RE: Digest for competition-corner-participant-discussion@googlegroups.com - 2 updates in 1 topic

[JC TOWNEND]

Hi friends and allies,

I have really enjoyed this trip down memory lane, and the idea of trying to re-establish some similar competition for young people going forward.  However, the group seems a bit haphazard and the setup on Google groups with random emails and unorganized threads is challenging.

 

If we are going to go forward effectively, it’s clear there are 3 streams:  a stream dedicated to the pursuit of establishing a new competition, possibly a stream creating fun and interesting problems amongst ourselves, and a stream creating potential problems for students once item 1 is complete.

 

I am interested only in stream 1.  However, I agree with others that the idea that this would cost $500k-$1 million per year seems extreme.  Especially if we are able to get volunteers, of which I could imagine there would be hundreds available who would be dedicated to the pursuit.  And I’m concerned that people willing to invest significant sums (in the 5 digits) are dropping out.  Stream 1 requires a real leader who has time to dedicate a large amount of time to the pursuit, and will organize some meetings of interested parties or members where we can talk live and quickly get through ideas.

 

The first requirement is a thorough review of what is already available to high school students, and what is missing.  Do we have connections to current mathematics teachers at the high school level?  It also needs to be modernized with the problems of the day – how to prevent online cheating, which is so much easier than it was 40 years ago.  I expect it would be best hosted by a university with a passionate professor and grad students who get just some seed funding.  And before going grandiose with the travel and rewards, it has to be tested in concept. Also recognize there will be child protection issues that need to be built in, hence collaboration with schools and unis is a better setup than corporations.  And finally, this is only worth pursuing if it is sustainable – that means it cannot be led for 3-4 years with passion and die out when the driver is missing.  It also means it cannot rely on £1 million/year corporate funding – which is fickle.  It needs to be inexpensive enough to be able to find funding consistently for 10-20 years, and needs an establishment that does not require the consistent passion of a single person, but that can be transitioned over the years.

 

I think this is an amazing opportunity.  I do not have time to lead it.  I hope someone does.

 

 

Kind regards,

 

-JC

 

  JC Townend / CEO, UK & IRELAND

 T  +44 (0) 20 7332 7832 

  Assistant: Eleni.L...@lhh.com  T  +44 (0) 7467 753219 

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Please note that I may work outside of normal office hours – however this does not mean I expect you to respond outside of your working hours.

 

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Digest for competition-corner-participant-discussion@googlegroups. com - 5 updates in 1 topic

