SMITH HUBBARD & TICHENOR

GOLDENGATE’S

for October 7, 2012

POSTER CHILD

a2+b2≠ c2

…. > 2

IS RIDDLE, JR.’s

“LAST DIGIT THEOREM”

the REAL PROOF of

FERMAT’S LAST THEOREM ? But First …!!

From the desk of FEELING LUCKY ….

Greetings, Players! Yes, YOU ARE THERE! S,Y.M.-Zonia™ is the PLACE! Welcome! Welcome back!!! From all of us here at operations west, Unit D-37, Payless Self-Storage, Corner California & Scotts Sts., Pacific Heights, S. F. You know: The PLACE of Tense Yet Pleasant Anxiety! Next door to the new dispensary @ D-36

IT’S TWINS!!!! (See below …)

Last Week’s RIDDLE, Jr., Jr.,(Sr.), - This Week’s RIDDLE Jr., Jr., (Jr).

BUT LET ME FIRST EXPLAIN …. Feeling Lucky, p. 2

PLAYERS!!!! You may well wonder why I’ve captioned this “Editor’s Desk” “FEELING LUCKY” – as if to hearken back to the famous FEELING LUCKY issue of early summer [The reference is to the T. 25. N. R. 2. W., W.M. or T. 25. N. R. 2. W. M.D.M.,? (June 3, 2012) – Ed.] -- and, indeed, in a certain lame sense, this is the case .. But, let’s face it, that was surrogate luck, wasn’t it? Casino luck… Fake luck generated by some Gargle algorithm -- programmed, online luck.

[Funny : that same FEELING LUCKY issue, was the last time I ran Titutlar Leader’s old poster …. -- Ed.] At any rate …

I‘m talking about real GOOD FORTUNE now: not some silly algorithm spewing out quasi-knowledge “volumetrically measured” – but REAL LUCK – luck of the kind that can only come when Providence itself spins GREAT WHEEL OF FORTUNE IN THE SKY, and the wheel spins ‘round and ‘round and ‘round and the little clicker-thingy clicks and clicks and clicks, and wheel spins ‘round slower, and finally slows down and the clickety-thinger -- the clothespin clamping a playing card in your bicycle spokes -- finally … comes to rest …. in the … slot …… that ….. reads …

TITULAR LEADER OUT OF TOWN!! (Wowee!!!)

Yesssss! I mean – NO KIDDING: the word is she has been OUT OF TOWN all week!!! IN ABSENTIA from Port Orford (Oregon) (Yes!! It’s apparently true …… <Phew> ) And she may be for … yet another week!!! [Dare I say -- Wowee!!!! – Ed.] And so…. and so, she has not seen and may not have even been told about Last Week’s BIRTHER Issue [Image on preceding page – Ed.] which will fry her – I just know it. Let’s face it: I might never live it down. SO-- You see what I mean… about real luck.

WHERE is she? Truly Our Own Titular Leader could be literally ANYWHERE. One rumor I heard, which seems to deserve some credence, is that she went NORTH on Hwy 101, to … interview a young man who has applied for the position as S.Y.M.-Zonia™’s WEB-DESIGNER – who lives farther north, from Port Orford, (Oregon) , and up the Oregon coast. She may have decided she needed to interview him personally – as one of the finalist candidates: a man whose family heritage is said to lie [Get this, Players !!… -- Ed.] in Idiotville (Oregon), [YES: Apparently for real! -- Ed.] but who now hails from Tillamook (Oregon). Supposedly she is to discuss plans for development of our new S.Y.M.-Zonia™ WEBSITE! [Well, Wowee!!- I could soon be REALLY famous!! … -- Ed.]

On the other hand, there was a wind-surfing tournament at Floras Lake, in which Stephanie competed, and which Rupert Roget, P.L.S. (Ret.) attended. Rupert saw her afterward: evidently she was being SCOUTED by a swim-wear or sports-wear manufacturer … from up in Portland (Oregon). EITHER WAY, Players – she’s out of town, and so probably did not see Last Week’s issue, and nor may she not have yet seen This Week’s Issue also..!! Wowee!!. THEREFORE:

RECAP … and UPDATE !!

SO, as you will recall, it was LAST WEEK while I was WINTERIZING the place here in D-37 and tacking up this Styrofoam® sheeting over the walls, for a little more insulation against the chill of these Golden Gate mornings that I was obliged to PULL DOWN Dromgoole’s old poster of Titular Leader –- [See the HIDDEN PICTURES III issue: What’s So Significnt About Peter S. Duval’s Lithograph, etc. (May 27, 2012) -- Ed.] -- but, as I did so, I noticed .. a distinctive BULGE under Stephanie’s tmmy, and also that there were two or three posters – maybe more!! –layered one on the other, and they had been glued together so that it merely looked like one: but the glue was flaking out and the posters were peeling apart !! And so, when I took the poster(s) down I laid it/them on my desk, and fumbled around for – the Light of L.-L.U.V. …. which soon revealed that the Stephanie poster was pregnant … it was no ordinary poster; but a BIRTHER, which with me acting as a sort of editorial mid-wife, had beewn delivered of a NEWBORN IDEA!!

