Menumaple packages, projects, etc. mathematical quotations |
Mathematical QuotationsInspiration:when i was young, i forgot to laugh. later when i opened my eyes and saw reality i began to laugh and haven't stopped since. ~soren kierkegaard it's a fact. people are always saying brilliant, insightful, or just plain funny things, and i like to collect the things they say. some of my favorites over the past 10 years follow: Graduate Professors(within this section): [spring 2008 | spring/fall 2007 | fall 2006 | spring 2006 | fall 2005 | spring 2005 | fall 2004 | spring 2004 | fall 2003 ]spring 2008i lost my visual aid somewhere on the walk from the hotel to the convention center today, so if you'd like to see this in 3d, you'll have to walk to broadway and look for it on the ground there... ~speaker at the 2008 joint math meetings (homework assignment on my advisor's webpage for his graduate experimental math class)
[back to the top (of this section)] spring/fall 2007programming can be boring, so when you have a lot of variables to name, make it fun. if you know another language, you can write a hate letter or a love letter about your enemies or your friends just with your variable names! ~dr. z. dr. greenfield: (interrupting a seminar speaker who was writing a very complicated equation on the board) that looks horrible!
there's always a question of how to say things the shortest way. i could say "the graduate student of dr. z. who is excellent at research, excellent at teaching, has a great personality, and is also a female"... or i could say "lara". the first one is true, but the second one is much shorter. ~dr. z. "so the question is to bar or not to bar, which, while not quite as dramatic as hamlet's big question, still is worth considering" ~eric egge >> Hi Dr. XXXXXX,
the good news is... it's really really hard to bore a photon. ~roger penrose one of the biggest hangups in mathematics is that we need to get over the "so called infinity". ~dr. z. [back to the top (of this section)] fall 2006anything that doesn't fit in one blackboard just doesn't seem right. ~igor pak i'm just going to tell you the answer, because i can't compute this quickly in public. ~igor pak when n is... well, that's the smallest number (thinks)... ah ha! one! ~igor pak people used to think all theorems are provable, then came Godel... of course false theorems were never provable to begin with. ~zeilberger ok, I don't have a proof of the riemann hypothesis just yet, but i will now show proofs of other equally deep things. ~zeilberger the problem is all human beings are snobs. ~zeilberger after all, analysis is contained in combinatorics. ~zeilberger a human is a lousy computer with certain built-in macros programmed by evolution in a suboptimal way. ~zeilberger marketing is still a problem for computers. the best they can do is collaborate with lousy humans. ~zeilberger : You defined many things in this lecture. Did you ever define beauty?
[back to the top (of this section)] spring 2006my real name is 'his royal highness, supreme monarch of the county of middlesex and regent of highland park', and i declare that you should call me that for the rest of this conversation. ~Dr. Greenfield if your parents are brother and sister then you are your own first cousin... that is not very common today, except for my dog. ~Dr. Z. the idea behind dynamic programming is this: if i'm the best person in the room, and you chop of my head, then i'm still the best of all the headless people in the room. ~Dr. Z. so the moral of the story is... in research, if someone smart tells you to do something, go ahead and try it... if someone smart tells you NOT to do something, then by all means do it and see what you get. ~Dr. Z. if you want to impress your boyfriend or girlfriend, make sure to mention Hidden Markov Models. ~Dr. Z. publishing math is all about good marketing. ~Dr. Z. [back to the top (of this section)] fall 2005this is hard, so don't spend more than say... 2 years on it. ~Dr. Josef Beck you should like this proof because it is short and striking... like a good joke. ~Dr. Beck analysis is worse than false. it's true but completely meaningless. ~Dr. Doron Zeilberger mathematicians are always proud of drawing bad pictures. ~Dr. Beck Leigh: so why is that true?