"Lin Gold" <lingol...@netzero.net>: Oct 10 06:45PM OK, I've regrettably asked for "No email" status from this group. Although I was willing tocontribute some money to George's project, like George, I've had to change my mind whensomeone thinks it takes $500,000 or so per year to do the project and nobody thinksdifferently. As for the math problems, I don't do them anymore (maybe some AI discussionwould be interesting, but that's probably another group.) Let's see if my "No email" status works. Lin   ---------- Original Message ---------- From: competition-corner-p...@googlegroups.com To: Digest recipients <competition-corner-p...@googlegroups.com> Subject: Digest for competition-corner-p...@googlegroups.com - 5 updates in 1 topic Date: Sun, 10 Oct 2021 06:54:14 +0000     competition-corner-p...@googlegroups.com Google Groups Topic digest View all topics finite field problem - 5 Updates finite field problem Walter Effross <eff...@wcl.american.edu>: Oct 09 11:21AM   I'm still getting the messages. Several times, I've tried to unsubscribe by sending an e-mail to the address listed for that; each time, I get back a message saying that it's invalid because I'm not a member. Best regards, Walter ________________________________ From: 'David Ash' via Competition Corner Participant Discussion <competition-corner-p...@googlegroups.com> Sent: Friday, October 8, 2021 10:53 PM To: Competition Corner Participant Discussion <competition-corner-p...@googlegroups.com> Subject: Re: finite field problem It might be good if Walter verified this--or at least if he verifies if it did not work since he wouldn't see this if it did! I'm still seeing the total number of members as 116 which is the number it has been for a little while now. Also if you click on 'My membership settings' you can adjust the amount of email you get from GG. If someone wants to occasionally check in on how this discussion is going but wants to minimize spam, they can adjust the settings to get less or no email when people make postings. On Friday, October 8, 2021 at 6:23:26 PM UTC-7 igl...@gmail.com wrote: I do think it worked. You are not in the member list any more. On Friday, October 8, 2021 at 4:38:00 PM UTC-5 Walter Effross wrote: Could someone please unsubscribe me? I've tried the instructions at the bottom of these e-mails, but I'm still in the loop. I'm still happy to talk about the project, going forward. Thank you! Walter ________________________________ From: 'David Ash' via Competition Corner Participant Discussion <competition-corner-p...@googlegroups.com> Sent: Friday, October 8, 2021 5:29 PM To: Competition Corner Participant Discussion <competition-corner-p...@googlegroups.com> Subject: Re: finite field problem There are, I believe, many possibilities for p(x) that will work, but some are easier to prove than others. Yes, x^10+x^3+1 is irreducible over GF(2) and proving that is one important step. It does then follow that 1, x, x^2, ..., x^9 form a basis but unfortunately this basis is not in the form that we are asked to find a basis. If p(x)=x^7 works, we'd have to somehow prove that x^7, x^14, x^28, x^56, ..., x^3584 form a basis. I'm not sure that you've proved that. It may very well be true--I haven't worked out the details but do know that there are a significant number of polynomials p(x) that work--there is not just one unique solution. However I believe there may be other polynomials p(x) which work and which require much less rote arithmetic (computation) to prove. On Friday, October 8, 2021 at 1:33:11 PM UTC-7 t...@bellefleurbooks.com wrote: Dear David: My inclination was wrong. Step 1 was a waste of effort. When you skip step 1, step 2 amounts to computing p(x) assuming that 1, x, x^2, . . . , x^9 form a basis. There are multiple possibilities for p here, the simplest being p(x) = x^7. Nevertheless, you still have to prove that 1, x, x^2, . . . , x^9 form a basis (step 3) which is equivalent to proving that x^10+x^3+1 cannot be factored. You have much the same issue (step 3) in your approach. You state that x^9+x^7+x^6+x^3+1 is not 1, but it could be equal to 1 if x^9+x^7+x^6+x^3 = 0, i.e., if the two polynomials, x^9+x^7+x^6+x^3 and x^10+x^3+1 shared a common factor. In fact, they do not, but you have to prove as much. Proving that x^10+x^3+1 cannot be factored, or something like this, is something to look for in the proofs submitted. It is a good problem. Sincerely, Tom On 2021-10-08 12:28, 'David Ash' via Competition Corner Participant Discussion wrote: -- You received this message because you are subscribed to the Google Groups "Competition Corner Participant Discussion" group. To unsubscribe from this group and stop receiving emails from it, send an email to competition-corner-partici...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/competition-corner-participant-discussion/476565e3-22c5-4c54-9750-ba91d18f47ban%40googlegroups.com<https://urldefense.com/v3/__https://groups.google.com/d/msgid/competition-corner-participant-discussion/476565e3-22c5-4c54-9750-ba91d18f47ban*40googlegroups.com?utm_medium=email&utm_source=footer__;JQ!!IaT_gp1N!i9yyLUT28okFJ7zGmjCCTokdQjR1Vxkr0oLcG72pHNrOa4co3yiR316g1aHZqOKrPg$>. -- You received this message because you are subscribed to the Google Groups "Competition Corner Participant Discussion" group. To unsubscribe from this group and stop receiving emails from it, send an email to competition-corner-partici...@googlegroups.com<mailto:competition-corner-partici...@googlegroups.com>. To view this discussion on the web visit https://groups.google.com/d/msgid/competition-corner-participant-discussion/b4df0fe1-3e34-403a-b9bc-61364e8e2f67n%40googlegroups.com<https://urldefense.com/v3/__https://groups.google.com/d/msgid/competition-corner-participant-discussion/b4df0fe1-3e34-403a-b9bc-61364e8e2f67n*40googlegroups.com?utm_medium=email&utm_source=footer__;JQ!!IaT_gp1N!iSMyVRWzY9nvxFgbciwcegiRmOKoAKZgyXYFsPQjQaLxaUpVL6Gip1F0RKq8NscBPw$>. Istvan Lauko <igl...@gmail.com>: Oct 09 10:02AM -0700   I did communicate with Walter. He is still a member, but now he does not receive any emails. I wander, if we should do this as a default for all, who are not active here (would hate to generate unwanted emails for anyone). Unfortunately there is no option for weekly or monthly "digest", only daily. On Saturday, October 9, 2021 at 6:21:16 AM UTC-5 Walter Effross wrote: Istvan Lauko <igl...@gmail.com>: Oct 09 10:05AM -0700   I mean I wonder.... (a case in point) On Saturday, October 9, 2021 at 12:02:01 PM UTC-5 Istvan Lauko wrote: t...@bellefleurbooks.com: Oct 09 05:02PM -0500   Dear David: I proved that p(x) can equal x^7, but I did not provide the proof. You know how to do it. By the way, every solution, p(x), has an x^7 term. I can prove this too but have not provided the proof. The original problem is a good problem--a little more challenging than the Sierpinski tower. Sincerely, Tom On 2021-10-08 16:29, 'David Ash' via Competition Corner Participant Discussion wrote: David Ash <david_...@yahoo.com>: Oct 09 04:31PM -0700   Tom, Yes--it appears to be true that every solution must have a (nonzero) x^7 term. To see this, first observe that it is fairly easy to show that for any element t in GF(2^10), t^1024=t. So if we repeatedly square any element of the field, we eventually get back to the original element. Note that the basis we are asked to construct basically involves taking an element and then squaring it nine times in succession to produce the other nine elements of the basis. Next we look at the squares of each of 1, x, x^2, ..., x^9: square of 1 is 1 square of x is x^2 square of x^2 is x^4 square of x^3 is x^6 square of x^4 is x^8 square of x^5 is x^3+1 square of x^6 is x^5+x^2 square of x^7 is x^7+x^4 square of x^8 is x^9+x^6 square of x^9 is x^8+x^4+x Note that the operation of squaring never introduces an x^7 term unless we already have an x^7 term to start with. Since a basis, by definition, must span the entire space, the only way a basis generated by squaring can span x^7 terms is if the initial element includes an x^7 term. This might be a good alternative problem to the original problem BTW--instead of asking people to give an example of a p(x) that works instead ask them to prove that p(x) must include an x^7 term. On Saturday, October 9, 2021 at 3:02:37 PM UTC-7 t...@bellefleurbooks.com wrote: Back to topYou received this digest because you're subscribed to updates for this group. You can change your settings on the group membership page. To unsubscribe from this group and stop receiving emails from it send an email to competition-corner-partici...@googlegroups.com.

