Happy 410th birthday, Fermat!
I was alerted to the fact that it’s the mathematician Fermat’s birthday by today’s graphic at Google:
Which reminded me to recommend to you the truly marvelous documentary “Fermat’s Last Theorem.” It’s posted on YouTube in five parts. Here’s the first, to whet your appetite:
I have a truly marvelous comment which your spam filter is too narrow to accept.
Hey, it’s just a doodle. What’s everyone getting so bent out of shape about?
*yawn* Pure maff. Thrillsville.
Apologies to the aficionados of pure math, but I’m one of those who find a mathematical theorem interesting only when there’s some practical application to be gained from it. Math for math’s sake is like debating how many angels can dance on the head of a pin.
Yes, I realize a lot of Fermat’s discoveries and innovations had practical applications. But this post is about Fermat’s Last Theorem, which doesn’t as of yet.
It’s like the study of prime numbers (which was one of Fermat’s main contributions, by the way): For its sake, I don’t see what’s the point. Show me how primality can be taken advantage of for:
1. Constructing a lunisolar calendar–the interplay of 12 and 13 months
2. Doing checksums–ISBN book numbering uses 11 for that purpose
3. Building a rotor–one matching gear has a prime number of teeth to ensure full matching cycles
4. Digital encryption–based on the difficulty of factoring large prime numbers
and I’m hooked. That’s why I’m a full-time programmer and small-part-time mathematician.
I just wonder how many people got turned off of math once it got too abstract and useless. Less trig equations to solve for their own sake, please; more trig equations to solve for the goal of constructing something tangible, thank you.
Well, I have to take back my glib, off-the-cuff response. I’ve just watch all 5 parts of that documentary and it is simply marvelous. Inspirational and highly recommended… the math is just a subset to a very human story. Invest the time. You’ll be rewarded.
I *liked* this series and I’m an “enjuneer” for God’s sake. (I WILL brag that I have developed some pretty complex computer software including that used for real time process control and automation of gas chromatography, the terminology of which can still be seen in the literature forty years after I worked on it.)
You never know when some obscure mathematical truth will be used to do something practical or be a building block for that.
That’s “Texexec’s Last Theorem”. 🙂
That’s “Texexec’s Last Theorem”.
Hopefully not.
Much “pure” mathematics has later been found to be very “practical” — one obvious example in the first part of the twentieth century was Heisenberg’s “Matrix Mechanics” formulation of quantum mechanics.
Eugene Wigner’s 1960 paper The Unreasonable Effectiveness of Mathematics in the Natural Sciences is still worth reading.
But not everyone falls in love with mathematical beauty for its own sake. I don’t understand how that is possible, but I accept it.
I for one am completely enchanted by number theory, especially analytic number theory.
A very nice, accessible introduction for non-mathematicians is John Derbyshire’s Prime Obsession.
Jamie Irons
Aww Neo, you’re just trying to get in good with all us nerds. I’m with ziontruth here. Not that I don’t enjoy math, but it must be calculating something for me to find it fun. That’s why I’m an experimentalist as opposed to a theoretician.
Jamie Irons,
“But not everyone falls in love with mathematical beauty for its own sake. I don’t understand how that is possible, but I accept it.”
Some people can spend hours in the library reading on the theory behind architecture, whether or not they plan to build anything; for others, the beauty is in the process and result of actually using this theoretical knowledge in order to build something.
I don’t know if the one attitude is better than the other–it’s a subjective question, so my answer is as good as yours. Ultimately, being a contemplative type vs. a purposive one is a matter of personality, and that rarely changes. I have a vague understanding of the enjoyment one can derive from learning something for its own sake, but I could never feel it the way you do.
One of my recent buys is The Golden Ratio by Mario Livio, about the number phi (which is (1+√5)/2, or about 1.6180339). Most would classify it as a book about math for math’s sake, yet even here I found myself enjoying less the parts about Pythagorean mysticism and more the parts about rose petals, old bookhand proportions and classical paintings–in other words, the tangible and the practical.
So if a mathematician goes psycho, would he write a theorem instead of a manifesto?