always keep your opinions to yourself... until you have tenure. ~Dr. Beck professors aren't any smarter than grad students. we just know something you don't and try to play the cards like we're smarter. you will do this when you are a professor too. ~Dr. Beck any comments?... questions?... remarks?... if not, i'll just start talking and you can't stop me. ~Dr. Beck [back to the top (of this section)] spring 2005why give a simple proof if you can give a complicated one? complicated ones are much more fun! make it seem simple and people will think you aren't very smart. ~Dr. Doron Zeilberger i don't want to make a precise statement, but i'm willing to say this is spiritually true ~Dr. Jeff Kahn Dr. Kahn: does anyone know a word that begins and ends with he? (writes "he...he" on the board) no one? ok... it'll be on the next homework!
if two monkeys give you a copy of shakespeare, chances are one monkey plagairized the other monkey ~Dr. Zeilberger the proof of the pudding is in the eating. ~Dr. Zeilberger Mike: which anderson do you mean?
i just got a letter yesterday from God... i mean from don knuth. ~Dr. Zeilberger one can argue about whether that's really a script I, but i have the chalk, so ha! ~Dr. Kahn here's the part where we all go 'duh!' ~Dr. Diane Maclagan ...and what is x1 to do? is she going to be an old maid ALL her life? of course not! because people in this universe would rather get divorced than see a good friend be single forever. ~Dr. Zeilberger, getting a little carried away with an explanation of hall's matching theorem in his algorithms class A faculty member says "Be there or be square. If you're not there, you could not have a greater chance to be less square." ~in a mass math seminar announcement questions? ok, well just shout me down... that's the way we do it nowadays ~Dr. Kahn ok, so the conclusion is, i can't draw a gothic m, but you can think of this as one morally. ~Dr. Maclagan (sam and i are the first two to combinatorial commutative algebra class one day... we had just learned/reviewed simplicial homology in the previous lecture)
Dr. Maclagan: so the argument for writing an exact sequence like this is because this is the order you should think about it, even if the arrows aren't so aesthetic when they go right to left
good morning! so the purpose of today's class is to teach you all a secret -- my secret method for getting as many brilliant publishable papers as you want. ~Dr. Zeilberger because the biggest caterer to mathematical papers is still humans, we must cater to humans. ~Dr. Zeilberger Since when are we serious in here? it's all laughter and merry-making. ~Dr. Butler (in a mass email to the whole department) the people entering in 2003 and later were recruited by me. modesty forbids my saying how great you are, and you wouldn't believe it anyway. but it is true! (no group hugs, OK?) ~Chuck Weibel, our math grad director
>Date: Sat, 12 Feb 2005 15:16:54 -0500 (EST)
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[back to the top (of this section)] fall 2004there is an argument that we should call this a "WC complex" instead of a "CW complex", but then that would just sound a little funny to our friends in europe. ~Dr. Steven Ferry once upon a time there was a very smart mathematican... his name was fermat ~Dr. Zeilberger this is basically a tautology, but one should drink some coffee before declaring it to be a tautology. ~Dr. Ferry ...& at this point we spike the chalk and do a victory dance ~Dr. Ferry let's do this again -- i don't see uniform joy spreading throughout the audience as much as i'd like. ~Dr. Ferry oh good -- you are virgins at this... you are qualified to conjecture ~Dr. Zeilberger in 15 years, you may or may not remember homology, but you will definitely remember me crawling around and ducktaping the vents. ~Dr. Ferry does anybody know how to spell ullman? how about u(l^a)ma(n^b) ~Dr. Kahn so this theorem has an interesting history... it was proved in 1939 when they figured the subject was too new for anyone to care, and they were probably right... so then there was this war; you probably heard of it... 21 years later they get around to publishing the thing. ~Dr. Kahn so if there were audio responses these problems, we'd be done! now, how do we tell people in WRITING the good news that you're redeemed if you study analysis? ~Dr. Stephen Greenfield but you can never trust anyone... not even lara ~Dr. Zeilberger premature optimization is the root of all evil ~Dr. Zeilberger "Dear (potentially) Immortal Lara, ..." ~Dr. Zeilberger (in an email, regarding a pattern i found in my homework for his class that to our knowledge then, no one had found before) Dr. Greenfield: functions like this didn't exist until the 1600s... they were banned from existing by the holy roman emperor and only brought into existence by martin luther.... the cantor lebesgue function was one of his 95 theses
