going to read the following paper and try to prove three unproved conjectures that I saw proposed in this paper authored in part by a Harvard math professor that seems to be related to topology:
>
> "Coincidences between homological densities, predicted by arithmetic"
>
> I haven't really started looking at the paper yet, but as usual, I'll go through the paper, identify the key sections that I need to pay attention to, and make a few passes through it to write down any difficult-to-remember defined terms or terms that I do not understand the meaning of and need to clarify. It shouldn't take too long to understand the problem...maybe I'll get the three conjectures proved within a week while I re-include chess into my daily routine.
>
> I'm sharing a little about this partly for the sake of continuing to characterize my professional brand (in case I can sell IP, have to get a job as a programmer, or start a startup), partly because I feel like discussing my recent mathematics activities, and partly because I think some readers interested in familiarizing themselves with open problems might benefit from my thoughts above on how to get into understanding a new mathematics research problem when such readers might have a solid undergraduate-level understanding of math but no experience with a particular field or subfield.
>
> Thanks for reading my post...Happy Almost New Year!
>
> -Philip White (philip...@yahoo.com)

(If I can find correct proofs, I will probably publish them here.)

On Thursday, December 30, 2021 at 6:49:45 PM UTC-5, B.H. wrote:
> On Thursday, December 30, 2021 at 6:48:22 PM UTC-5, B.H. wrote:
> > Hi everyone,
> >
> > While I wait for things to change, I have been playing a lot of chess against bots. I decided to give myself a break tomorrow, since I've been playing a little bit too much and my focus and endurance have been affected.
> >
> > Thus, tomorrow, I am going to read the following paper and try to prove three unproved conjectures that I saw proposed in this paper authored in part by a Harvard math professor that seems to be related to topology:
> >
> > "Coincidences between homological densities, predicted by arithmetic"
> >
> > I haven't really started looking at the paper yet, but as usual, I'll go through the paper, identify the key sections that I need to pay attention to, and make a few passes through it to write down any difficult-to-remember defined terms or terms that I do not understand the meaning of and need to clarify. It shouldn't take too long to understand the problem...maybe I'll get the three conjectures proved within a week while I re-include chess into my daily routine.
> >
> > I'm sharing a little about this partly for the sake of continuing to characterize my professional brand (in case I can sell IP, have to get a job as a programmer, or start a startup), partly because I feel like discussing my recent mathematics activities, and partly because I think some readers interested in familiarizing themselves with open problems might benefit from my thoughts above on how to get into understanding a new mathematics research problem when such readers might have a solid undergraduate-level understanding of math but no experience with a particular field or subfield.
> >
> > Thanks for reading my post...Happy Almost New Year!
> >
> > -Philip White (philip...@yahoo.com)
> (If I can find correct proofs, I will probably publish them here.)

(I made a minor mistake--it looks like there is only one un-proved conjecture.)

On Friday, December 31, 2021 at 10:21:23 AM UTC-5, B.H. wrote:
> On Thursday, December 30, 2021 at 6:49:45 PM UTC-5, B.H. wrote:
> > On Thursday, December 30, 2021 at 6:48:22 PM UTC-5, B.H. wrote:
> > > Hi everyone,
> > >
> > > While I wait for things to change, I have been playing a lot of chess against bots. I decided to give myself a break tomorrow, since I've been playing a little bit too much and my focus and endurance have been affected.
> > >
> > > Thus, tomorrow, I am going to read the following paper and try to prove three unproved conjectures that I saw proposed in this paper authored in part by a Harvard math professor that seems to be related to topology:
> > >
> > > "Coincidences between homological densities, predicted by arithmetic"
> > >
> > > I haven't really started looking at the paper yet, but as usual, I'll go through the paper, identify the key sections that I need to pay attention to, and make a few passes through it to write down any difficult-to-remember defined terms or terms that I do not understand the meaning of and need to clarify. It shouldn't take too long to understand the problem...maybe I'll get the three conjectures proved within a week while I re-include chess into my daily routine.
> > >
> > > I'm sharing a little about this partly for the sake of continuing to characterize my professional brand (in case I can sell IP, have to get a job as a programmer, or start a startup), partly because I feel like discussing my recent mathematics activities, and partly because I think some readers interested in familiarizing themselves with open problems might benefit from my thoughts above on how to get into understanding a new mathematics research problem when such readers might have a solid undergraduate-level understanding of math but no experience with a particular field or subfield.
> > >
> > > Thanks for reading my post...Happy Almost New Year!
> > >
> > > -Philip White (philip...@yahoo.com)
> > (If I can find correct proofs, I will probably publish them here.)
> (I made a minor mistake--it looks like there is only one un-proved conjecture.)

Hi everyone,

It looks like I have a very good approach to proving or disproving this conjecture--it seems that it comes down to "new techniques for establishing the values of infinite limits."

I have very good secret (?--if these ideas were not known before by others) ideas about real analysis. I'm not sure if I will have time to continue looking at this problem tomorrow--it will be mainly back to chess activity-wise for me--but I will surely post a comment on Usenet if I have resolved the problem. I may not state the proof of the solution if I wind up preferring to keep it a secret, but I'll be sure to at least post if the conjecture is true or false if I can prove this result.

-Philip White (philipjwhite@yahoo.com)