• Square root on the

  • High pot in use

    Who said modesty knows no bounds? It is bounded by mod(s) times mod(t). ------------------ Ramanujan's last bow -------------------- Ramanujan did mathematics somehow; we still can't figure out even now. He left his mark on ``p of n", and wrote pi in series quite often. The theta functions he called 'mock' are subject-matter of many a talk. He died very young - yes, he too! He was only thirty-two! His name prefixes the function tau. Truly, that was his last bow! --------------------- The Italian Mathematician : A recent Italian immigrant to New York wanted a job, but the foreman won't hire him until he passes a little math test. "Here's your first question," the foreman said. "Without using numbers, represent the number 9." "Without numbers?" the Italian says, "Dat is easy." And he proceeds to draw three trees. "What's this?" the boss asks. "Ave you got no brain? Tree and tree and tree make nine," says the Italian. "Fair enough," says the boss. "Here's your second question. Use the same rules, but this time the number is 99." The Italian stares into space for a while, then picks up the picture that he has first drawn and makes a smudge on each tree. "Ere you go." The boss scratches his head and says, "How on earth do you get that to represent 99?" "Each of da trees is dirty now. So, it's dirty tree, and dirty tree, and dirty tree. Dat is 99." "All right, last question. Same rules again, but represent the number 100." The Italian man stares into space some more, then he picks up the picture again and makes a little mark at the base of each tree and says, "Ere you go. One hundred." The boss looks at the attempt. "You must be nuts if you think that represents a hundred!" The Italian leans forward and points to the marks at the base of each tree and says, "A little dog came along and crap by each tree. So now you got dirty tree and a turd, dirty tree and a turd, and dirty tree and a turd, dat make one hundred. So, when I start?" --------------------- Here are two recent ramblings : When Hom becomes \otimes and life seems drab and dreary, Join the club of problem-solvers in group theory ! My group could be a-belian; what’s a mere million ?! Isomorphic copies could have hues of a chameleon ! My matrices – my dear Homs – are often elementary. In such a case, the group can have even the center {e}. Aut I convince any more ? Life’s normally N or G ! -------------------------------------- The young William Burnside became an orphan -   something that is neither easy nor fun.   Influence of his work is far-reaching   on any group-theorist's research or teaching.   His `Burnside problem' was a beacon   illuminating a future path as only he can.   His works were aplenty;   last was on groups of order 25920.   `Subliminal, weird' appears on the WWW;   and the anagram `I will aid numbers' is number 2.   I'm tempted to add one of my own   which might become one day well known !   On comparison, it's anyone's guess   that `I'm brain-wise dull' !   ------------------------------- [OLDER RAMBLINGS] (Un)Abel to solve ? ------------------- The quadratic was solved with ease. The cubic and biquadratic did tease but were solved nearly the same year. It was the quintic which made it clear that algebra developed by degrees ! Marking the end of a conference on geometric group theory --------------------------------------------------------- Meenaxi has projected Assam-in-a better light thro' many a semina(r). GGT comes to an end; HNN ceases to extend - the swan song is by A.Camina ! A Greek interpreter ? --------------------- One day, at home, I heard a squeak and thought it was a mouse. 'Twas but a boy learning Greek in my neighbouring house. One often heard him speak in sigmas, etas and taus. He knew Latin. French and German though he was barely six! Moreover, there was simply no one to rival him in mathematics. It's said, `it's never too late', a revered and familiar maxim. But, `it's never too early' one may state after just one look at him ! `Who's this boy?' you wonder who lives near my house? His name spelt as under - is Carl Friedrich Gauss ! --------------------------------------------------------- | Theme: Fermat's last theorem | |-------------------------------------| I -- Solved first by the great Cauchy. What a mistake made - Gosh, he! Then it was Kummer's time. He did every regular prime. Germain came and shouted `Whoopee! Done, if we know about $1+2p$'. The uproar after Faltings, Gerd went `Mordell's done; spread the good word!' We know who then jumped into the fray whose elliptic curve could exist no way! Ribet said `Taniyama does put a stop to all this fuss!' And then Wiles was heard telling Taylor now's the time; let's go and nail her!' We conclude from this saga of Fermat the importance, above all, of Karma! II -------- Once upon a time, a judge did muse on a question of no apparent use. The proof - had it been written