As a former engineering student who worked mainly with the application of theorems rather than their proofs, I can say the proving them is much more ardulous than the alternative. I was forced to take several pure mathematics classes with pure mathematician teachers and learned they are a whole nother breed of cat. Their world is so esoteric, their language so beautifully inscrutible to the casual observer, that it’s safe to say most people who speak other languages fluently couldn’t begin to understand the question, let alone the answesr.
This is one of the finest YouTube series I’ve ever seen. Thank you, Neo, for posting it. Doesn’t Andrew Wiles fit the perfect prototype of the lovely, quiet, brilliant yet infinitely intense and humble pure mathematician!
Oops, got so absorbed in the world of numbers and theorems I clearly lost what small grasp I had of spelling and typing…..
Again marvellous video series.
ziontruth
Actually, I don’t mean at all to demean a preference for the pragmatic.
A few years back I read the Livio book and much enjoyed it.
Phi, like pi, has a way of showing up (as you know from Livio) in all sorts of unexpected places!
The mere contemplation of Euler’s identity
e^(pi*i) + 1 = 0
makes a Platonist out of me!
Jamie Irons
FYI, this appears to be an abridged British version. The Nova version was 60 min (not 47 min) and narrated by Stacy Keach.
@gs
LOL
I guess everyone who loves math tries to solve that one… though my twist was trying to figure out the likely candidate that Fermat may have thought he had, which is not quite the same thing as finding a solution, unless you believe he actually had it, and its not some complicated relative of a wave function equation that only a few could even understand at all…
“”Doesn’t Andrew Wiles fit the perfect prototype of the lovely, quiet, brilliant yet infinitely intense and humble pure mathematician!””
Webutante
His personality oozes goodness and innocence. Like he has some fortunate inability to be distracted by life’s temptations. A marvel just to watch and hear.
Oh, while i have a likely candidate relative to a small class of simple topology in algebra, the best thing i have is a solution for how genetic information or rather electronic version of it can expand into a multicellular problem solving paradigm. that is, grow solutions that start from a single germ out to a final state which then functions as a whole to solve problems. Had to get over about 3 or 4 key things to make it workable, one being how, for the purposes of this functional system, does one handle the stopping problem as far as the functional unit is concerned. that is, to put it in layman’s terms, is your prime 18, 19, 20? or if you go to 100 years old, will that work better? would earlier be better? its not solved by just picking an arbitrary amount, or a varying amount, or tying it to the problem solution (local minima and all that)…
if anyone wants to work on some of the big classics and walk away with a million, you can go here
http://www.claymath.org/millennium/
I also have a solution for searching through huge amounts of unordered data in which a single threaded version depending on structure can do a million compares per clock tick (handling straight matches, wild card matches, wild card matches with varying gaps, and matches by quantity condition). it can be linked up and is scalar using standard parts off the shelf… unlike FPGA solutions, or computers, top clock speeds in available chips are over 50ghz… at that speed i could search 14 human genomes, looking for 100,000 1000byte matches… in a second
Fermat like me is an autodidact…
though unlike me, he is great 🙂
he was a lawyer, and they say “amateur mathematician” (see wiki)…
I was lucky to be born at a time when the science of computers was just starting to explode… and i in the 70s had access to them… my career started on mainframes before pc computers existed yet…
but unlucky to be born in a time where they decided to operate on the bell curve and make a plateau… and unlucky to now live in a situation where any effort to distinguish yourself through talent or ability and experience is seen as putting others down and violating equality (among other things)
there is a long history of contributions from autodidacts whose training or credentials do not relate to their areas of remembered contributions…
though i am sad that today they do not have the fertile receptive fields of the past…
Frank Lloyd Wright
Gustave Eiffel
Michael Faraday
Srinivasa Ramanujan (a personal favorite)
Karl Marx
The natural historians Alfred Russel Wallace and Henry Walter Bates
“Darwin’s Bulldog” Thomas Henry Huxley
[yes, related to that later Huxley]
The social philosopher Herbert Spencer
Mythologist Joseph Campbell
Buckminster Fuller
Thomas Alva Edison
Abraham Lincoln
Eliezer Yudkowsky, artificial intelligence researcher.
