There’s a lot that I like about how mathematics operates as a social discipline. We have a great respect for the history of the subject, which in particular includes acknowledging the work that has come before us. In the end, we ultimately agree that it is the mathematics which does the talking. Each of us has our own tastes (of course) and some of us are more prone to be excited about our own work than others, but we are remarkably free from bullshit (about the actual mathematics, at least). This is what all of science should aspire to.
Perhaps this is why I find the self-promotion surrounding the Ramanujan Machine so distasteful. (I wasn’t going to bother wasting any more time on this but here I am, last time I promise.) The idea of trying to automate methods for finding identities is an interesting one. But if want to claim that you have found something new, then some justification is required. For a start, you should at least be expected to do a cursory search of the literature. Perhaps you should even consult an expert? If the authors had been content to be more modest with their claims, merely explaining that automation was their main goal, and that they were merely hopeful to use these ideas to make new discoveries, I would have had no issue at all with their paper. Of course, nobody would have heard about the paper either. I already complained last time about the overblown rhetoric, but since then, my interactions with one of the authors indicated that the rot lies deeper still.
The author in question seemed happy (while listening to my previous complaints) to indicate that the novelty is not in producing new mathematics but in automatically generating formulas “without knowing Gauss’ work”. As I indicated above, that’s a reasonable and modest claim. But then, the same author will tweet out to the world the false claim that his program has discovered new and amazing mathematical conjectures. (A rather curious set of tweets to @elonmusk @yurimilner @stephen_wolfram @RHDijkgraaf; is the common thread people who have access to money that can be spent on math?) Don’t imagine for a minute that this is not a deliberate and conscious decision: the press stories generated about “automating the insight of Ramanujan” don’t happen on their own — they need the hook of “exciting conjectures” to be “newsworthy” and this is exactly what has been peddled via a concerted publicity campaign. The best way to describe this entire story is as follows: this is what happens when you import startup culture into mathematics. Maybe such Janus-faced interactions are commonplace in Silicon Valley where qualifiers are merely a distraction from a good sales pitch. But it’s an utterly abhorrent mindset that I think mathematicians must strive to banish at all costs. In particular, the choice to deliberately obscure the fact that the program has generated (as yet) nothing considered remotely new by an expert while simultaneously boasting of a triumph in automating intuition is not just absurd, but is an intellectual fraud. Ramanujan would roll over in his grave.
Caveats: The paper has a number of young authors who I consider completely blameless. The possibility of redemption still awaits in the next version of the paper.
Random Continued Fraction: I give you one of the author’s lastest tweets, in which one of their amazing conjectures has been generalized! (By a 15 year old apparently, well done to him, I hope he doesn’t waste any more time on this). I’ll spare you the amazing gif animation that builds up to this final climax:
Well … OK I guess? But, pretty much exactly as pointed out last time, not only is the proof only one line, but the nature of the proof makes clear exactly how unoriginal this is to mathematics:
(There is actually something vaguely interesting about how certain specializations of complicated identities are harder to prove than the original identities, but that is only tangentially relevant to this post.)