Edit (17/02/21) I changed the title of this post which was unnecessarily incendiary.
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 absurd; 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.)
… the novelty is not in producing new mathematics but in automatically generating formulas “without knowing Gauss’ work”
Maybe they should re-name it Ramanujan Zero (after DeepMind’s AlphaZero), indicating their tabula rasa machine learning approach.
No — the name “Ramanujan Machine” is their greatest triumph! It’s a brilliant publicity move which gives the entire enterprise the patina of exotic brilliance without any of the reality. Moreover, it’s probably also important to note that this is definitely not a zero knowledge approach — they fed the program the form of continued fractions of a particular kind (with linear/quadratic entries), presumably because there were existing continued fractions of such kind already (in the work of Euler, for example). And they produced… special cases of results also known to Euler.
“…not only is the proof only one line…” looks like 3 lines to me.
Anyway, this behaviour is not uncommon in the ML community. It’s all about how loud and for how long you can blow your trumpet, and even the journals don’t bother to reign it in. Observe the case of the famous “earthquake paper” which was shown to be an amateurish fraud https://towardsdatascience.com/stand-up-for-best-practices-8a8433d3e0e8
Touché. To be fair, the first line really shouldn’t be necessary for anyone with a classical mathematical education, I was just trying to “communicate with the man on the street.” And the second full stop can be replaced by a semicolon.
I (sadly) suspect you are right about ML. The good news is that there isn’t enough money in pure math for most hucksters!
The paper is amazingly bad. None of the authors are mathematicians as far as I can see. I think the word “new” appears 50+ times in the paper. Looks like they updated the paper to include your observation from last time about the Gauss continued fraction without mentioning the source (the authors admit here they read your blog: http://www.ramanujanmachine.com/idea/some-well-known-results/). Classy!
One can be grateful for small mercies.
The updated version that they are submitting to a conference, now on the website, has this lovely quote:
“Indeed, since the original version of the paper and the project website went
online, several of the conjectures have been proven by contributions from the community. In the past, the
development of such proofs sometimes led to new discoveries, such as the consequences on number theory
of the proof of Fermat’s last theorem [15].”
Given the context, I think this is a truly unbelievable attempt to advertise >_<
pure envy? 🙂
This comment doesn’t make any sense. But I approved it because it is amusing to think it that this random poster is related to one of the authors.
I wonder, why did you bother commenting on Ramanujan machine? Is it a societal duty to inform other people that forced you to? It appears that you do not get any pleasure from writing about it (as opposed to writing about number theory).
Now published in Nature itself, it seems. I haven’t checked to see if it is the same, through and through, as the arXiv version, but there are obvious chunks that are more-or-less identical.
To be fair, there are some conjectures on its webpage that have quadratic and cubic terms in the successive denominators, which aren’t immediately handled by Euler’s hypergeometric formula.
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Ok. This is not amazing. Since CAS has been developed, there are several initiatives to find conjectured relationships for some mathematical constants. As far I can remember, Jesús Guillera, Zhi-Wei Sun, among others have published a really large number of conjectured series based on the work of Ramanujan in recent years. Some of them have been subsequently proven. The work on continued fractions (CF) has the same goal. It provides new conjectured relationships for constants like Pi, Catalan Constant, zeta values and more. I think this is not too much different from the mathematical work previously performed and it lacks novel or deep results. For instance I would expect to find a CF having enough acceleration to prove the irrationality of Catalan Constant, but there is nothing closer to accomplish this. What makes it different is the way used to communicate such results. Ramanujan Machine is a pure marketing name to make widely known such work. This behaviour is not common in the Math community. I agree with such criticism, I also believe the fact that these results, ten years ago, would have been amazing, but today they have not much punch. However, I acknowledge the unorthodox way this team has made popular such tough topic to accomplish the publication in science-based Nature magazine and previously in some portals like phys.org among others. I really doubt that they can publish in some ICI prestigious Math Journals. The formula findings have no much research substance.