Well, as you know, after the crisis of the moment had passed, I was able to collect myself sufficently, to identify the newborn, and introduced it to the world Last Week, !!! [For further details, see Last Week’s issue on the Riddle of Rational Phi -- (September 30, 2012) – Ed.] Mother and child are doing well ….

BUT THEN … when I turned to replace the poster on the wall, this time over the Styrofoam® sheeting, I REALIZED that there was … still something in there!! I mean .. it was TWINS!!! Yes!!! And let me just say … H____ S____ !!!

There was another little baby CONCEPT in there, that was now FULL TERM!!! PLAYERS -- due to lack of space, (and in order not to risk further inebriating Titular Leader) I won’t recount the precise details of this second Caesaerean surgery I performed, in order to deliver T.O.O.T.L. Ass. Dr. Beckon’s POSTER of this NEW IDEA … Suffice it to say, it was much like the first [See Last Week’s issue – Ed.] that for now, she had another POSTER CHILD to raise alongside the first one, and to bring her comfort and joy in her spinsterhood !!

PLAYERS: I don’t want to say too much about the child’s PATERNITY, you know !! However, suspicions have coallesced around Herbert S. Riddle, Jr. – which makes these two brain-children, Riddle, Jr.’s juniors. Indeed, this week’s latest younger twin, bears a striking resemblance to it’s older sibling, and has all the earmarks of being another … Riddle, Jr., Jr. Only, to tell them apart, well call this younger Riddle, Jr., Jr., Riddle, Jr., Jr., Jr., and his older sib, we’ll call Riddle Jr., Jr., Sr..

And just WHO you might ask, is this apparent father, Herbert S. Riddle, Jr., anyway? That’s a conundrum ….

PLAYERS ….

YOU ARE NOW ENTERING

Place of tense yet pleasant anxiety

IS RIDDLE, JR.’S “LAST DIGIT THEOREM” the REAL PROOF of FERMAT’S LAST THEOREM?

“I have discovered a truly remarkable proof which this margin is too small to contain.”

Pierre Fermat

PLAYERS!! SO -- This Week’s POSTER CHILD issue is just the little brother of Last Week’s SPECIAL DELIVERY BIRTHER issue – as the material discussed here, was BIRTHED from the Stephanie poster just shortly after the “Rational PHI” baby, at which birth I personally attended, JUST LAST WEEK !!! Got it? Okay – so: let’s get to it:

Organized chronologically -- it appears perhaps the first reference to Fermat’s Last Theorem in this baby, occurs in a letter addressed to one “David”… [See the notes below – Ed.] BUT!!! Who is David? You ask? Well, I’ll tell you: “David” is … presumably an otherwise anonymous Director at the Globe Press, I think, or maybe an elusive member of the O.M.I.G.O.d.; and the letter and probably written by the first editor of the P.Y.M.™ Puzzler, none other than Edmund Elmendorf IV … on assignment in … Oregon City(?) (Oregon) of all places. Edmund is probably also the individual mis-named as “Edward” in some of the communiques [French-derived!!! – Ed.] I ran last week…. The letter -- the one below, not the one last week -- is dated December 5, 1997 – and a portion of it is extracted below.

HOLD IT, PLAYERS: I’d better back up a bit!!! Hmmm..

Fermat’s Last Theorem has become something of a curiosity to mathematicians, who are … well, pretty confident now, since they haven’t been able to find it… and maybe they’ve even grown a little SMUG … that Fermat himself was “puffing” or just mistaken about his claim to have found a Proof – which some might call a “So-called ‘Proof’” of his asserted Theorem --

a2 + b2 ≠ c2 ….. c >2

PLAYERS: I’d better back up a bit more !!! Mathematics is a discipline exercised by the human mind or intellect, regarding the values and properties of NUMBERS (q.v.), and was commonly practiced by a wide of variety of human beings, before the universal adoption of calculators and the general displacement and atrophication of the mathematical faculty. MATHEMATICS was at one time practised by humans, using a portable hand-held device known as a PENCIL applied to a personal P-pad using a form of coding known as NOTES AND DOODLES, occasionally accompanied by DIAGRAMS – and using a form of proto-software -- sometimes called “using your noodle” or thought. This proto-software had been rendered almost universally available through a distribution system called GENERAL EDUCATION which included training in this MATHEMATICS – or “math.” OKAY ….