this was zero when i looked at it this morning, so it's probably still zero now. ~Dr. Ferry the original jacobi conjecture is not due to jacobi... it's due to a bad guy, probably a nazi... he published in a german journal in 1939... so either he was a bad guy or he was just dumb and oblivious to politics ~Dr. Zeilberger [back to the top (of this section)] spring 2004i plan to keep a pretty good pace in here, unless you all specifically ask me to slow down... which is precisely why i started out in the wrong room and came to the first class 10 minutes late. ~Dr. Kahn it is very important when you come to this class to bring a fresh set of indeterminates! ~Dr. Wolmer Vasconcelos this set is hard to get rid of... kind of like roaches in a new brunswick apartment. ~Dr. Roe Goodman and you'll notice that the only real numbers i know are integers ~Dr. Kahn the late night approach to this proof is... (blah blah blah)... end of proof, open another bottle... (pause, and some general laughter)... well, of course you all don't do that; you're first year students, you use hushed cathedral whispers when discussing mathematics... but i'm old, i'm an athiest now when it comes to set theory. ~Dr. Goodman my doctor says i can only prove three theorems a day, else i will get too excited. ~Dr. Vasconcelos here's a term i said i wouldn't use in this class... but i woke up today and decided i would be a liar. ~Dr. Kahn i guess the more brackets you write around something, the more likely it is to be true. ~Dr. Chris Woodward the orthogonal polynomials are kinda like families in the mafia -- each serves its own purposes ~Dr. Goodman most of you are beating me. you're getting almost all the homework perfect. next time i will take my revenge and give you my conjectures to prove. ~Dr. Vasconcelos this is easy... provided you're clever... provided you're gauss for example. ~Dr. Goodman i first saw that proof when i had had much cappuccino. that really etches it in your mind. ~Dr. Vasconcelos this class is not just a grocery store -- today i will give you cooking utensils. ~Dr. Vasconcelos math puts its premium on being right, engineering puts its premium on being relevant, physics puts its premium on who gets a nobel prize first. ~Dr. Goodman this problem is to see if you have any intuition... if you don't, you may belong in medical school. ~Dr. Vasconcelos today we talk about "rings in linear algebra"... "rings in L.A."... wouldn't that be a great movie title? ~Dr. Vasconcelos um, the general rule is you can run far away from analysis or from algebra, but not from both. ~Dr. Woodward in summary, minors are good... you shouldn't serve beer to them, but they're good. ~Dr. Kahn the first proof of this was due to lovasz... probably when he was in 1st grade or something ~Dr. Kahn these are really simple things... even an undergraduate on spring break could do this part ~Dr. Vasconcelos and contrary to some state legislatures, you can't make pi = 1. ~Dr. Goodman so as the british say, i will now do an integral for you... in public. ~Dr. Goodman goodman: it's kinda like replacating this classroom and assuming the universe is full of rooms of people studying analysis 2.
i have philosophical difficulties with velocity. if you have philosophical difficulties, have them when you are old... after you have learned the stuff. ~Dr. Vasconcelos of course mathematics is wonderful and anyone who goes to graduate school in mathematics is much more brilliant than anyone who, say, chooses a starting salary of $100K on wall street instead. ~Dr. Goodman evil is out there... but we still have to finish class. ~Dr. Vasconcelos analysis is about convergence and beautiful formulas. ~Dr. Goodman this isn't in folland... of course i'm not trying to say he doesn't know it though. ~Dr. Goodman when do you want to turn in your homework? i'm a mathematician, so i'm flexible... what you think takes a week takes a year... what you think takes a year takes the rest of your life. ~Dr. Woodward Dr. Goodman: ...and then the function has to pull a count dracula and turn into a discontinuous one...
