Atiyah Riemann attack/ post mortem/ autopsy, Primes torch carried on

😳 o_O 😥 hi all. am writing this with some heavy heart. in some ways there are a lot of angles to this story, in another way there are none at all. (to paraphrase one cold/ sarcastic respondent, nothing to see here, move along.)

the Riemann hypothesis is one of the worlds most premiere and probably hardest open problems, unsolved after 1½ century, and has a $1M Claymath prize now almost 2 decades old.[31]

coincidentally, just did a brief survey on links between Riemann and physics/ quantum mechanics, a connection that was noticed decades ago by Dyson and has gotten further attention over the years.[39] this crosscutting nature is somewhat rare of deep math/ physics problems, and esp wrt number theory. it even has significant connections to TCS.[13][14]

Atiyah recently announced a “simple” proof presented at the Heidelberg Laureate Forum one of the premiere scientific conferences in the world.[1] preprint is available on google drive (although these links are at risk to rot quickly, rats).[20] he is one of the worlds premiere living mathematicians.[34] he will be 90 years old in less than a year. theres an outstanding series of youtube lectures by him ranging over wide topics including physics + math crossover.[9] wrt the proof “attack” theres substantial reaction across multiple blogs [4][12][26][29][30][44] and mainstream media including quick-to-react New Scientist.[42][2]

there was mass buzz and excitement in cyberspace, eg across social media such as reddit quickly accruing hundreds of comments, some superficial, some substantial.[5][7][10][11] (many people from laymen to professionals are interested in this problem, with good reason, theres real scientific drama here, a relatively rare occurence in that world.) alas, even much to my own chagrin, a lot/ most of that seems to have collapsed quickly in the immediate case. o_O

before the definitely far-from-funny analysis, the episode is evocative of some relevant cartoon humor, which display a kind of timeless wisdom wrt capturing certain deep archetypes definitely in play here. sydney harris famous cartoon I think you should be more explicit here, xkcd number theory/ collatz eventually all your friends will stop calling you, and smbc old physicists, we had a lot of good times.

Atiyah had already offered a proof of the 6-sphere problem within the last year, and it was not accepted by any other mathematicians.[6][8] and, digging deeper, its not exactly/ “merely” because of a “mistake”.

so there is apparently another “problem” going on. think this deserves some words, but am trying to be empathetic and sensitive at same time. sometimes, there are some situations that really have no emoticon to cover them…

insiders/ the mathematicial intelligentsia has been aware of Atiyahs “situation” for awhile but there is no open acknowledgement. there seems to be tiptoeing, whispering, innuendo, gossip. in short, they dont want to talk about it, openly that is.[3][10] aka some “beating around the bush”[37] and/ or “ostrichism”.[38] confronted directly about it (as just happened/ played out in chat room last wknd), the response might be defensive, grouchy, surly, biting, or worse. aka a 3rd rail. a diplomatic response might be “time for him to retire”.

in psychology and hollywood movies in addition to the classic “mid/ ½-life crisis” for 40somethings there is now recognized another concept of a ¼-life crisis for 20somethings. it looks like we are witnessing what might be delicately called a sunset crisis. its well understood that late life changes such as retirement can have substantial psychological impact ie be disorienting, upsetting, stressful, or worse. maybe for a living legend lifetime all-time high achiever like Atiyah, even more.

am going to try a bit )( to delicately-as-possible tiptoe around the landmines myself here. there is an old hindu parable about the Blind Men and the Elephant which any active research area or open problem can be related to. but here we have the Elephant in the Room.[35] here this necessarily is not so much an analysis as something leaning toward/ bordering on a diagnosis“trigger warning” this analysis is nec going to say a lot about psychology!

so, caveat, rushing in where angels fear to tread™, from the earliest days here now over ½ decade ago its long considered a sterling virtue, now essentially a tradition, to pull no punches™, tell it like it is™… but ofc please dont shoot the messenger™…

one must be careful about Ageism[40] in this situation. but there is something worse than Ageism (a human discriminatory urge/ prejudice) that is real, it is called Age, and sometimes it involves deterioration of mental faculties, that is a statistical/ biological/ medical fact. this is similar to mental illness, although that can strike the young. is senescence leading to senility, dementia, alzheimers, parkinsons, considered mental illness(es)? it seems like a quibble to argue they arent. an “illness” is sometimes a temporary situation but while many mental illnesses are “treatable” they are often not “curable”. and lets face it, aging is the ultimate incurable condition.