would've covered France and Britain. That would've been the end of the news! III ---- Fermat's last theorem. Let's go and hear'em ! Wiles's Taylor-made proof may be what's called a tough baby but, let's atleast cheer'em ! IV ------- X^n + Y^n + Z^n = 0 did give birth to \Z[\rho]. I hear now there is a solution done by people in collusion and one of them is a hero ! --------------------------------------------------- Mason makes noose! -------------------------- (Appeared in The Statesman, Calcutta) Plumby Mason's confidential secretary Dalala Street who held a big share of his responsibilities at the office said, "Lt.Drag is on the phone, chief." The face that turned towards the trusted assistant was flushed with deep thought and its chiselled features were granite hard in concentration, and unquestionably belonged to Plumby Mason. "Yes, Drag?" he said over the telephone. The slow drone of Drag's voice pulled him out of his reverie. "Are you free Mason? I want to see you urgently. Actually, I need your help." "YOU need MY help! Well, well! Sure, come along to my office. I can give you six and a half minutes plus a ride in the elevator." Mason replaced the receiver on its cradle. "Hang it Dalala! Why would Drag want my help? Call up Tall Fake and ask him to step down for a minute." Tall Fake was Mason's highly trusted, long-limbed sidekick who suitably humoured Mason's ego and assisted him otherwise by leading the police on all sorts of false trails. As soon as Fake's code jingle was heard through the ventilator, Dalala let him in. Not counting the charwoman and the author, this jingle was known only to the three of them, and it went like this: "Soon as I heard that voice so sweet I knew it must be Dalala Street. Here I come, here I hasten at the behest of Plumby Mason. My first is Tall, the second Fake; if you don't play ball, go jump in the lake." "Lallapalloosa" said Fake seating his main frame on the big study table with the PC. Fake moved in a loose-jointed manner and his favourite way of relaxing was to rest his hands on the console, the small of his back on a couple of paperweights, tying his long legs twice around diagonally opposite legs of the table, after having removed and placed his shoes on the big overstuffed sofa. "Hi Dalala! Hiya Plumby! What is cooking?" Plumby described simple harmonic motion as was his wont (as well as his will) while deep in thought. "I don't know for certain. Drag wants my help for some reason. I expect, it is about the Prime Minister's visit to us. You remember that the PM was carrying some secret document when he came to consult me. But, just at our doorstep, someone attacked him and snatched the document - which, I gather, was a microfilm - away. I did manage to lasso the culprit but he seems to have passed the papers on to some crony somehow. It is a pity that the lasso strangled him to death. Otherwise, we might have forced the truth out of him. Unfortunately, the PM has not been able to disclose as yet how he had hidden the valuable film. Now, when Drag comes, you peep through the key-hole and watch his expression. If he....." he was hurriedly interrupted by Skirty, his switch-bored operator. "Mr.Mason, Lt.Drag is coming in. He wouldn't wait." "Hullo Mason and Dalala! Hi Fake!" greeted Drag coming in and seating himself. Tall Fake unwound himself, looked at his watch, yawned and said, "I guess this is where I go out." "Bad business this, Mason. Can you tell me exactly what happened during the Prime Minister's visit? Let me give you a friendly tip that the D.A is not quite happy about the death of the culprit. As I understand it, you tried to lasso him and his neck got stuck in the noose by accident. It is not clear how he ties in with all of this. The only identification we found on him was a card which gives his name to be a Mr. Sale Sman hailing from Tough Lux, Au Revoir." Mason's leonine features were suffused with an extra large frown of concentration. He smoothed his mane, brushed his whiskers and told his tail,..oops, tale. "The PM called me up on the telephone and an appointment was fixed for 826 BC. Miss Street met him on the side lane and escorted him in. Simultaneously, the culprit, who, incidentally, is unknown to me, also tried to enter. The resulting crash brought both of them down. It was immediately obvious to me that the rascal was an international spy. So, I made a lasso by pulling out my telephone wire and threw the (telephone) book at him, flinging the lasso at the same time. I didn't know that the lasso would wring his neck through the collar on account of being made from telephone wire. I saw that the Prime Minister had hit his head on the Cabinet and had passed out. Since the Prime Minister was also bleeding a little, I administered to him at once. I, Plumby Mason, repaired the leak, that is, stopped the bleeding entirely on my own. He soon recovered consciousness and faintly smiled at