this is not a physics class... you can't just go putting 0s in denominators and expecting it to be ok. ~Dr. Vasconcelos if you flip around the arrows in this theorem you get a new theorem. it is said everyone who works on this stuff has an even number of papers. ~Dr. Vasconcelos physicists know how to use infinity creatively, but that requires a Ph.D. ~Dr. Goodman yeah, these are equivalent in the sense that they're both true. ~Dr. Kahn this proof is special -- i go from the easy case to the general case using magic -- i call it high tech. ~Dr. Vasconcelos there's actually a condition to using the Fubini-Tonelli theorem....and it's NOT saying the rosary or invoking the name of your favorite politician. ~Dr. Goodman you ask about grades. my answer is this: i use an oracle, so i have no control, you have no control.. the fate of algebra students is written in the stars. ~Dr. Vasconcelos [back to the top (of this section)] fall 2003...and then God rewards us with a dual basis. ~Dr. Siddhartha Sahi this is what we call an exercise... you are not obliged to answer me immediately, and i am not obliged to answer you how to do it right now either. ~Dr. Vladimir Retakh the proof of this is dull and would take a lot of chalk, so i won't do it ~Dr. Daniel Ocone Dr. Retakh: and what is tuesday?
Dr. Ocone: nothing in math is named after the person who did it
Dr. Retakh: and how do we introduce Z to students?
Dr. Sahi: yes, so take your time and kind of swish the proof around in your mouth... get a sense of its flavor
in mathematics there are three kinds of statements: true, false, and so vague that you cannot tell. the last one is the absolute worst. ~Dr. Hector Sussmann so i've been grading. by and large everybody's homework is fine except for vagueness and some unsubstantiated wild assertions ~Dr. Sussmann isn't this proof rather like a high power chess game? always one step away from disaster, but still going strong ~Dr. Sahi and so, one may ask, how will i determine your grades? there is one philosophy that says only God deserves an A, only the professor gets a B, and all the students get C. this is a good one, but I think maybe I will use another. ~Dr. Retakh a good argument is always on the brink of apparent nonsense ~Dr. Sahi this is an abstract calculation. i will omit it because i am tired. ~Dr. Sahi, 2.5 hours in to his final lie algebras lecture [back to the top (of this section)] [back to the top (of the page)]
Undergraduate Professors(within this section): [ spring 2003 | fall 2002 | spring 2002 | fall 2001 ]spring 2003(biography made up to accompany an abstract for our math research group, courtesy of adam hughes) "Lara Pudwell likes reeses pieces pancakes, Steve Klee is a scuba diver by night, Margie Brewer is a staple queen, and Adam Hughes is a party in a box with a cup of cheer."
you know, there's always all this talk about how there's not enough women in math departments and so they feel lonely and like they always have to prove they're as smart as the boys. i don't know if i believe that or not... as for me, i think the boys like to have the girls around. ~Dr. József Beck, Rutgers professor I met on my visit here [back to the top (of this section)] fall 2002topology is the study of elastic geometry -- this means a topologist is basically someone who can't tell the difference between a teacup and a donut. ~Dr. László Fehér if you don't understand something in this class, blame it on my accent -- now, none of you can do poorly in here because i just gave you a valid excuse for everything! ~Dr. Antal Balog [back to the top (of this section)] spring 2002i can't intergrate the @*(^% function anyhow ~anonymous professor, during analysis class i'm not gonna make it as a computer ~Prof. James Caristi anyhow we still have to do a class evaluation... remember this is an individual evaluation of the course... do not compare answers with anyone... apparently in past years, some classes make this into a festive occasion... remember, class evaluations are NOT a festive occasion. ~Prof. Greg Hume people like this (math graduate students) are just compulsive... you see how Lara is here... take her and magnify her about 10 times and you have it... and that's not necessarily a bad thing ~Prof. Rick Gillman "i have papal dispensation from the department." ~Prof. Caristi "they say Lisp really stands for list processing, but any good programmer knows it really means lots of irritating stupid parenthesis" ~Prof. Hume "remember, your job is to make things easy for me, and my job is to make things difficult for you" ~Prof. Hume it's times like this i'm sure God must be a mathematician. ~Prof. Bill Marion mathematicians peak at about 23 and then it's all downhill... good luck. ~Prof. Michael Watters (Valparaiso University, biology department) [back to the top (of this section)] fall 2001in all my years of administration, the best thing i learned is that if you postpone things long enough, they will go away. ~Dr. John Sorenson there should never be any homework assignments over a break. this is one of my theorems. When i'm dictator, it'll be one of my laws. ~Dr. Sorenson When I was a kid, I heard geniuses had bad handwriting, so I cultivated bad handwriting. ~Dr. Sorenson [back to the top (of this section)] [back to the top (of the page)]
