A virtual currency called bitcoins has been in the news recently. It is said that in order to "mine" bitcoins, you have to solve hard mathematical problems.
Now, there are two kinds of mathematical problems. The difference is best explained by the following beautiful quotation from Langlands :
[T]here is an appealing fable that I learned from the mathematician Harish-Chandra, and that he claimed to have heard from the French mathematician Claude Chevalley. When God created the world, and therefore mathematics, he called upon the Devil for help. He instructed the Devil that there were certain principles, presumably simple, by which the Devil must abide in carrying out his task but that apart from them, he had free rein. Both Chevalley and Harish-Chandra were, I believe, persuaded that their vocation as mathematicians was to reveal those principles that God had declared inviolable, at least those of mathematics for they were the source of its beauty and its truths. They certainly strived to achieve this. If I had the courage to broach in this paper genuine aesthetic questions, I would try to address the implications of their standpoint. It is implicit in their conviction that the Devil, being both mischievous and extremely clever, was able, in spite of the constraining principles, to create a very great deal that was meant only to obscure God’s truths, but that was frequently taken for the truths themselves. Certainly the work of Harish-Chandra, whom I knew well, was informed almost to the end by the eﬀort to seize divine truths.
Question Which kind of mathematical problems do you have to solve in order to mine bitcoins ?
Let me clarify that I'm not interested in mining, only in knowing whether the problems are divine or devilish.