one is reminded of the concept of entropy in thermodynamics and the 2nd law that says there is unavoidable increasing entropy in the universe. the manifestation of that in the human realm is Age. a simple example nearly everyone can identify/ relate to is tooth decay. something physical. a much more heavy aspect to ponder is mental decay. cartesian dualism notwithstanding— or the illusion pierced— our minds are run by our brains, right? “something physical”…

we discussed this at length on a chat line (among two other physics Phds, math Phd, etc), and a remark was made: “its like a skeleton popped out of the closet”.[41] in another word, re the title:


⭐ ⭐ ⭐

there are proofs that are mistaken, and there are proofs that are incoherent. in physics this is known as “not even wrong” as quipped almost a century ago by the sometimes caustic quantum pioneer Pauli.[36] (quantum pioneers faced very similar problems of separating signal from noise in research/ academia at the time.) definitions dont (really) define. etc. for example can anyone state definitely what a Todd function is invoked in his proof?[27] it all may even be written in impeccable/ flawless latex, but if an expert looks at it, they find that its similar to a “(technical) word salad” in places. “word salad” is a another symptom of various mental deteriorations.

years ago saw a similar case alluded to in this blog in earlier days. a Purdue Phd in CS wrote up a complicated ~75pg proof on P vs NP using my favorite, monotone circuit theory. it took me 6 weeks of back-and-forth with the author to figure out what other experts probably realized within a few minutes of scanning the paper. it seems like an oxymoron when stated outright, but there it is: highly (superficially!) polished gobbledygook… so “lesson learned”! the hard way! not exactly the one expected/ intended/ hoped for! and contrary to my own approach, within the scientific community one can forget the idea of professional courtesy, camraderie, or fraternity: its tossed out the window in these “outlier” cases as a perceived waste of time…. possibly fully justifiably so…

notice, Phds are never revoked, but some proofs are “retracted”!

another element. dislike using the word “crank” but sometimes theres no alternative. an aspect of crank physics is to work on deriving deep physics constants. this has been done successfully in the past by the worlds greatest physicists. however, a new derivation of a physical constant is an extremely rare breakthrough, it has happened a few times in a century (it would be really neat to see a historical survey of this by an expert, am not aware of any, the typical focus would tend to be on 1-at-a-time). crackpots directly or intuitively understand this. they are drawn like moths to the flame. and Riemann is a very big flame. so you get many “amateur” attempts/ attacks.[17]

Atiyah is lately turning to physics, analyzed/ “deriving” the fine structure constant in physics, preprints available.[28][15][21][22]

this leads to analysis/ topic of crank psychology. the diplomatic version is in Aaronsons “ten signs a claimed math breakthrough is wrong”[19] and the less diplomatic, more harsh version is Baez “crackpot index”.[18] alas multiple items can now be ticked off in both for Atiyah. (might go into more detail later, its in the chats, for now “you do the math”)[23][24][25]

have been looking for P vs NP angles over decades, and one runs into this phenomenon there. one key aspect of Crankery that have personally noticed, maybe not widely reported by others, is that they dont seem to understand/ grasp logical refutations. more accurately, they adamantly reject careful refutations. in a word, denial. the words “uncomprehending or oblivious” come to mind although this can border on delusional in worst/ extreme cases.

this relates to long/ deep psychological research on a concept called (mental) rigidity. just doing a quick google search this 2002 scientific study finds not-so-surprisingly that rigidity is curvilinearly related [correlated!] with age! (and ofc associated with various mental illnesses such as OCD (obsessive compulsive disorder) and schizophrenia incl a core feature of ASD (autism spectrum disorder)! …)

do others think reference to this type of Crankery is in poor taste? but even with my own distaste for the term, have found it to be unavoidable in some relatively rare but unmistakable/ clearcut cases. ie here, the insiders are saying this is exactly what is going on with Atiyah: one might say that there is a difference between “gaps vs incoherencies”, and experts have personally, apparently to some degree even face-to-face, pointed out the incoherencies of his papers, without coherent response, so to speak. (surprise! “[anti-]? reciprocity”!) 😮

in scientific circles, a retraction is a public embarrassment and humiliation, but sometimes this still honorable simple action separates the lucid from the cranks— its an admission of error. to err is human, to forgive is divine. in the case of a recent ~1yr old P vs NP proof attack by Blum covered in this blog, it was retracted within about a week after the withering-but-correct cyber peer analysis that quickly ensued as it went viral (various parallels to present circumstances). as my grandfather said in a phrase that rings thru my head whenever asking an attractive woman out on a date, cant get hung for trying™…!

