“[I]t’s time,” writes Eleanor Saitta in the May 27 issue of The Nation, “that we put our faith, and our funding, toward math instead of our battered privacy regulations to keep us safe from prying eyes.” The title of the article is The Key to Ending Mass Surveillance? Math. The article explains the difference between content and metadata and the economics of surveillance (by government agencies as well as commercial enterprises), issues with which most activists are already familiar. What mathematics has to do with the problem is not really made clear in the sole reference to the “key” promised by the title:
Encryption is a category of mathematical operations in which one string, a key, is used to transform another, the plain text, in an encoded version according to a specific algorithm. Once the text is transformed, reversing the transformation without a key takes tens or hundreds of orders of magnitude longer than the encryption did. A secure, unsurveilled Internet depends on widely shared protocols between different systems—two smartphones, for example, or a smart meter and the local electrical substation—and all secure protocols depend on encryption and related operations. Correctly encrypted content is generally not something that can be spied on. Intelligence agencies are not magic; we have no reason to believe that the NSA boasts mathematical advances relevant to decryption beyond what the unclassified world has.
I suspect we do have reason to believe that the NSA’s mathematical capabilities, while not magic, are rather more extensive than Saitta thinks, if only because the NSA is reputedly the world’s largest employer of mathematicians. But Saitta is right to hint that mathematicians could just as well devote our skills to developing methods to stymie rather than to facilitate surveillance. At the Shakespeare and Co. reading with Villani, one question from the audience (at around 58:10) addressed applications of mathematics. Historically, the questioner said, “a lot of theorems… found very significant applications in various industries.” And he went on to ask, “Do you think … that every theorem we have, either currently or in the future, will be found to have practical applications? If this is the case, is math conceptually simply a way to describe natural phenomena?” While Villani responded to the question as asked — “a tiny portion of theorems have applications, a small but bigger portion inspire applications rather than having them directly” (and then went on to a very nice 4-minute explanation of general relativity and GPS), I attempted to turn the question around (after a 1-minute digression on Plutarch and Archimedes) by asking, “in whose interests are these applications?” I used the example (already cited here) of how number theory has contributed to driving independent bookstores out of business, but I could also have mentioned surveillance, as I did earlier in the reading.
The larger point is that it is always assumed that applications of mathematics are in the general interest. But I don’t believe there is such a thing as “the general interest” where most applications are concerned. In the wake of the Snowden revelations, the Notices of the AMS has been hosting a discussion (now winding down) of the specific responsibilities of mathematicians in connection with the use of mathematics (and sponsorship of mathematicians) by intelligence services. The very interesting suggestion that mathematics can also be used to protect citizens from surveillance is equally deserving of discussion. Unless there is money to be made from applications of this sort, I fear the discussion won’t happen on its own.