another fav of mine… but as noted my work is in the solution of the multicellular paradigm for cellular automata based computational self organized organic problem solving through the creation of solutions iteratively using a biological model. 🙂
i have figured out how things are incorporated into and out of the genetic model, since its not a blueprint structure (no blue print system would work we take for granted there must be one, for we exist, but there is no model there)
Autodidacticism (also autodidactism) is self-education or self-directed learning. In a sense, autodidacticism is “learning on your own” or “by yourself”, and an autodidact is a person who teaches him or herself something. The word “Autodidacticism” finds its origin in “Didacticism”, an artistic philosophy of education.
given my lack of sleep, always thinking, poor social skills in terms of reading people, i spent all my life studying…
but i dont advise it…
no place to bring your work and retain authorship…
I watched this documentary a year or so ago (via Steve Sailer, it’s at google videos in one piece), and thought it was great. The math is obviously beyond me, but I liked the portrait of this guy who is one of those lucky people who found his calling in life, and then was able to devote his life to it and actually reach the pinnacle of his profession. A math friend of mine said he imagines this is to the math world as Einstein’s relativity is to the physics world.
The story is that of achieving one’s childhood dream. Few actually manage to do such a thing. It was an overwhelmingly spiritual experience when he realized that, after all those years of intense work, his dream had been achieved. Wonderful!
The unfortunate thing is that after climbing the Mt. Everest of mathematics, there is no childhood dream left to work toward for Dr. Wiles. Life is a journey and when some peak early they spend the rest of their life looking for a new challenge that excites them. May he find new and exciting challenges.
I had the pleasure of knowing a math genius much like Wiles. He never achieved such a breakthrough, but his great pleasure in earning a good living doing something he enjoyed so thoroughly was an inspiration to see. He and I were friends because we both liked rock climbing. That involves solving problems as well.
I had little grasp of mathematics beyond basic algebra until someone stuck a dollar sign in front of the numbers sometime during my sophomore year in college, and bingo! My interest in math was ignited, and my career as an accountant was launched (after a military detour mandated by an ROTC scholarship). I’ve since moved on to a different occupation altogether, but I’ve maintained an interest in mathematics, both the practical and the theoretical variety. Not that I really understand it that well, but I find math in all its forms to be endlessly fascinating.
Theoretical math is important to society.
Webutante says, “… pure mathematician teachers and learned they are a whole nother breed of cat. Their world is so esoteric, their language so beautifully inscrutible to the casual observer, that it’s safe to say most people who speak other languages fluently couldn’t begin to understand the question, let alone the answesr.”
I lack the ability to grock higher math, I’m simply too much of a dullard, but math on this plane is valuable to society. From theoretical math comes great discoveries. I bow to the ‘god’ of esoteric math.
This was a wonderful documentary. The world needs all kinds of people: those who can focus on the abstract, those who can dedicate themselves to applying abstract principles, and those who can tell when a kid needs a hug. It’s great when films like this help us to get to know one another.
expat: those who can focus on the abstract, those who can dedicate themselves to applying abstract principles…
I would agree in the abstract but disagree in practice of how it is, and is worse today than in the past…
I am finding out that for people like me without a connection, the world goes out of its way not to need us.
My life is basically my work.
Temple Grandin
If I did not have my work, I would not have any life.
Temple Grandin
I like to figure things out and solve problems.
Temple Grandin
I obtain great satisfaction out of using my intellect.
Temple Grandin
All are similar things I have said, and i would bet others who are similar would also say.
Genius May Be an Abnormality: Educating Students with Asperger’s Syndrome, or High Functioning Autism
http://www.autism.com/ind_genius.asp
I am becoming increasingly concerned that intellectually gifted children are being denied opportunities because they are being labeled either Asperger’s or high functioning autism. Within the last year I have talked to several parents, and I was disturbed by what they said. One mother called me and was very upset that her six-year-old son had Asperger’s. She then went on to tell me that his IQ was 150. I replied that before people knew about Asperger’s Syndrome, their child would have received a very positive label of intellectually gifted.