David Ash <david_...@yahoo.com>: Oct 10 02:44PM -0700 Hi Lin,   It's rather strange, given the stated focus of this group, that as soon as we actually start talking about real math problems, people start losing interest.   These days AI is of interest to me only to the extent that it is rooted in rigorous mathematics. I find that other branches of computer science have done a far better job than AI in rooting their disciplines on a solid mathematical foundation. An example of this was when I worked in finance. The various options pricing models, like Black-Scholes and proprietary variants thereof that we developed, were rigorous and ready for the cutthroat environment of the trading floor. The AI models that we looked at, by comparison, were smoke and mirrors and not ready for prime time.   AI does raise some fascinating ethical and philosophical questions but, yes, those probably are best discussed elsewhere.   With regard to the costs, I also was surprised that the costs suggested by István were as high as they were--and I actually think his numbers added up to closer to $1M, not $500K, per year. However I don't have enough information to propose an alternative budget. Before István provided his estimates on here, I had been working from George's estimate of $50K in startup costs from page xlvi of The Book in the Aftermath. Granted, that figure was from 1980, but adjusted for inflation that is $166K in 2021. That's still quite a bit lower than $500K or $1M per year. I'm not ready to opine on which way we should go, but if there are ways of doing this on more of a shoestring budget, we should explore all alternatives.   It is also a bit unclear as to what capacity the former CC participants are being considered for participation in the journal. Would we be being paid for our participation (I noted that István's numbers include a number of paid roles); would we be paying for our participation (i.e. we would donate to fund this effort); or would we be volunteers, contributing mathematically but neither giving nor receiving money?   I personally might be willing to donate to the effort, but the amount of funds I could donate would be in the low five figures. So I can't do $1M or $500K or $166K on my own. Even $50K would be a stretch for me. However if I were donating I'd want to be involved mathematically as well. I don't need to be paid but I do need to be involved mathematically to consider donating.   I think we are going to need a Zoom (or many) to nail this stuff down, but I also think it needs to wait until István and Gabi are ready, and I'm sure they are really busy, like probably everyone else. So I can be as patient as needed. However a lot of people--like Walter, Lin, and perhaps myself--seem to be adopting a bit of a wait and see approach. There is interest but there isn't enough detail yet to commit. I know we are waiting in part in hope that we will generate more interest, but my sense is there won't be a lot more interest or commitment until we formulate the structure a bit more. I already ran the idea by one person I know. His strong suggestion is that we need buy-in from multiple strong universities throughout the US--Wisconsin is a good start but it won't get us all the way to where we want to be. It is tough to ask people for help, though, until we know what we are asking them for.       On Sunday, October 10, 2021 at 11:47:36 AM UTC-7 lingoldstein wrote:

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[David Ash]

Hi JC,

Thanks for these comments--it is good to have a new voice joining the discussion!

