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gets to find referees to do the job at some point the effect is going to be that i am just going to reject papers in that area unless they are obviously extremely strong since it s honestly a huge annoyance to email 10 people to get a single response even when i am just asking for a quick opinion which could honestly take under 10 minutes some areas are definitely worse than others honestly every time i get a paper related to the equivariant tamagawa number conjecture i die a little since it s so hard to find anyone to review those papers how long should a review take it would be nice if you could do it within about 3 months at the point where i am finding people to review the paper i am generally hopeful that the paper will be accepted under such circumstances i am usually inclined to allow 6 9 months for the paper to be reviewed i often ask referees to take a quick look early on to get a sense that they will be inclined to give a positive recommendation on the paper as well whether you think 6 9 months is way too long or relatively short probably depends on your own experiences from my perspective however it s such a difficult job getting people to agree to review that when i ask someone for a report in december and they say i would be happy to but i won t get a chance to get to look at this paper in detail until the summer i am almost always going to happily agree of course some papers are harder to referee than others also it may and does happen that even after a positive quick opinion and a positive early indication from the referee the paper is rejected the usual reason that this happens is that it is only when the reviewer looks at the paper in detail do they decide it is not as interesting as they first thought the only way to avoid this is to only get referees who agree to write reports within 3 months but if it takes me 6 months to find such a person then it doesn t really solve the problem what annoys you most about referee reports beggars can t be choosers but it does annoy me to wait 9 months for a review and get back a one sentence response it is fine it s honestly just embarrassing to me to have to send back such a report to the author after so long can t you at least find a few spelling mistakes typos i have received such reports on a number of occasions and then basically had to review the paper myself what pleases you most about referee reports when referees time and time again selflessly put effort into helping the author make genuine improvements to their paper as editor are you judge jury and executioner the closer a paper is to my own expertise the more likely it is that i have my own initial impressions of the paper i don t believe that my job is to be purely a functionary and that i add value by having my own opinions i have on a few rare occasions even solicited people to submit papers and i would like to do so more frequently although often by the time papers are on the arxiv they have already been submitted in the end i do believe that the process is impartial although of course railway trains are impartial too but if you lay down the lines for them that s the way they go posted in mathematics tagged math zeitschrift quick opinion review reviewing yes minister 10 comments the ramanujan machine is an intellectual fraud posted on july 17 2019 by galoisrepresentations 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 posted in mathematics rant tagged continued fractions de fractionibus continuis observationes elon musk euler gauss intellectual fraud ramanujan robert dijkgraaf startup culture stephen wolfram twitter yuri milner 10 comments en passant v posted on july 7 2019 by galoisrepresentations warning today s persiflage comes with possible extra snark due to sleep deprivation the ramanujan machine i learnt from john baez on twitter about the ramanujan machine a project designed to help reveal the underlying structure of the fundamental constants of mathematics it seems that more effort has been spent on hype rather than on learning anything about continued fractions and there is nothing there that would be surprising to gauss let alone ramanujan despite the overblown rhetoric sample nonsense from the website suggest a proof to any of the conjectures that were discovered by the ramanujan machine have a formula named after you the chances of finding anything novel by these methods seem slim while i m all for the use of computers in mathematics at this point for these type of identities we are very much in a world where the guiding hand of human mathematical intuition is very much required as for the new conjectures that are animated on their flashy website screenshot below well the less said the better it s harder to say which one is sillier to pretend is original the latter is a specialization of a specialization of a specialization of a specialization of gauss 2f1 continued fraction identity sending the four parameters to hint when your result is a specialization of a formula on wikipedia it does not count as original the former is even more elementary and proves itself by induction the rest of the paper is littered with mathematical trivialities and grandiose bombast all the other new identities are similar trivializations of gauss hypergeometric continued fraction or just known infinite or finite sums in disguise via euler s continued fraction what would be a much more interesting project is to find a way of taking a continued fraction and recognizing it as a specialization of one of the very many known results lest i be