me when he suddenly stiffened. "The Microfilm! The Microfilm! It is gone!" That was all he could say when he came to a full stop and went into a coma. But, I heard that with the help of an injection of apostrophe' and a dose of colons, the doctors have nearly managed to invert his coma. This is all I know. And yes, I got my telephone fixed again." "Thanks Mason. let me know if anything Concrete develops. As of now, the whole issue is shrouded in mystery" said Drag and ambled off. "I guess that is that. This is the first mystery that I couldn't plumb the depths of. I give up. Let us go, have dinner" said Mason locking up the office. Mason, Street, Fake and Skirty called it a day and went off to the corner drugstore to have burgers with bicarbonate of soda. Next morning saw Mason promptly at his office at nine. It did not occur to him that among the contents of the waste-paper basket so assiduously emptied out by the charwoman, might be a Prime Minister's starched handkerchief slightly smeared with blood. Meanwhile, the handkerchief seemed to shrivel in disgust at the mountains of garbage around it. I prefer to think that it was trying to hide its secret well. --------------------------------------------------------------------------- On Hercule Poirot ----------------- Dear Monsieur Hercule Poirot had come one day to borrow my collection of Agatha Christie. Said he, with eyes misty, "today, Hercule Poirot tells the secret of his little grey cells. Very long ago - it's almost history - I did solve a wee-little mystery. Though it was run of the mill Dame Agatha used her skill to create and boost my image filling page after page after page. The public thinks I'm great. It doesn't know I've to wait for Agatha's latest thriller to find out who's the killer! This is my secret sorrow" said the great Hercule Poirot. ------------------------------------------- An ancient Indian proof of the Riemann hypothesis ? It has only been realised recently that the Riemann Zeta function is none other than the Raman Sita function - the name got corrupted after reaching Germany. The line known to the West as the critical line was known to the ancient Indians as the `Lakshman Rekha'. This observation taken in conjunction with the work of Ravan (a.k.a Raw one) completes the proof of the Riemann Hypothesis (Ravan's work shows that Sita vanished only when she stepped on the critical line (See [V])). The name of Vashishta also reached Germany but they could make nothing of it and abandoned it merely quipping `Was ist ..?' The great Hanu Man's character was also much appreciated in the west and Hollywood portrayed him as a hero clad only in his undervest and a huge cloak with a large H, flying over the seas to rescue damsels in distress. (Note added in reproof) : An onymous referee points out that at the moment of vanishing, Sita was seen in another plane where she was known to the Indians as the `Pushpak Sita' (and again, known to the Western world by its corrupted version `pushback seater'). [V] Valmiki - `Rama's last bow', Ramayan II. -------------------------------------------------------------------------- A satire on attire -------------------- (In `support' of a notice put up in TIFR by some of the sartorially shocked administrative staff) Recently, it has been observed that the number of `half-pant wallahs' in the Institute has increased alarmingly and we, the members of the Knickerbocker Association, have decided to act now or it might be too late. Our earlier criticisms have been trousered calmly by these `Half-pant wallahs' who have continued to infest the Institute premises in their half attire. What is more, we fear that soon there will be `half-pant wallis' in the Institute if the `Wallahs' are not curbed immediately. So, we propose the following guidelines regarding the dress code: Only `firangis' are allowed to wear `half-pants' inside the Institute premises. The only other people who will be exempted are : (i) ones with a black belt; and (ii) Patrick, of course. An Institute member can enter the Institute wearing half-pants only in the following two exceptional situations: (i) she/he must be wearing full pants under the half pants, or (ii) when there is a power cut (or a full solar eclipse) and it is completely dark. A family member of a staff member could wear half-pants inside the Institute premises if she/he has not attained the age of 12. If her/his birthday falls on that day, the time of birth will be taken into account. A member seen jogging in half pants in the Institute premises will be made to run three more rounds than she/he bargained for. Rules regarding Institute members wearing skirts are the same as above (These don't apply to Scots). Any claim by an Institute member that his/her full pants had shrunk into half pants due to repeated washing will be thoroughly investigated. Rules regarding shirt-buttons, hair-style, method of drinking soup etc. will be