Just to clarify my own level of commitment--I am potentially willing to commit both my time (as a part time, not full time, volunteer) and my money (not beyond low five figures) to this project.

However almost everyone who has opined on this project, including you, seems to agree on one point: for this project to succeed it is going to require buy-in from unis and/or high schools--probably both. I also agree. However, that is, unfortunately, what I do not bring to the table: I can bring some time and some money to this project, but I'm not in an academic career myself. For the project to succeed, I think it will take someone from academia willing to also commit to the project. That person might not necessarily be making a huge time investment, but they would need to be willing to lend their name--and, by extension, the name of their uni--to the project. I think it will take someone with the relative security of tenure and with ten years or more to go before retirement.

There may well be people in this group who match these criteria--or, if they have less than ten years to retirement, at least have enough years left before retirement to help get the project well started before they switch to emeritus status. Unfortunately I'm not such a person myself. I would not necessarily expect a huge time commitment from such a person, but it would need to be someone we can call up at any time and get at least a few minutes of their time if their support is needed.

[Gabriella Pinter]

Hi,

Thanks for all the comments and for taking the time to post.
Basically we share the sentiment. We have committed to help to bring the book to life to document George's effort decades ago and committed to start this platform (which is less than adequate)  but we too have a number of parallel commitments going on. We tried to put dollar amounts on George’s vision of a national Mathematics Student Journal and a North-American problem solving competition based math talent development effort. The production of such journal with appropriate content (sans competition problem component) (depending on scope and quality) would have it's own expense. The problem competition component effort as was suggested has its own. The scope, the ways and the means for  both are up for debate. We scaled/projected the Wisconsin problem competition effort numbers and put them out. The size of the proposed effort startled us as well as others. (The proposed effort with grading and strong mentoring does not scale well.)  The ‘sticker shock’ may have discouraged people from joining this conversation.

We think that  mounting a national effort to math centered talent development through problem solving, starting from zero in the currently proposed form is vastly ambitious and in fact has more of a headwind in the current cultural/political landscape than it had decades ago (note that the current structures of mathematics education and talent development are being under attack for exhibiting strong racial bias, and Walter's comment earlier that it is culturally-politically a non-controversial, safe sphere may not be correct).

An attempt for a freely and widely accessible resource to strengthen the scale and quality of mathematical talent development either needs to be large and centralized, (with governmental support), or it needs to be developed organically and be aimed at complementing the variety of talent development initiatives currently present in the US (math circles, AoPS,  a variety of year-round and summer math camps and math competitions, Julia Robinson Math Festivals, Brilliant, expii, COMAP math modeling competitions for middle and high school, SIAM modeling competition, WI Talent Search, MIT Primes, RSI, etc....).  Yes, the journal would need enthusiastic volunteers. There are a number of those around and many of them are already active in different initiatives that reach segments of the middle school high school student population. We think George argues that the organic, incremental (and patchwork) approach is not sufficiently effective, leaves out very large swatches of the student population, and for the scale necessary it cannot fully rely on voluntarism, and it needs consistent funding.

However, it seems that a more organic approach is more appealing to the group here and it seems more viable. What would it look like? What do you think is reasonable to start with?

David mentioned commitment from people in academia. This can most certainly be secured but people would need to know what to commit to. State universities are not in a very good condition right now, at least here in Wisconsin. Graduate and undergraduate students may provide some workforce, but at UWM teaching assistants earn 15K for 9 months and most of our undergrads are working in outside jobs to support their studies. So it’s unlikely that we can get volunteer support from our university.

We’d be happy to talk if there’s interest or continue the conversation here.

Gabriella and Istvan

[jeremy resnick]

Greetings All,

Wanted to share the thoughts of someone (me!) whose spent their whole adult life in high schools as a math teacher, principal, and director of a network of charter schools.

I can see two purposes for a talent search/development effort:

1) Awakening an appreciation for the power of mathematical thinking among those who have an aptitude for it but who would otherwise have little opportunity to encounter it. 

2) Enriching the experience of those whose talent has already been discovered and who are already likely to end up in some kind of math connected life.

I imagine that most of us who participated in the Competition Corner would be in bucket #2 (but I don't know).  I certainly was.  I wasn't among the strongest of the participants (and never made it to USAMO or through any other nationally selective screen).  But my high school had a math team that competed locally and had AP mathematics offerings.  Competition Corner was fun, but I don't think it opened a whole new set of life possibilities for me.  My aptitude had already been discovered, and I was on a track to go to college.  I absorbed from my college professors and peers the directions I might go in terms of careers.  For many reasons, I ended up a teacher-but I wouldn't include my involvement with Competition Corner as significant to the broad direction of my life. 