This is one of several ways that they are leveling the top of the bell curve to create a plateau.
There is a continuum of personality and intellectual traits from normal to abnormal. At what point does a brilliant computer programmer or engineer get labeled with Asperger’s. There is no black and white dividing line. Simon Baron-Cohen, an autism researcher at the University of Cambridge, found that there were 2 ½ times as many engineers in the family history of people with autism. I certainly fit this pattern. My grandfather was an engineer who was co-inventor of the automatic pilot for an airplane. I have second and third cousins who are engineers and mathematicians.
As do I, as my family is all engineers, researchers, handymen/janitors, artists, musicians, mathematicians, teachers, and me in information theory/applications engineering
So expat, where does one go with what one has?
I can point to TONS of such missives as to we need more of X and tons more of Y, and while your at it, can we get a basket of B…
the left in control of schools, basically claims there is no such thing as innate talent, etc.. and so its fruits i am finding are reserved for those approved by the guilds… sorry, you can knock on that door, and hardy will never answer as in the past, as behind the door is a brick wall. the door serves as a mechanism for people to waste their time believing and hoping.
A review of the literature indicates that being truly outstanding in any field may be associated with some type of abnormality. Kay Redfield Jamison, from Johns Hopkins School of Medicine, has reviewed many studies that show the link with manic depressive illness and creativity. N.C. Andreason at the University of Iowa found that 80 percent of creative writers had mood disorders sometime during their life. A study of mathematical giftedness, conducted at Iowa State University by Camilla Persson, found that mathematical giftedness was correlated with being near-sighted and having an increased incidence of allergies. I recently attended a lecture by Robert Fisher at Barrow Neurological Institute in Phoenix, Arizona. He stated that many great people had epilepsy, people such as Julius Ceasar, Napoleon, Socrates, Pythagoras, Handel, Tchaikovsky, and Alfred Nobel. An article in the December 2001 issue of Wired magazine discussed the link between autism and Asperger’s, and engineer and computer programming. The incidence of autism and Asperger’s has increased in the children of technology company employees. A little bit of autism genes may provide an intellectual advantage and too much of the genetic may cause a severe case of autism.
Can’t add up? We are either born with a mathematical brain or not
http://www.dailymail.co.uk/sciencetech/article-2024570/Cant-add-We-born-mathematical-brain-not.html
I have worked very hard all my life, and in my capacity as a professional am expected to make anything work that they come up with and I don’t get much if any leeway (And i am not exactly treated humanely either).
The Lemelson foundation has been collectivized:
http://www.lemelson.org
lemelson.hampshire.edu
Lemelson MIT program
web.mit.edu/invent
[besides, a careful examination would show that they make only safe bets, ie… the support is either for successful adult inventors (giving them candy to motivate thousands of others to want candy too), or school kids who are not expected to really invent or succeed in whatever they work on, so the outcome doesn’t really matter]
Peer review isnt what it used to be, and not have the CV your out of the picture, as your not a peer. the Guilds are high on rhetoric and ideas, low on actual practice, execution, and maintaining the reality of them. (they also delude themselves that in the absence of any critical examination, the rhetoric is valid (and the failures and situations they also hear make no sense))
we believe:
Build a better mousetrap and the world will beat a path to your door.
Ralph Waldo Emerson
“There is the happiness which comes from creative effort. The joy of dreaming, creating, building, whether in painting a picture, writing an epic, singing a song, composing a symphony, devising new invention, creating a vast industry.”
Henry Miller
Temple Grandin
People today do NOT respect talent, as talent the way we have it is and is made to seem a dime a dozen. which depending on the talent may be so given some can be acquired through effort and focus.
but today, if i do what temple suggests is whats good, i will be in more trouble for it than i have been. Why? because my effort to rise up or distinguish myself is seen by the younger set as “downgrading” (their term), and i guess degrading. So such initiative is seriously punished.
