## the ABC conjecture

Posted in Books, University life with tags , , , , on November 27, 2012 by xi'an

Both Pour la Science and La Recherche, two French science magazines, had an entry this month on the abc conjecture! However, ABC being a common accronym, it is alas unrelated with my research theme. The abc conjecture is a number theory conjecture that states that if a and b are integers with no common factor and a small number of prime dividers, this does not hold for c=a+b. This is the abc triplet. (More precisely, the conjecture states that the quality of the triplet abc:

$q(a,b,c) = \log c / \log \text{rad}(abc)$

is larger than 1+ε for a finite number of triplets abc.) A proof of the conjecture by Shinichi Mochizuki was recently proposed, hence the excitment in the community. In La Recherche, I read that this conjecture is associated with an interesting computing challenge, namely to find the exhaustive collection of triplets with a quality more than a given bound 1+ε.

## Bad graph of the day

Posted in Books, Statistics with tags , , , on October 30, 2009 by xi'an

Another meaningless graph found in the November issue of La Recherche: a histogram of the predictions of the World population by 2005 attached to a brief discussion of the challenges of providing food for this population. No mention is made of the source(s) for this absurd agglomerate of predictions, (could I add mine as well?!) while the discussion picks the median prediction for its reference number: as if Science was run by majority rule… As an unflattering coincidence (for La Recherche!), the other French monthly popular science magazine Pour la Science has simultaneously published a rather well-argumented special issue on randomness (by Jaroslaw Strzalko, Juliusz Grabski and Tomasz Kapitaniak who are Polish physicists), refering to one recent paper by Persi Diaconis on the randomness of coin tosses. Being associated with Scientific American certainly helps in producing quality papers! (There is also a paper by Ivar Ekeland in the same issue, as well as the paper by Andrew Gelman already signaled.)

## “Pour la Science” almost goes Bayesian!

Posted in Books, Statistics with tags , , , , on October 22, 2009 by xi'an

After the strange views held on Bayesian statistics by the popular science magazine La Recherche, it is  more than comforting to see the other popular science magazine Pour la Science to publish a more balanced paper on the role of statistical evidence, both frequentist and Bayesian. And by Andrew Gelman! This paper is actually a translation into French of a paper of Andrew with David Wiekliem, published earlier in American Scientist. I can only make one complaint about a missing reference to Laplace (the true father of Bayesian statistics!) who did study the difference between male and female births in his Théorie Analytique des Probabilités.