It would be most helpful to hear from participants who see their involvement (in retrospect) as more akin to #1--and who would be testimony to the potential life changing impact of what we might develop.

I would be very interested in a talent search that was focused on purpose #1.  A big effort aimed at youth who encounter mathematics and mathematical thinking anyways (perhaps a few years later or in a less pure way) just doesn't have the same appeal.

Here is a reflection from Titus Kaphar on his journey.  He's an artist, but I think his story could be helpful to us.

"I didn’t do well at school. I failed most of the classes that I took. I got kicked out of kindergarten. I was suspended very often in high school. I wasn’t a good student to say the least. I went on to junior college only because I was trying to impress a woman who would later become my wife. Long story short, I took an art history class in junior college and it opened up the world to me. It made me realize that I had a kind of visual intelligence I never knew existed, and that if I could understand the world through images—and sound also—I could figure things out. So I went from being a very poor student to being on the dean’s list, and that was mind blowing to me."

https://news.artnet.com/art-world/titus-kaphar-erasure-art-history-1497391

Jeremy Resnick

[david_...@yahoo.com]

Thanks for your thoughts Jeremy, Gabi, and Istvàn. I agree with Jeremy that #1 is going to be very important for the journal and appreciate his thoughts there. However I want to say something about #2--those who have already been identified as having mathematical talent and seem destined for a "math connected life."

I don't think it is as much of a given as you might think that such a person will end up in a "math connected life" even if that is their intention. I would want the journal to support them in staying in a "math connected life" if that is their goal--because I think that is harder to do than you might think.

I need to define my terms here though: I do not, in general, consider a career in tech working as a computer programmer to be a "math connected life." There are exceptions such as if the programmer is applying advanced math to computer science or math is the domain of application of the programming. But in general the vast, vast majority of computer programmers use little to no mathematics in their work and are not leading a "math connected life" by my definition of mathematics.

At one time my undergraduate uni, Waterloo, awarded Bachelor of Mathematics degrees to graduates in computer science. This has since been changed and such graduates now get Bachelor of Computer Science degrees. Although a bureaucratic change, I think this change accurately reflects the fact that tech, although having some of its roots in math, has grown apart from math and should now be considered a separate field.

People working in tech are encouraged to keep their tech skills current to remain relevant and employable. The same encouragement regarding math skills is usually not provided unless, again, the programmer is one of the small percentage actually applying tech to math problems. Most people leading tech connected lives can and will see their math skills wither as the greater economic demand for the tech skills tends to dominate.

Perhaps for some, this is not a problem. If someone wants to work in tech and is happy evolving away from math it is not my intention to try to stop them. But hope is that the journal would, in addition to supporting #1, will support those in #2 who want to lead a "math connected life." It is harder to do outside of academia than you might think, and we all know academic jobs are scarce.

I know I'm not the only person with a math background who finds that a career in tech is not mathematically satisfying. I've talked to others with strong mathematical roots who agree with me, often quietly and in private, that there is something dissatisfying about a career in tech for a mathematician.

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[david_...@yahoo.com]

I would also add that while I would primarily categorize myself in #2 when it comes to CC, it was definitely through math competitions in general that I was identified as a mathematically precocious kid. No one individual math competition was life changing for me, but the overall experience of participating in many math competitions in youth certainly WAS life changing for me. George was an important leader of that community.

 #1 is very important but the efforts of #1 can be wasted if #2 isn't in place--and #2 isn't the no-brainer people sometimes think it is.

Sometimes what is needed for someone in group #2 is not further enrichment of their mathematical skills, but development of soft skills needed to fully realize their mathematical potential. Sometimes promising young mathematicians don't fully realize their math talent due to weak social skills. Too often when a young mathematician shows weak social skills they are treated harshly like it is a moral failing or something. IMHO that is the wrong way to nurture mathematical talent. My hope would be that the journal play a role in helping to develop the softer skills in a positive, nurturing, non judgmental way.

I think both #1 and #2 in Jeremy's analysis are essential and neither one makes sense without the other. In my own youth #1 was actually very strong but #2 was much weaker. To the extent that is still true (is it?) the journal does need to focus on #2 while keeping #1 strong.

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[david_...@yahoo.com]

Also I'll comment briefly on Gabriella and István's comments. BTW do you prefer Gabriella or Gabi?

I do think it is important to identify what resources are currently out there--AoPS, Math Circles, etc. I would probably start by talking to the people who run the various efforts to get their thoughts. I would approach it from the perspective of augmenting, not replacing, the current efforts of others. Nurturing math talent after it has been discovered is something I think a journal could help a lot with--but that may be only my personal bias.

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