NOW … Where was I? Ah – yes: Fermat’s Last Theorem. Find this online …

NOW since about 1993, efforts into deriving a proof of Fermat’s Last Theorem – given above – have been sort of “joined at the hip” with efforts to solve a “lesser included” conjecture propounded by a mathophile Texas banker named Andrew Beal who put up prize money for anyone who could provide a proof for his own conjecture:

zm = xa+ yb … . . . . . .

x, y, z, m, a,b positive integers . . . . m, a, b>2

In 1997, the value of Beal’s Prize money for deriving a proof of his conjecture, had been upped to a rather tidy little $50,000 pot -- PLAYERS: it is at about this point, that Stephanie’s POSTER CHILD appears to have been first conceived. YES -- The material born second appears all to be dated from 1997—the year following the Rational Phi offspring. In fact, most of it dates from ONE MONTH – namely, December, 1997… And a number of references by Riddle, Jr. to “Beals’ and “Beal’s conjecture” refers to Andrew Beal’s prize problem.

PLAYERS!!! There’s more background to this than I really have room to fit into the margins of the S.Y.M.-Zonia™. [Yuk yuk !! Get it? – Ed.] Suffice it to say you can Gargle your way to some interesting material on the issue – including this handy dossier by Texas mathematician Daniel Mauldin who is acting as administrator of the Beal Prize LOOK IT UP or CLICK TO ENLARGE You choose.

Andrew Wiles PLAYERS: One more thing – in the notes and narrative which follow, Riddle and Elmendorf each make occasional reference to one “Wiles.” Andrew Wiles’ name, is another which is intertwined with the history of mathematical work on Fermat’s Last Theorem, especially during the mid-to-late 1990’s. In 1993 Andrew Wiles propounded a “proof” of Fermat’s Last Theorem, which legend has it, was about 400 pages long. Speaking for himself, Andrew Wiles stated of his 400 page magnum opus :

"It was so indescribably beautiful; it was so simple and elegant."

Okay. Sure. However, at 400+ pages, and dependant on centuries of theoretical mathematics that Fermat had no conception of, Wiles’ proof was NOT Fermat’s own “…truly remarkable proof which this margin is too small to contain.” And, when someone was finally found who had the energy to read through it , Wiles’ proof was also found to be dead wrong. Or – to speak professionally and precisely, when Wiles’ “simple and elegant” proof was checked, it was found to contain a “gap” - corresponding to the well-known mathematical gap-filler [AND THEN …. A MIRACLE

OCCURS!!!] Andrew – next time, have someone look it over FIRST.

As it turned out, the “gap-filler” was of about --oh, let’s say …. 100 pages long ….

So, in classic “back-to-the-drawing-board” fashion – not a bad thing in itself -- Wiles thereafter “filled the gap” with a document of about another 100 pages – for a total output of some 500+ pages of the “simple and elegant.” After getting his proof of Fermat’s Last Theorem famously wrong, and then for being so off the mark as to take 400 pages to get it wrong, and requiring another 2-3 years and 100 pp. go “fill the gap” Andrew Wiles, being a fortunate Brit, won the $1M prize and was further be-knighted … wait: I mean knighted ….by one inclined to fudge the numbers: her Royal Whizzness, QEII – whose name is, after all, synonymous with Quantitative Easing …

OKAY, PLAYERS: You can delve into more of this online. For purposes of this week’s issue, that brings us up to date!!!! By which I mean, that brings us to a point ca. 1997, which is apparently MIDWAY between Riddle’s work on Rational Phi [Once again – see Last Week’s issue, So What Is Phi, After All: a Rational or an Irrational Number?-- And Who’s Counting? (Sept. 30, 2012) – Ed.] and the present matter …

First, there’s this stack of Riddle’s notes on legal paper, which date largely to almost anywhere in 1997, and lie intermediate between that aforesaid work on rational Phi, and the up-coming breakthrough on Fermat’s Last Theorem. Maybe…. 100’s of pages. As the editorial department has determined that these notes are of no interest to posterity, but may be useful to poterity, they have been handed over to our new neighbors running the licensed Medical Marijuana Dispensary next door in D-36, where they will be used to roll doobies.

Nobody reads that sort of stuff anyway. HOWEVER … some other material gets a little closer to the bone: the bone of contention that is. The first is a paragraph in a letter from Elmendorf to “David”, dated December 5, 1997, where we first learn from Elmedorf that Riddle is undertaking to scale this mathematical “Mt. Everest”: the secret he thinks, lies in the volume of … lead bullets !??!

WOWEE!!

PLAYERS: it seems that the implication is that this major- league original mathematical discovery [If such, indeed, it is! – Ed.] is deriviative of some real-world hands-on very much physical experimention!