considered a luddite i should note that when it comes to infinite sums and integrals this is something that mathematica does amazingly well so respect to the people who worked on that 3blue1brown i don t really get the appeal to be honest yes i know i m not the target audience the presenter has a geometric perspective which gets shoehorned into everything whether it is appropriate or not i watched two videos both of which seemed to miss or at least elide at least one key underlying mathematical point the first was a video on quaternions the fundamental property of is that it is the unique non commutative division algebra over the real numbers but the video really only talked about the multiplicative structure in which case you may as well talk about are you really visualizing quaternions when you only think about the multiplicative structure then there was this video on the riemann hypothesis the video does a reasonably good job of explaining analytic continuation in terms of conformal maps not that i think of it that way but this is a perfectly reasonable way to think about it however the entire video ignores once again the key point that what is amazing is that the zeta function has an analytic continuation at all rather than it is unique time stamp 16m 45s the closest the video comes to acknowledging this is the quote which through more abstract derivation we know much exist which is somewhere between wrong suggesting that the extension exists for formal reasons and misleading using abstract to mean something like beyond the scope of this video or something how can you start to think about the riemann hypothesis without appreciating why the analytic continuation exists i guess the video helps bridge the gap between mathematics and physics popular accounts of physics have long since enabled people to think that they understand something about physics while actually not really having any real idea what is going on now people can think that way about the riemann zeta function as well the number of views of these videos is in the millions hatcher on class groups i learnt that allen hatcher author of a wonderful and free textbook on algebraic topology is writing a textbook on the geometry of binary quadratic forms i m sure it will be a great read and i don t quite mean to lump it together with the two examples above although i do notice that it does not appear to mention in any way class field theory that seems to be a strange omission couldn t the book at least have a sentence or two indicating that two centuries of algebraic number theory has been built on generalizing gauss work on the class group posted in mathematics rant tagged 3blue1brown allen hatcher analytic continuation class field theory euler gauss gauss 2f1 continued fraction hypergeometric functions mathematica quaternion algebras ramanujan machine riemann hypothesis su 2 twitter 2 comments the stable cohomology of sl f_p posted on june 19 2019 by galoisrepresentations back by popular demand an actual mathematics post today s problem is the following compute the cohomology of for a mod p algebraic representation step 0 is to say what this problem actually is it makes sense to talk about certain algebraic representations of as n varies for example the standard representation or the adjoint representation etc for such representations one can prove stability phenomena for the corresponding cohomology groups but my question is whether one can actually compute these groups concretely the simplest case is the representation and here one has a complete answer these cohomology groups are all zero in higher degree a computation first done by quillen and which is closely related to the fact that the most of the references i have found for cohomology computations of special linear groups in their natural characteristic consider the case were p is very large compared to n but let me remind the reader that we are exactly the opposite situation one of the few references is a paper of evens and friedlander from the 80s which computes some very special cases in order to compute note however that p should still be thought of as large compared to the partition which defines the corresponding stable local system s in order to get started let us make the following assumptions anzatz there exists a space x with a pro cover such that 1 the corresponding completed cohomology groups with coefficients are for i 0 and vanish otherwise 2 if is the mod p reduction of an appropriately chosen lattice in a added non trivial irreducible algebraic representation of then for i small enough compared to the weight of some version of this is provable in some situations and it may be generally true but let us ignore this for now one explicit example is given by the locally symmetric space for and taking the cover corresponding to a prime of norm p satisfying certain global conditions the point is this anzatz allows us to start making computations from the first assumption one deduces by lazard that where m is the adjoint representation but now one has a hochschild serre spectral sequence the point is now that one can now start to unwind this even knowing nothing about the differentials and make some conclusions for example 1 2 in particular the first cohomology always vanishes and the second cohomology is non zero only for the adjoint representation where it is one dimensional one can see the non trivial class in h 2 in this case coming from the failure of the tautological representation to lift mod p 2 note of course i am not claiming that the first cohomology vanishes for all repr...