is there some tendency of logicians to become mentally ill esp in late life? mental deterioration is sometime milder than so-called “craziness” and other times one blends into the other. there are many (semi-) famous cases: Nash, Goedel, Cantor, Post, Grothendieck (Genius or Crank—Both!). they seem to stick out. whether there are more mathematicians who lose their mind at the end of their life than the general population is very much open to question.[16]

this blog is titled an “attack” as hard problems involve. here maybe somewhat less in the sense of “problem attack” than “heart attack”. which brings up the topic of quixotism and tilting at windmills, a 4-century old observed phenomenon showing in the classic fiction of Cervantes.[32][33] this is a whimsical account of a serious issue: (late life) mental deterioration or illness. Don Quixote is harmless maybe to others but maybe not to himself, he is also mentally ill. has anyone analyzed this novel from the pov of mental illness?

another old expression seems to come into play: better to be silent and thought a fool than to speak up and remove all doubt. this has a double meaning here in the context of the community silence/ “omerta” on their now-tarnished/ fallen leader/ hero…

Don Quixote is portrayed as a sort of poignant/ humorous fool by Cervantes showing some blurring of the idea. apparently mental illness might take the guise of a fool. the Fool is a nearly universal archetype eg seen in Tarot cards (a ripe time to ponder its meaning). but of course mistaking or misattributing mental illness for “mere” foolishness is a sort of foolishness of its own… presumably many fools are not mentally ill and for that they might be grateful (if they had enough sense)…

looking of the definition of Quixotism refers to “enemies or adversaries”. it might not seem to hold here, but wait! a great living TCS theoretician Jukna has talked about circuits as “the (worthwhile/ dangerous) adversary” in his writing. so in our inevitable anthropological tendences, there can be a personification of an inanimate object or even concept as adversary eg Hillary vs Everest.

(realize am being sketchy here myself, and there are a key few quotes out there in cyberspace that were compelling for me and think surely will be for others, they are buried in reddit/ chat threads cited here and may dig them up and cite them here, but thats very timeconsuming. hint: might do this on request + it would help if anyone replies to this post in a respectful or at least noninsulting way.)

⭐ ⭐ ⭐

but there can be some silver lining in this cloud/ “consolation prize”. the primes are a 2millenia old fascination dating to the greeks, and this renews attention to the “atoms of numbers” (that old metaphor is becoming increasingly/ presciently/ delightfully apt these days with the Riemann-QM link). there are eg 5 excellent popsci books on Primes/ Riemann and hope that some new people will be drawn to read/ learn about it.[a2.3][a2.6-9]

theres some outstanding new work on analyzing the statistical nature of primes by physicist-chemists Torquato et al, there was very impressive/ loud press releases and coverage.[a2.1][a2.2][a2.5] none of it mentioned the word “fractal” but think it is highly applicable. came up decades ago with the idea that primes have a fractal nature in college but wasnt able to fully justify it. think it is increasingly accepted across different refs, but havent done a survey on that (really wish someone would). easily a book could be written on it. any takers? maybe Atiyah? (lol!) more seriously, maybe his students… the torch will be carried on at dawn even as the sun sets on one generation…

(speaking of cranks that dont respond to reasoned logic, some ugly troll(s) have been out lambasting/ hounding my innocuous/ totally harmless empirical approach to collatz over quite a few comments now in this blog, possibly picked up some gadflies from reddit it seems. shoo! didnt your mommies teach you, if you cant say anything nice, dont say anything at all? on edge of my seat to hear their erudite verdict on Torquatos unequivocal breakthru assuming they ever get around to noticing it… oh wait nevermind their shallow uninformed knee-jerk devaluation/ denigration/ dismissal is wholly predictable so let me just save you the trouble here… be careful what you wish for, you might get it, so on 2nd thought hope they remain speechless…!)

yet nevertheless (ignoring the naysayers/ anklebiters/ luddites/ troglodytes etc) empirical-physics approaches to number theory/ math finally “officially” introduced/ vindicated under bright lights in late 2018… more to come, stay tuned… at least reddit science noticed it, ~8k votes and ~½k comments!)