Hmmm.

Then there is a note from a few days later, exponents ….

And so it goes, Players, with this new POSTER CHILD !!! Seemingly rambling, almost random notes, until ….

SUDDENLY, Players, on or about December 16, 1997, there is an extended epistemological entry [That means, it’s in a letter – Ed.] by Elmendorf, saying that “Sandy faxed in last night that he had ‘just found the path Fermat went down’”… Along with this letter, appears a corroborating FAX!!! … of the very same date! Players -- I apologize for the excessive profanity. The creative process can be a passionate one – so I hear!!!

Finally, PLAYERS!!! On the next page, and writing just a little later in the evening, Elmendorf offers a short primer – based upon his sadly limited comprehension – of Riddle’s solution to Fermat’s Last Theorem, which Riddle has framed in terms of “L.D.’s” – which stands for Last Digits; and which he captioned his Last Digit Theorem: which cuts thorugh, well, maybe as much as 500 pages of circumlocutions, to get right to the kernel of things: namely that to prove the particular dis-equity, as that propounded by Fermat’s Last Theorem, one does not need to establish that EVERY entire numeral value is different from other EVERY OTHER enire numerical value – but only that, for whatever numbers are entered into the Theorem (and, so squared) the LAST DIGITS of those numbers will be dis-equal. Voila!! And so, PLAYERS, there you have it, I guess!!! IS that the real answer?? BUT … what do YOU think….?

… IS RIDDLE, JR.’S “LAST DIGIT THEOREM” the REAL PROOF of FERMAT’S LAST THEOREM ???

Let’s look …. !!!

PLAYERS!!. Here’s a few more pages of Riddle’s notes: the date is the same date given in Elmendorf’s narrative: it is Decmeber 16, 1997! It’s handwritten [Added, in another hand: probably Elmendorf’s – Ed.] and appears also in the fax header/footer. What did that fax say [See p. 7!—Ed.]? Riddle thought he solved Fermat’s conjecture in …

1. LAST DIGIT THEOREM © 1997 Herbert S. Riddle Jr.

2. LAST DIGIT THEOREM © 1997 Herbert S. Riddle, Jr.

3. LAST DIGIT THEOREM © 1997 Herbert S. Riddle, Jr.

… how many pages?

Players -- I don’t know about you, but I counted three pages – which is the page count declared on the Fax, of the same date. And then, my astute eye detects an annotation near the bottom left-hand corner, which is written out in language – unfortunately laced with profanity: sorry about that – that seems to be almost preliminary to the Fax itself, to wit:

H--- S--- -- This solves Fermat’s conjecture by limiting his possible solutions of Z c [to the finite] Qty [?] possible ..[..?]

So … there could be a connection. And, Riddle himself clearly seemed to think that his LAST DIGIT THEOREM was ALSO the proof to Fermat’s Last Theorem, or Conjecture. But he was unable to state precisely how ….

INDEED, Players -- the last line or two of Riddle’s epochal haiku was cut off by the fax header – as so often happened!! Remember? And with the customary mystifying results. So, in the end, there appears to be an INCOMPLETE RECORD as to just how Riddle would have connected his LDT to FLT.

FURTHERMORE, numerous other inconsistancies plague this story, and compromise its substance. For instance:

- Does Riddle’s fax, in which he declares he has solved Fermat’s Conjecture in three pages, refer to the three page fax comprised of Riddle’s notes, outling his Last Digit Theorem?

- What were the last two lines of Riddle’s haiku ?

- Why, if he wanted to be taken seriously, did Riddle use so much profanity, so profusely?

- Elmendorf’s letter [See p. 7, above – Ed. [But, p. 2 of Elmendorf’s letter!! – Ed.]] states that “Sandy” faxed in “last night” that he had found the path that Fermat went down. But both the letter and the “H--- S---” fax, are dated December 16, 1997. Can this discrepancy be overcome? It looks pretty dicey at this point …

Likewise, Elmendorf declares in his narrative, that “Sandy” “just had the insight on the proof here at his kitchen table, at 5:49 p.m.” [That’s at p. 8 above, but p. 4 of Elmendorf’s letter, above – Ed.] – But the “H---S---” fax is date-stamped 5:37 p.m. the same day – that is, over 12 minutes before Elmendorf’s version. Furthermore, the remaining three pages of the Last Digit Theorem are date-stamped between 5:36 and 5:38 p.m. – that is ON EITHER SIDE of the “H--- S---” fax. This is almost certain evidence of document tampering, is it not?

Furthermore, who is Riddle anyway? A reincarnation of Zerah Colburn? Who is “Sandy”?

And what about Beal’s Conjecture? Uh-oh. Sorry. Way too late…..

YOU ARE NOW LEAVING

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