Friends and Colleagues(within this section): [ the grad school years | my REU | the undergrad years ]The Grad School Years"You can do it! Here's how I know: your brain runs on math, unlike most people's brains, which run on glucose. You get dizzy without math at certain intervals. Proofs are to Lara what sandwiches are to the rest of us." ~jenny "wow lara, you sound like mathematical dr. seuss!" ~colleen Thanks. I should have known this. My excuse is that I have been mercilessly brainwashed with double and triple integrals for the past few weeks and so if asked to compute the volume of the unit cube I'm likely to set it up as a triple integral. ~email from an anonymous calc 3 student P.S. I always look forward to your quizzes, they are normally fun in a wierd math kinda way. ~email from another anonymous calc 3 student we just covered that the poking function is not an equivalence relation. it can be reflexive if you want it to be, but it is rarely symmetric or transitive. usually people randomly poke and the others just smile and nod... but with most functions, there's just a lot of smiling and nodding anyhow. ~ben leigh: so then we can always find a sup within epsilon of that pizza hut! once i spent a whole day doing that... you know, putting + and - in front of zero and watching it disappear... it's like 'look! it did it again!' every time. ~eric Question: Why can't you grow wheat in Z/6Z?.....because it's not a field ~steve klee I've always considered statistics somewhat pornographic. ~eric "Julius Caesar borrowed a day from February so July would have 31 days. Brutus couldn't finish his homework, and he got really mad. That's not my abstract, but I'll send you one a few minutes before the deadline, since I seldom put off tilll tomorrow what I can put of till the day after tomorrow." ~sujith me: hi colleen! what do you know today that i don't know?
so you're saying almost every rational number is purple? ~sam scott: what's your favorite compact hausdorff space?
"Two triples is messin' if they have a common hypotenuse." ~gizoogle.com, translating eric's website oncnmoumatitev laegrba ~colleen's default IM away message scott (singing, with motions): i'm a little teapot short and stout... but i'm in grad school and i might drop out "diff eq gets lost, lose 3 days" ah...the joys of playing oregon trail with math subjects ~steve klee ben (in my office, talking math with leigh as i walk through):...so i guess this is kinda analogous to L^p spaces in that...
steve: i was going to say 5.5, but what's the fun in responding with a rational number?
i am a sigma algebra... woooo!!! i am a sigma algebra... wooooo!!!!! ... i am the walrus! ~eric (during class, whispering, on account of one professor's bad handwriting) dude, tell me that doesn't say 'g(x) is a pimp' ~scott schneider me: "so did you ever figure out what the utility workers were tearing up your road for for the past month?"
roses are red and
(On IM) Auto response from (me): if only my computer were as smart as ekhad...
(at dinner with several other math people and a small child, the child was allowed to order dessert if he'd save half for his sister at home, and then proceeded to beg for half of her half, etc...)
baxter: everyone loves triangles!
In any case, I'm not convinced of the pickleness of this graph. Please go back and check the details; I am sure you will find an error. It is also severely lacking in pickelocity, which anyone in the field will tell you is absolutely essential. So unfortunately, you have not solved the famous (still open, and will be open for quite some time) Pickle Hypothesis. ~eric you are 2/3 of the way to a PhD in math, not pickles ~dave anonymous graduate algebra homework excerpts:
student: FYI, i don't like the units you gave on the quiz, so i converted all the pounds, feet, and seconds to kilograms, meters, and seconds, ok?
avital: so that must be hard
...and the proof is just a bunch of combinatorics... no real mathematician would be interested to do it. ~jinwei me: *singing* do you know what i know?