So again…
What do we do with all the people that take up such an endeavor? the idea of getting more on the path is fine if in motivational missives, but then what?
and what does one do about the “Tall Poppy Syndrome”?
en.wikipedia.org/wiki/Tall_poppy_syndrome
Tall poppy syndrome (TPS) is a pejorative term primarily used in Australia, but also in New Zealand, Canada and other Anglosphere nations to describe a social phenomenon in which people of genuine merit are resented, attacked, cut down, or criticized because their talents or achievements elevate them above or distinguish them from their peers.
The term originates from accounts in Herodotus’ The Histories (Book 5, 92f), Aristotle’s Politics (1284a), and Livy’s History of Rome,
and so i suspect no cure is forthcoming…
Some sociologists, notably Max Weber, believe that in certain social groups, the acquisition of prestige and power is a zero-sum game, and this situation may provide a rationalization for the hatred of “tall poppies”.[10] In such groups, there is only a limited amount of prestige for its members to share in and only a fixed quantity of attention, authority and material resources that its members can give to each other. Therefore, for someone to rise in status, another person must fall. A person who is more prestigious is an obstacle to another person’s rise simply by being more prestigious, and a person who suddenly rises is an outright threat to the other’s current status.
This zero-sum pattern can be found in small groups characterized by fixed hierarchies and where there is little movement in or out of the group.
understanding it does nothing for changing it or finding more opportunities. ie. in my case the boss is too dim to see that by all succeeded the department can grow, and opportunities can be made as the more valuable you are and your contributions, the more they allocate to you.
there is also a “Crab Mentality”
Srinivasa Ramanujan had Hardy as his connection to pull him into the world and not be erased…
Temple Grandin had the woman who discussed her shirt
but today, who would dare mentor a person from outside of the designated protected classes (of the future)?
you see expat… what you dont realize is that they are in a way, removing such contributors. its why our standing has deteriorated over and over, and so forth. by declaring the condition and playing games, they also declare unfit ability, and an unapproved status.
they believe that we are what we are programmed to be and people like temple grandin and others, who may not share the ideal of reinforcing collectivism (as individuals), are erased. (for the record if i remember correctly temple is for collectivism).
you can go to tons of motivational places who have nice titles that say “bringing innovation to life”, and offer business plan ideas and such.
but then when you go to the place to get a step forward as without it you cant proceed, you find out that the state has stacked the cards so much that you cant proceed for reasons having nothing to do with validity, or ability. (SBA8a program gives such overwhelming advantage, if your not part of the program, your basically out if you have no other resources).
we love to look at Steve jobs, but forget about Wozniak….no?
we hear Watson comment, and that he is baked for some misstatement from the pc doctrine… but what happened to crick?
we focus on bill gates and Melinda his personal secretary turned wife, and the loads of money they will redirect from state to charity and reap social reward for… but if you ask people, who is Nathan Myrvold, they would go “hunh?”
granted, out of all this Nathan has a billion dollars and is doing ok…
but look around.. what drives manufacturing is the ideas that are the purpose behind the people and the machinery and the reason for the factory to be.
social engineering is mutually exclusive to self determination, they cant exist in one place any more than matter and antimatter. in fact, its more like the fact that contamination has no small place in the concept of purity. ie, you cant have any of it, and be pure… ie.. you cant have ANY social engineering and believe without delusion in some way that self determination still exists (or ever existed?).
the whole area is now dominated by the “totalitarian administrators” (one of which has a nice op ed in the daily news suggesting we paint lines on the street and fine people hundreds of dollars for not walking in the lines properly, or standing too long in a zone, or looking at a window outside the window watching area!!!! of course, is anyone thinking how totalitarian that is (or rather fascist, the same end but through different means)?
From Harvard Business Review:
The new rules for bringing innovation to market…
http://www.globalsolve.com/Documents/strategic%20Planning/1/New%20Rules%20for%20Bringing%20Innovations%20to%20Market,%20The%20%28HBR%29.pdf
sorry, i missed the pamphlet on the old rules…
you know this is a crock piece of crap work the second you read a sentence like this:
“Markets, by their very nature, resist new ideas and products.” then it goes on saying despite this companies love it..
why would companies love something taht he says drive profits, growth, and sharholder value… but the market doesnt want, or like?
see why innovators cant innovate?