put up in a separate notice. ---------------------------------------------------------------------------- Mixed motives? -------------------- (This is a preliminary version; a later version appears in the Mathematical Intelligencer.) The train was now moving at a nice jiggly pace and gave periodic shakes like a man caught without his sweater on a cold night. The young man had bloodshot eyes; evidently he hadn't slept properly for many days. He was bespectacled and clad in a Khadi Kurta and jeans which hadn't seen water for a considerable period of time; obviously a man of spartan tastes in the matter of attire. His eyes gleamed back with a ferocity that spoke of some deep and sinister purpose. Every once in a while, he would jump out of his seat in his restlessness and walk along the aisle, cross the vestibule and return after a five-minute stroll. Monsieur Pi Rho (though having retired from his profession two years back) could place him unerringly. Yes, his instincts told him that the young man was upto something, which, whatever it was, would not be too long in coming. The dinner was long past over, most of the lights had been put off, people had given up the pretense of reading and, indeed, most of them were snoring gently. Monsieur Pi Rho saw the young man take out a packet of cigarettes and move towards the door. Monsieur Pi Rho got up and strolling to the end of the compartment peeped out surreptitiously and saw the young man begin his smoke. Tiptoeing back, he pulled from under the young man's seat the dirty-looking brown bag which was the only piece of baggage the young man seemed to be carrying. He quickly unzipped it and looked inside. In the dim light, he could see sheets of paper. Monsieur Pi Rho pulled out one sheaf and peered at what appeared to be some handwritten instructions. Monsieur Pi Rho began reading. `We are provided with a scheme and a map which is proper to a point' read Monsieur Pi Rho With widening eyes, he skimmed through the page to see if any person or place was mentioned. Beyond cryptic words like `the group can act freely but discreetly' (the last word had been misspelt), `go to a cover to kill the classes' and `blow-up if necessary', nothing specific was mentioned. Evidently, some group was planning an ambush but where and on whom? Who were they? (These people expressed themselves in a strange language somewhat like MonsieurJingle from the Pickwick Papers). Monsieur Pi Rho didn't have too much time before the young man's return. He quickly turned a couple of pages and saw the heading `Motives'. Here the language was even more exasperatingly vague. There was again mention of a group whose representatives were deemed to be traceless. Also mentioned was a corpse (again misspelt) which was totally disconnected (yuk!) on which some functions still existed but were rapidly decreasing. Whose could it be? And where? Presumably in some local field. Somehow, the job of this corpse was threefold:\\ (i) Split some (presumably rival) group;\\ (ii) decompose certain representatives of the group; and\\ (iii) infiltrate by powers of ideals. These people even talked of ideals! Monsieur Pi Rho pondered for a moment on this mysterious group's ways. He turned to the last page and THEN HE KNEW! There it was clearly written `BULLET IN THE AMERICAN MATHEMATICAL SOCIETY!' We hear that now heavy security has been posted at the American Mathematical Society. The other day a mathematician was seen entering the premises with his dog. Unfortunately, the dog left residues at every pole and this led to the mathematician being arrested all of which shows entrance to the sanctum sanctorum is really complex. ------------------------------------------------------------------------------ Wanta (medal at) Atlanta ------------------------------- `It Paes to be Leander' said someone with candour. Others couldn't add to our tally and could only dilly-dally leaving it to Leander not to meander! (After a dismal hockey performance) -------------------------------------------- Time was when Indian hockey ruled the sport along with Paki. Nowadays, when I see their game it makes me say with shame `ab bhi kuch kasar rah gaya hai baki?!' Googly from Hooghly --------------------------- There is a lad named Saurav hailing from the city of `Haurav' (Howra). When we beat the Pakis hollow people quipped `Khoob Bhalo, truly Saurav is our nation's Gaurav!' ------------------------------------------------------------ On the great bat(tle) ---------------------- Eyeing his rivals - the Kaurav, Arjun thought of the Pandavas' Gaurav. `To beat the enemy's army would be very trivial for me if only we had our Saurav!' -------------------------------------------------------------- Best Vish ------------- Lightning kid is again born. Voila! Kasparov is gone! I wish Vishy Anand carries on and on and on and on and on and on! --------------------------------------------------------------