Atiyah is like the captain of a ship going down with it, not unlike Don Quixote fighting galliantly to the bitter end, and there is both some real noble honor, and indefatiguable human spirit/ tragedy in that, but it appears his entire crew has now deserted him (at least in defense of his math + physics). and few dare to speak of it. aka lost marbles[43]

borrowing from physics metaphors, a reputational slow/ fast-motion train wreck. a star collapsing into reputational black hole.

speaking of mental illness/ health… from mania to depression… with some anxiety mixed in… 😮 😥 o_O 👿

hey didnt really want to write all that, but the lurking/ slinking-away mathematicians left me no choice. really wished someone else had written something like this before diving into the pandoras box myself instead of taking many hours to piece together the full/ real story. sometimes blogging is a dirty job but somebodys gotta do it. caveat emptor to the next guy.

whew! that was a lot to write. yeah, this is very triggering for me (“too”) can you tell? heres a mental note of some key dramatic stuff from chat dialogue maybe for next time:

  • retired elderly/ outright hostile curmudgeon TS telling me crossly that Atiyah has been informed about his errors by other experts, is unresponsive, and “go take your math Phd and write your own analysis” after asking for more tangible peer review than a rumor…
  • cohort/ sidekick MM calling discussion of the topic spam and proposing to (temporary) block anyone discussing it
  • reference to Nash giving an incoherent announced talk in front of aghast mathematicians! dont think that was in the movie, but what a scene that would have been, cant believe they skipped it!
  • reddit comment by an insider saying that eg other fields medalists have talked to Atiyah and hes not listening and Atiyah has the hots for physics lately against mathematicians…

“until next time”…

⭐ ⭐ ⭐

(9/28) some more fallout developments (whew, hard to keep up) many from the usually brilliant RJL P vs NP blog + further copious surfing (some on a free day off).[45] math SE direct question about definition of Todd function but not really a direct answer, same on mathoverflow.[47][48] oh just found this on mathoverflow, a meta question struggling with what to do, official mathoverflow mod statement, and mod Trimble saying I think this one is for the blogs, if anyone wants to take it up(yeah wouldnt that be nice)[51]

more MSM coverage, the science article mentions Atiyah (privately) circulating a 12-page “proof” of Feit-Thompson (which normally takes ~350 pgs). nobody is talking about that much, but this is more red flag crank math.[46] new scientist reports of “skepticism”.[49] it cites another 2010 article suggesting that fine structure “constant” may vary over the universe, something other physicists are pointing out.[50]

and speaking of Big Archetypes In Play… some other english phrases/ idioms/ vernacular now come to mind, there are so many applicable to this situation, and have to maybe find some consolation/ distraction/ diversion in etymological origins research? (1) screw loose (2) off ones rocker (rocking chairs were also seen historically as more appropriate for the elderly… my grandparents had one!) oh, (3) lol! which reminds me, how about this one for the mathematicians reactions?

this is 3 messed-up proofs in less than a year: (1) Feit-Thompson, (2) 6-spheres, (3) Riemann. as a physics Phd cohort remarked/ quipped in chat/ discussion with others shortly on reviewing the fine-structure constant angle,

because if you want to tackle one mystery, you might as well tackle them all at once…[x]

speaking of elephant in the room… that reminds me of Einstein. hes in a class by himself. he did attack multiple key physics mysteries in his life, successfully. rare geniuses like him seem to come around about max 1 per century and honestly Atiyah with his Fields medal + Abel prize (maybe only both held by 1 other living mathematician, Milnor) is definitely in that class. Einstein did tend to become more isolated in the end of his life as he rejected some fundamental QM findings/ foundations (later followed up/ explored in the them of nonlocality of Bohms/ Bells work) and pursued an idiosyncratic grand unified theory that no other physicists considered viable or possibly even sensible. some extreme accounts might have even called him a pariah… speaking of math, “more parallels”! however in contrast Einstein was apparently very reserved about publishing/ circulating his unfinished/ provisional ideas, ie he knew they were incomplete (in english vernacular ½-baked!) but here again theres a distinction between eccentricity and incoherence…