[back to the top (of this section)] My Research Experience for Undergrads (summer 2001, Trinity University, San Antonio, Texas)"this overhead smells like it's going to explode... oh well, let's just let it explode and keep going." ~Dr. Chapman Paul: "so, what we see here is basically lemma 1.2 reincarnated... how neat is that?"
"ugh... now my algorithm gives a bunch of nice stuff plus a nasty term... we'll just ignore the nasty term and keep going." ~Paul on the dry erase board in our REU computer lab
"where you be at??? ok, so we're including ebonics in this draft of the paper... it's the cultural part of the REU experience, eh?" ~Dr. Chapman "Proof: pick two elements and fling them out the window." ~Paul "you are not playing with the cold hard logic and efficiency of a true hearted veteran.... but look at his finger technique... i see flashes of brilliance." ~Josh (in reference to minesweeper) Dr. Ponomarenko: "I have no idea what you just said"
"the first rule about prime jump systems is... don't tell anyone about prime jump systems." ~Ben [back to the top (of this section)] The Undergrad YearsA fact field is a figment of Lara's imagination. It is a field of random 42-filled facts, all of which have inverses (opposite thoughts), one of which is a unit (and leaves the other thoughts alone), another is a zero (no thoughts at all), none of them are zero divisors (they all lead to SOME conclusion...imagine that!), there are no ideals other than the trivial one and the whole thing (none of the thoughts steal and absorb other thoughts!), and they may be infinite (lots of thinking). As I said, this is a FIGMENT of Lara's imagination, because such an organized and well-structured thought pattern is only imaginary.... ~ian renner "a sequence is convergent if when the little green men tell you, 'ha ha you better find a number.........(blah blah blah).' then you say 'i found that super number, little green men..... (etc.), now let's go eat dinner to discuss world peace', and they say 'sounds good to me, let's go to kék rozsa!' "~definition courtesy of marianne karplus i'm an engineer: i'm not even worthy to spit on your homework! ~nathanael bokelman Hmm in retrospect maybe you and I were doomed to get letters after our names based solely on our behavior. What are you going to do when you teach in grad school? Will you encourage singing in class? List Silly Putty as an recommended class material? That would be excellent. Music is mathematical after all. And Silly Putty, well, can relieve stress. ;) ~jennifer riem "In a spree of sarcasm, while discussing grad school with another math friend of mine, I drafted the following hypothetical statement of purpose: I feel we should both use this on our applications; it would guarantee us admission anywhere.
(sitting with a BSM (budapest semesters in mathematics) friend at an applebees in lincoln, nebraska:)
look lara: you don't need the phd, you have the shuffling gait, the old person umbrella, and the huge cup of coffee, you could already pass for a professional mathematician now ~jennifer riem hail lara, calculus queen of the universe ~david kelley on freshman calc papers i've graded
so basically, you (the math dept) have trained all the creativity right out of us... that's just sad. ~joe puetz i've done a max-min analysis of this situation (being in analysis of algorithms class) and decided that running away to mexico is the best move. ~laura felch me: i still need a topic for cs colloquim...
