You can also look at articles on popularisation on my web site. At Bangor we have run Masterclasses for selected 13 year olds and covered a variety of topics: spherical geometry, higher dimensions, knots. See also my presentation “Out of Line”.

Hope that helps.

]]>I am a high school mathematics teacher in Australia, but have been recently working with an 8 year-old boy who is having mathematical discussions with me that go well beyond the Australian National Senior Curriculum.

I am in the process of trying to provide him with opportunities to be challenged in his mathematics (Senior Level) while still provide social and emotional connection with his peers. Do you have any advice or programs or resources that would be useful in ascertaining what the capabilities of this young boy are? His interests are so far beyond his age that I am sure there gaps in his understanding of mathematics if it were to be taught in a linear, scaffolded manner. I want to provide a focus and purpose to his mathematical studies, including filling in the gaps, without tempering his natural curiosity and interest to push the boundaries of what he is capable of understanding.

Any advice would be much appreciated.

Regards, Luke

]]>A question I’m interested in is the validity of climate models that show a large human contribution to global warming. These global climate models are quite complex mathematically. Perhaps you could offer some new insight into the validity of such models.

Bob Clark

]]>I’ve read that professor Durán (a mathematician from Venezuela) claims to have the proof of the following conjectures; “There is an infinite number of Mersenne primes” and “there is an infinite number of Fermat primes”, this is the link that i found: http://www.el-nacional.com/sociedad/Venezolano-demostro-teorema-planteado-anos_0_550145051.html, and, As a consequence of it he said that is completly proved the infinity of perfect numbers, these are the papers:

1. Mersenne Primes Cardinality (2013): http://www.open-science-repository.com/mathematics-70081967.html

2. Fermat Primes Cardinality (2014); http://www.open-science-repository.com/mathematics-45011817.html.

I hope you can read this comment and take this seriously enough to post about it.

Capablanca. H

]]>I observed one interesting prime factorization of the three consecutive numbers 2013, 2014 and 2015, 2013=3x11x61, 2014=2x19x53 and 2015=5x13x31, they are all factorized into three distinct primes. I guess there should be no other three consecutive numbers with this property but I can’t find a proof. What do you think? ]]>

I just wanted to say that this is an awesome blog about math. Learned a lot through it. Thank you.

I also wanted to ask you if you could add a link to my website on your link list. It is a free wiki about mathematical proof: http://proofs.wiki/.

Best regards, Brunner Nathan ]]>

I think the moderator should be able to review and cut and paste as much into a post as he/she likes. I have a hint for others, on a problem, but I don’t want to include the entirety of my hint, without a moderator making their own judgment — knowing of course that I have taken the time to write up the hint, in weighing how much of it will be passed along.

]]>You say you want more than a hint, you want a full path laid out? Well, that is like a child asking for you to do his homework when you are the parent.

I will, however, try to help with the incentive structure if a specific, credible request is made by a group (of some defined nature, but not a group closed to new admitted). Some form of joint prize is likely to be necessary; how to ensure that the prize cannot be appropriate by a few is the trick.

As background motivational material, I do not want to see this happen, as recited by Prof. Godfeld at some length — and about which I have seen numerous similar, frankly silly, childish and egotistical attempts to gain individual credit for a process that yields results over time:

http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf

That two of the finest mathematicians between 1940 and 1980 should have had such a dispute is evidence of the extreme power of individual incentives, against the collective, unless a structure is put in place to harness those incentives.

One year; I conjecture I can do it in two if folk don’t start posting ideas to form a collective effort to do so, without free-rider incentives, and incentives for people to “cherry-pick” for self-aggrandizement, in blunt terms.

If the challenge is not accepted, I will, reluctantly given my other time commitments, step in and attempt to solve the Twin Prime Conjecture, which, without hints to you, I believe I can do given what I now know within no more than two years.

I look forward to notification that Prof Tao takes this seriously enough to post it as other than a mere comment.

H. Schoenich.

December 22, 2014