anyway, for those still not talking about it/ addressing it/ confronting directly, what more signs do you want of some kind of mild unravelling and/ or mental instability? and not even counting the derivation of the fine structure constant. this is now like the boy who cried wolf.[53] fool me once, shame on you. fool me twice, shame on me. fooled 3x, yeah, shame on everyone (eg for sticking their collective heads in the sand). now fear that some lurid tabloid story is going to be written on Atiyah, like those written years ago on Perelman, suspect its really just a matter of time. from the science article, somewhat conspicuously still avoiding the general issue of lucidity, seemingly harmless quotes from the Emperor himself,[52] but in larger context, maybe some further evidence of quixoticism/ windmill tilting/ outright crankery:

“I am throwing myself to the lions. I hope to emerge unscathed.” “People will complain and grumble,” Atiyah says, “but that’s because they’re resistant to the idea that an old man might have come up with an entirely new method.”

(9/29) 😀 ❗ 💡 ❤ holy @#%& cow sure am getting a lot of hits, record/ viral for this blog, thx everyone! more latebreaking news, from a brief/ bit )( vague comment/ tip on RJLs blog about “number crunching Riemann”, tracked it down and found Terence Tao/ Polymath15 are working on a very cool numerical attack. more world class vindication for numerical approaches into cutting edge math research/ number theory! (by the winner of the worlds most elite/ valuable $3M math prize)reddit likes it and thats saying a lot! take that @#$& nasty vicious badmouthing trashtalking luddite troglodyte naysaying detracting denigrating anklebiting hatemonger empirical math troll LOSERS! IN YOUR FACE! 🙄 😛 👿 😈

(10/1) still high views, just adding more links for completeness, other news outlets, mostly patriotic/ generally repetitive british reports, breathlessly talking about the $1M awarded as soon as its verified, none mentioning his other “attacks” context. ScienceAlert[54], Independent[55], Times[56], Mirror[57], NBCNews Mach[58], Azcarraga interview with lots of physics analysis[59], APeriodical linked to Heidelberg Laureate Forum[60] including a comment by Tim Gowers and other critical comments. reddit peanut gallery valvino, jkl9184 et al rain on the Tao/ Polymath parade of attacking Riemann Hypothesis via numerical work as “not pioneering” and “doubtful the project is even tackling the Riemann Hypothesis” lol! rigidly defiant until the end! just like Atiyah and my own beloved blog trolls! 😮 o_O

a. atiyah
a2. primes

16 thoughts on “Atiyah Riemann attack/ post mortem/ autopsy, Primes torch carried on

  1. Anonymous

    Hitting the nail on the head. This whole sorry affair was badly mishandled by the mathematical community. Shame on the HLF organizers who allowed this to happen. Shame on multiple experts in the field, who, when approached by the media, preferred obfuscation and misdirection to the truth. Shame on the journalists unable or unwilling to understand what that behavior meant.

  2. Anonymous

    You know so much about cranks. Why do you fail then to see how cranky your own Collatz writings are?
    they dont seem to understand/ grasp logical refutations
    Exactly applies to your reaction when people explain to you why “data science” on your generated sets of Collatz trajectories makes no sense.

    1. vznvzn Post author

      😐 yeah, ppl in glass houses shouldnt throw stones eh? not sure how many opponents there are to my collatz work, it is hard to tell, there are scattered mostly-anonymous comments some by common writer(s). think there are some semi-fair objections raised, others are not well-informed. am willing to discuss it at length with someone who has patience and can avoid the ad hominem arguments and think you will find it worthwhile in the end but probably not the beginning (due to an apparent lack of patience by my opponents/ naysayers/ detractors). some of this is already covered in earlier writing here, there are now over 60 blogs that lay out the general ideas/ framework. am not giving up on my approach for now, trying to convince me to might be as big a waste of time for you as you think my collatz work is for me. there are totally legitimate grounds to argue it wont ever work (eg the problem could be undecidable), but they are not definitive/ unequivocal/ provable right now. some of the grounds to argue the approach can never work in the end are not legitimate. someone who is free of entrenched prejudices and willing to learn something (aka “openminded” vs “closeminded”) could be convinced of that or at least come out of it with a fresh perspective/ pov.