i would say that most people who have taken probablity probably didn't like probablity. ~Aaron Scheunemann [back to the top (of this section)] [back to the top (of the page)]
Books"It is not possible to know where a grad student is and where it is going at the same time." (from PhDComics.com) "If you are in a losing position, it pays to follow the enough rope principle: make the position as complicated as you can with your next move.* "
"odd, i've certainly never come across any irreversible mathematics involving sofas. could be a new field. have you spoken to any spatial geometricians?" ~douglas adams (in Dirk Gently's Holistic Detective Agency) "oh, now, don't underestimate the abacus," said Reg. "in skilled hands it's a very sophisticated calculating device. furthermore it requires no power, can be made with any materials you have at hand, and never goes bing in the middle of an important piece of work." ~douglas adams (in Dirk Gently's Holistic Detective Agency) he used the number zero as a starter. zero, originally a hindu number, was introduced to the west by the arabs during the middle ages and was unknown to the ancient greeks and romans. how was *that*? he wondered. had nature so subtly hidden zero that all the greeks and all the romans -- millions of them -- couldn't find it? one would normally think that zero is right out there in the open for everyone to see...~robert pirsig (in zen and the art of motorcycle maintenance) "ah," said dirk, "it is a rare mind indeed that can render the hitherto non-existent blindingly obvious. the cry 'i could have thought of that' is a very popular and misleading one, for the fact is that they didn't, and a very significant and revealing fact it is too" ~douglas adams (in Dirk Gently's Holistic Detective Agency) most mathematicians are bipolar disorders waiting to happen... one of the reasons that mathematicians tend to be eccentric is that we confront failure and disappointment every day, and try to find ways to surmount it. ~steven krantz (in a mathematician's survival guide) ...In this regard, Euler presents a welcome contrast to the withdrawn, secretive Isaac Newton, one of his very few mathematical peers. It is comforting to know that genius of this order does not necessarily bring with it a neurotic personality. ~william dunham (in journey through genius) Fibonacci faced the challenge of adequately formulating the problem he was studying, one of the more difficult parts of bioinformatics research. The Fibonacci view of rabbit life is overly simplistic and inadequate: in particular, rabbits never die in his model. As a result, after just a few generations, the number of rabbits will be larger than the number of atoms in the universe. ~neil jones/pavel pevzner (in An Introduction to Bioinformatics Algorithms) The expression on the left of the equal sign here comes up a lot when you have to see how many different ways there are to do various things, so mathematicians have a special notation for it. They write it as: 10! You don't read this aloud as "ten" in an excited or startled voice, nor do you say "ten exclamation mark." You read it as "ten factorial."
consider the vexation in not knowing with certainty whether you are 3 feet tall or 6 feet tall, or that the distance from chicago to los angeles is 1,000 miles or 2,000 miles. buying a new pair of slacks or planning this summer's road trip would be a guaranteed headache. but believe it or not, astronomers are regularly saddled with such uncertainty when it comes to nailing down some of the most fundamental paramenters in cosmology. ~random astronomy magazine In the world of mathematics proper, the Pythagoreans gave us two great discoveries. One, of course, was the incomparable Pythagorean theorem. As with all other results from this distant time period, we have no record of the original proof, although the ancients were unanimous in attributing it to Pythagoras. In fact, legend says that a grateful Pythagoras sacrificed an ox to the gods to celebrate the joy his proof brought to all concerned (except, presumably, the ox). ~william dunham (in journey through genius) By Euclid's day, five such solids were known -- the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedrom. These aesthetically pleasing solids were featured prominently in Plato's Timaeus from around 350 B.C... It seemed evident (to Plato, at any rate) that fire, air, water, and earth must be in the shape of regular solids. It only remainded to determine which element had which shape.... Somewhat embarassingly, this put Plato in the unenviable situation of having run out of elements but still having a regular solid, the dodecahedron, left over. He lamely said this was the shape "...which the god used for arranging the constellations on the whole heaven." In other words, the dodecahedron somehow represented the shape of the universe. Because of this fanciful if not utterly bizarre theory in Timaeus, the regular solids have since been called the "Platonic solids". ~William Dunham (in Journey through Genius) ...A century passed, and another, yet no one could provide a "solution by radicals" for the quintic... If we called the earlier equation "depressed", this one must have been "utterly despondent". ~william dunham (in