the administrators and the mediocre are now standing astride the doors of access, as in the soviet world…
ergo, why the invention show on tv that actually invents or shows new stuff that is not hoaky crappy novelty products is military and firearms.
this Harvard moron basically recurses from “markets are inimical to innocation because they crave equilibrium”…
no.. PLANNED ECONOMIES are like that…
and thats what he either thinks we have, internalized it, or wants it and so speaks from that position never pointing out that your argying with him predicates accepting collective central planning.
but how can he start such a paper and ignore the whole concept of disruptive technology? or how ATM machines pushed out people (but they were replaced mr president by people who make and install ATM machines).
neo ludditism, totalitarian administration, central planning, etc… permeates everything.
the individual inventor is nothing…
as now they want collective inventing…
the new idea to aquire ideas and not have to reward the individual with them is playing work games.
all that is, is a variation on brainstorming, which is a means of stealing ideas without rewarding someone for them… ie, transfer the individual merit to the group, regardless of a persons actual contribution, which in the arrangement is unmeasurable, and always critical…
a social game… get ideas, keep salaries down, manager takes credit for organizing the petri dish, and ignoring which actually produce the solutions
Companies have been using crowdsourcing to get large groups of outside volunteers to answer a question or perform a task, but now they are finding ways to crowdsource internally–by using games and contests that entice employees to generate, hone, and implement
this is how you get mediocre talent to be motivated more than just leaving and watching american idol
problem is that they watch them beat up on the capable too, and way before they are old, they have little motivation… (for fake reward).
so none of these things work, as their sole goal is to circumvent reward and acquire freebies.
which is why my work is not self published, as the second i do, someone else takes it, and i am erased just the same… but if i am going to be erased, i will not be so for the benefit of others. eh?
i have already experienced getting a $100 dollar reward and a stage presentation for saving 20 million dollars for a billion dollar insurance rates bureau.
when they later asked me how they could motivate others to make similar contributions. i said implement a 1% reward from savings attained…
this would naturally reduce the overall savings of the whole thing by only 1%… spending that money on a stage dog and pony show, a check, and a maybe an acrylic desk object… is not really motivational…
1% would have been $200,000
the reward was 0.05% of what 1% would be
and 0.0005% of the whole savings
Needless to say, people are not motivated by that kind of reward…
so, lets hear peoples suggestions where such special people can go and not be visited upon by predators and gatekeepers, and racist/gender/orientation apartheid revolutionaries for the cause…
J.J. formerly Jimmy J.,
“The unfortunate thing is that after climbing the Mt. Everest of mathematics, there is no childhood dream left to work toward for Dr. Wiles.”
Or for anyone at all, for that matter. It’s telling that the areas of math I find most interesting are those that any mathematician would tell you have been done to death and hold nothing new to discover. For example, number bases. (Yes, that can be practical: using a number base that doesn’t render 1/3 as recurring digits can be a great boost to various practical applications–you no longer avoid thirds to keep the numbers tidy.)
Parker,
“Theoretical math is important to society.”
I didn’t say it wasn’t, I only said I’m not partial to it.
The purely theoretical mathematical-logical exercise of George Boole, of reducing every logical proposition to a set of true/false answers, was in his day considered nothing but leisurely philosophy. However, when Claude Shannon showed how Boole’s binary algebra could be used for implementing electronic circuits, it became the basis of all the digital technology we now use.
The trouble is, you can never know which theoretical exercise will result in a technological leap. You’re thus compelled to fish for research and hope that something will arise. Even then, managerial ineptitude could make it all for nothing, like notoriously the way Xerox failed to follow up on their slew of innovations in the PARC project (such as the Ethernet card and the graphical user interface), leaving it to outsiders who lacked the blinders.
Information theory is generally considered to have been founded in 1948 by Claude Shannon in his seminal work, “A Mathematical Theory of Communication”.
that’s MY favorite… been abstracting professionally for around 30 years…
and would love to show all the things that i have found over that time and alone
but again, the bigger question is not whether smart people in the US can solve problems, they can. that is a given over time and knowing a need…
the problem is what do you do with it after your done? a poem never read, a painting never seen, a solution never heard…. then what?