      the approach has already worked depending on the criteria of judgement. to continue this discussion plz contact me in stackexchange chat, you can retain your anonymity if you like. can walk you through the general research program. conceded: it seems to be true almost )( nobody else in the world is pursuing similar techniques/ approaches on collatz in particular even after years of promotion/ advocacy by myself. conceded: yes there are some elements of radical novelty to the approach and it can be misunderstood/ mischaracterized by those without the nec background. thats not a bug its a feature™

  3. Mathematech (@Math_e_matech)

    Besides the cranks who try to square the circle there is another, perhaps opposite side of the coin, form of crackpottery in academia – the notion that certain things are impossible to prove even when they certainly can be or have been proven. This usually affects high school teachers more than college professors and is the result of misunderstanding certain results outside their area of expertise. I encountered this several times in high school.

    For example, my grade 8 teacher was a stupid cow of note. One homework assignment was to write a definition of various sets in set builder notation. This included the set of prime numbers. So I wrote it as { n \in N : n > 1 and for all m \in N if n/m \in N then m = 1 or m = n } which is of course correct, but the stupid cow marked it wrong and insisted it was wrong because “there is no formula for prime numbers, you have to write { n : n is prime }” and no amount of common sense could convince her otherwise.

    The next case involved my grade 9 teacher who wasn’t a cow, but still a bit confused. She told us that Euclid’s parallel postulate stated that there is only one line through a given point parallel to a given line and that no one had ever proven this and it might not be true (note that we are talking Euclidean plane geometry i.e. R^2, here not non-Euclidean geometry). This sounded ridiculous to me and I immediately produced a proof of the statement within the standard high school axiomatic geometry – in which it is indeed provable as the aforesaid system allows the construction of parallel lines which are defined in terms of equal corresponding angles, all notions powerful enough to prove the fifth postulate. But no she insisted blah blah its not a provable statement. She was friends with a university professor (who should have known better) and she showed my proof to him and he spouted the same nonsense. Here we basically have a university professor who somehow thinks that what is essentially a linear equation in one unknown, might have more than one solution!! Only after taking some books out of the library and reading what Euclid really said and what the real issue was did I understand where their misunderstanding had come from, but there was still no getting through to them. To them it was statement magically unproveable in any axiomatization of plane geometry.

    An even worse case, I discovered in grade 10 that (a^4 + a^2b^2 + b^4) could be factored as (a^2 + ab + b^2) (a^2 – ab + b^2). Of course this is correct as anyone who can multiply terms can check and I had noticed it as occurring implicitly in the completion of the square approach to solving quadratics that was a standard technique being taught, although not stated as a simple formula. But no I was told I was wrong because … wait for it .. a trinomial can only be factored as two binomials.

    All these cases of being told I was wrong are examples of the flip side of the coin of crackpottery, where due to a misconception, no attempt all to check or apply logic to the claim is being made because “its known to be wrong”.


    1. Anonymous

      I commiserate with you. These were poorly trained teachers with a fixed mindset. Alas, training of most US math teachers leaves much to be desired (unlike, say, in Korea or Singapore). That also explains mass math ignorance and math phobia in this country. Brilliant math teachers exist. Making teaching jobs highly paid and prestigious (like in some Bay Area schools) helps a lot.

    2. vznvzn Post author

      comments are basically unmoderated here but dislike childish namecalling, please refrain from it, it is not nec to get your point across. you have some insight but not sure how deep it is from your characterization. re your parallel line example, that is a very key aspect of mathematical history/ development and is covered in math history textbooks. whether euclids 5th postulate could be “derived” was a nearly 2 millenia old open problem (hence clearly very hard, to say the least, wrt human intuition) and the solution led to the revolutionary noneuclidean geometry, an example of a paradigm shift in mathematics. can see how some misconception is possible. it might have helped if you found some authoritative reference that discussed the issue clearly and shared it with your teacher. the issue is not as basic as you might think/ assert.