journey through genius) "Adding, though pleasant and easy, is often inappropriate... Recall that mathematics as simple as '1 + 1 = 2' can be thoughtlessly misapplied: If 1 cup of popcorn is added to 1 cup of water, we do not end up with 2 cups of soggy popcorn." ~john allen paulos (in innumeracy) "Statistical analyses of works whose authorship is disputed (books of the Bible, The Federalist Papers, etc.) also depend on related clever ways of gleaning information from uncooperative (because dead) sources." ~john allen paulos (in innumeracy) "Zealots, true believers, fanatics, and fundamentalists of all types seldom hold any truck with anything as wishy-washy as probability. May they all burn in hell for 10^10 years (just kidding), or be forced to take a course in probability theory." ~john allen paulos (in innumeracy) "Math is Hard. Unfortunately, people are just not that good at mathematics. While intensely enjoyable, it also requires hard work and self-discipline. I know of no serious mathematician who finds math easy. In fact, most, after a few beers, will confess as to how stupid and slow they are." ~thomas a. garrity (in All the Mathematics You Missed) "Some careers seem to accumulate people who might easily have preferred to do something else. You will run into people who tell you that they practice law as a day job but they are really novelists or playwrights or jazz trombonists. Other people can't settle on something, or they see their careers in more purely practical temrs, and they drift into human resources management or advertising sales. Which is not to say that these people are not dedicated or fulfilled in what they do, but few of them consider their work a calling. No one drifts into being a mathematician. On the contrary, it's a pursuit from which even the talented are too easily turned away." ~ian stewart (in letters to a young mathematician) You're very sure of your facts. I couldn't trust the thinking of a man who takes the Universe - if there is one - for granted. I only decide about my Universe. My Universe is my eyes and ears. Anything else is hearsay. ~Douglas Adams (in the restaurant at the end of the universe) "Yes, my boy. I often wonder where the mathematics stops and witchcraft begins". ~the number devil [back to the top (of the page)]
MiscellanousIf I have seen further than others, it is by standing upon the shoulders of giants. ~Isaac Newton If I have not seen as far as others, it is because giants were standing on my shoulders. ~Hal Abelson do you mean you talk calculus with women you're NOT attracted to? ~dick solomon, third rock from the sun the creative principle (of science) resides in mathematics. ~albert einstein strenuous intellectual work and the study of God's nature are the angels that will lead me through all the troubles of this life with consolation, strength, and uncompromising rigor. ~albert einstein science without religion is lame. religion without science is blind. ~albert einstein i tell you don't listen to the economists... you know why? because they like math! and math is very much a part of the axis of evil. ~SNL 6/8/02 to number all the benefits, that number is to man
Mathematics is the handwriting on the human consciousness of the very Spirit of Life itself. ~Claude Bragdon Mathematics in general is fundamentally the science of self-evident things. ~Felix Klein Mathematics... the ideal and norm of all careful thinking. ~G. Stanley Hall Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different. ~Goethe A mathematician is a blind man in a dark room looking for a black cat which isn't there. ~Charles Darwin Pure mathematics is, in its way, the poetry of logical ideas. ~Albert Einstein clearly, then, the study of number is conducive to truth ~plato base 8 is just like base 10 really... if you're missing two fingers. ~tom lehrer Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world. ~Albert Einstein one must divide one's time between politics and equations. but our equations are much more important to me, because politics is for the present, while our equations are for eternity. ~albert einstein the most beautiful experience we can have is the mysterious. it is the fundamental emotion that stands at the cradle of true art and science. ~Albert Einstein mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. ~bertrand russell the important thing is to not stop questioning. curiousity has its own reason for existing. ~Albert Einstein the search for truth and knowledge is one of the finest attributes of man -- though often it is most loudly voiced by those who strive for it the least. ~Albert Einstein The whole problem with the world is that fools and fanatics are always so certain of themselves, but wiser people so full of doubts. ~Bertrand Russell teaching should be such that what is offered is perceived as a valuable gift and not as a hard duty. ~Albert Einstein one should not pursue goals that are easily achieved. one must develop an instinct for what one can just barely achieve through one's greatest efforts. ~Albert Einstein do not worry about your difficulties in mathematics; i can assure you that mine are still greater. ~Albert Einstein [back to the top (of the page)]
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