      1. Mathematech (@Math_e_matech)

        The fact that it took nearly 2 millennia to realize that Euclid’s first 4 postulates were too generic to capture the properties of straight lines in R^2 and that they applied equally well to say geodesics on hyperbolic surfaces (for which the 5th postulate doesn’t hold), does not change the fact that it is a simple matter to prove the statement about a unique parallel line in the case of R^2 or standard modern axioms of plane geometr that are equivalent to defining a flat plane as being isomorphic to R^2. And moreover that statement about a unique parallel is not in fact Euclid’s 5th postulate anyway, which as stated in his Elements does not even mention parallel lines.

      2. vznvzn Post author

        think you can do some more studying as in the wikipedia link cited. euclids 5th postulate the so called “parallel postulate” is equivalent to playfairs axiom “There is at most one line that can be drawn parallel to another given one through an external point. (Playfair’s axiom)”. … this is likely the reason the modern term for the 5th postulate is the parallel axiom. it is true euclid didnt describe it in that form. it took ~2 millenia to realize they are equivalent. noneuclidean geometry invention coincides closely historically with the discovery of general relativity by einstein and thats not entirely a coincidence. deep math + physics connections like those discussed in the blog. this was famously noted by wigner in 1950.

  4. Anonymous

    An “Emperor’s New Clothes” moment is certainly coming. In the meantime, countless media outlets have been proven negligent in their fact-checking duty, and (apropos irrevocable PhDs) an Oxford Math PhD (sic!) just posted a YouTube interview with Atiyah indulging his delusions.

  5. Anonymous

    Those empirical math trolls are so nasty. You should rush to Polymath15 and warn them about the threat. De Bruijn-Newman constant is in danger (and I heard they harrass people who try to compute new digits of pi too…)

    And while you are there, you can help those polymath PhDs with nec background. They definitely don’t fully appreciate the power of fractal entropy, lack skills to make plots with unlabelled axes, don’t know how to solve x^n=0 with Newton’s method, and use outdated programming languages like python and C instead of ruby. Everyone knows that ruby was made precisely for scientific computing and every student of math or engineering loves to read ruby code.

    Besides, those polymath people have no idea that writing breakthru in every second paragraph helps the progress of humanity immensely. They are too shy to scream Riemann Hypothesis in every sentence and talk about that boring constant instead.

    So, everybody will be delighted to hear from the great pioneer of empirical math and learn valuable lessons.

    1. vznvzn Post author

      😛 💡 lol! thats quite a colorful/ humorous/ imaginative/ clever story there! youre a real raconteur with some biting talent and sense of humor/ parody/ way with words/ finely honed sense of the ridiculous there! heres a wild idea, why dont you get a blog and expand on it? am sure you can do much better than many others esp with your obvious deep math + programming bkg. we can probably agree there are lots of worse ways to waste ones time in cyberspace. let me know when youre ready and will be happy to be the 1st to comment! idea: if you cant think of anything else/ better call it Snark Science… peace 🙂 😉 😛

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  7. Todd Trimble

    I’ve only skimmed this but do find some of these ruminations interesting. However, I wanted to let you know that Wiles is not a Fields Medalist. One example off the top of my head of another besides Atiyah who won both the Fields and the Abel is Milnor.

    1. vznvzn Post author

      😳 hi TT thx for dropping by! oops! thx for correction; think saw someone on reddit or elsewhere refer to Wiles as a fields medalist, forgot to check it, it did sound surprising, or maybe my mistake alone, fixing that immediately! thx for all the hard work on MO! + ofc plz let me know if you hear of any (other) mathematicians blogging on Atiyah etc 🙂

      1. Todd Trimble

        Well, I’ll let you know if I see anything. I found on Quora an answer to the question of who has won both the Fields and the Abel; they are Atiyah, John Milnor, and also Jean-Pierre Serre, John G. Thompson (the group theorist of Feit-Thompson fame), and Pierre Deligne. The Quora interchange also remarks on the case of Wiles, a kind of near miss for the Fields which may have led to the misunderstanding on Reddit:

      2. vznvzn Post author

        thx for the clarification it seems like it ought to be easy to figure out who the world “wizard” mathematicians are but its not a very well known fact who has won both Fields and Abel prizes. more mathematical obscurity there. did a little hunting and realized it was an RJL blog comment that had the misinformation about Wiles winning both. am going to write a correction citing your very helpful fact checking. thx much for your attn! 😀

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