Hard Problems at MSRI

I am here at the Mathematical Sciences Research Institute for the northern California premier of Hard Problems, a documentary about the Math Olympiad.

Quotes from the movie I thought were particularly good

1.  The subject of math rather than just the random facts I was taught in school
2.  Math is more of exploration than knowledge
3.  You cant really do math emotionally, that doesn't make sense.
4.  Math doesn't have to be straight out of the book,
5. For a really cool problem you can explain how its really cool without having to get in the gritty details, I think math is like that it speaks for itself its very beautiful.
6. I have a little bit of a distaste for schools.
7. I have this theory that the smarter a mathematician is the better a mathematician is, the less they like to work.... I don't know if its true, I haven't asked enough mathematicians
8. I don't do mathematics because its mathematics. I do it because of the astounding connections and creativity it allows (ending line, one I think that is very incisive about the nature of mathematics

And now, onto the Q&A panel.
7:05  Two interesting threads, the moderator brings up, the one about what the IMO is and questions about the IMO and then also about how to bring more people into the IMO and increase higher mathematics training, however, the question i find interesting, and want to hear about, is instead how we can take the lessons gained from the higher level math education to get better math education around the board not just for those kids gifted with math talent, but to increase math education overall.

7:15 Zvezdelina Sankova puts on an interesting presentation about the Berkeley math circle, it seems like a great way to teach math, why don't we adapt a math circle setup to teach math to all children?

7: 20 Melanie makes a great point on how most of the students who do the IMO have seen some exciting math whereas moth high school students have not seen any interesting math.

7:25 Competition aspect is an important hook. "competitions were the venue in which I learned that there was interesting math"

7:40 Guy behind me comments on how the math circles helped him teach and make better, Zvezdelina makes a point about how the BMC was supposed to me a trail program, and that the allocation of resources is making it happen at colleges and universities, not schools.


7:50 some douchebag in the back asks 4 annoying questions, I hope he dies in a fire.

7:50 Ryan makes a good point about how people are not exposed to interesting math problems.

7:55 I get a question in on the first quote in the list, Zevezdelina talks about how the math circle gives the problem first then develops the tools to solve it rather than just give students the tools of mathematics with no context rhyme or reason.

ill distill this into some final thoughts when I get home.

Mathematics of Steallar Death

Applied Mathematicians and Astrophysicists at Lawrence Berkeley National Laboratory have recently created a simulation of the last few hours of a white dwarf star leading up to a type 1a supernova. regular readers (ha, check it out, I made a funny) may remember me blogging about type 1a supernova earlier in the month. So I felt some obligation to post this awesome new finding about them.

For years type 1a supernova have been a standard candle for astrophysicists because it is theorized that they all blow up the same way, however, we have until now, a good computational simulation of the creation of type 1a supernovas has seemed intractable, which begged the question, "do they really all blow up the same way? if we cant simulate it, perhaps they don't..."

But, Mathematics once again came to the rescue as applied mathematicians Ann Almgren, John Bell and Andy Nonaka of Berkeley Lab's Computational Research Division,  developed MAESTRO, a simulation code of the problem. The real genius behind MAESTRO was to strip out the sound waves making the problem much more efficient and able to run on modern day supercomputers like the Jaguar, the Cray XT4, one of the worlds most powerful supercomputers.

read the full article Here at Science Daily.

Criminally Boring, A Rant About Math Education.

For years I assumed that, over time, I would get less and less angry with my high school math teachers. I was wrong. Instead, as it turns out, the massive failure of high school mathematics education serves as a constant pit of fury that I can call on anytime I need (especially when people say they hate/are bad at math, I'm convinced it stems from terrible education into what the subject is...).


Why do I harbor such rage? because it would be inconceivable to not be furious at the grand scale of the failure. When I ask people why they hate math, the most frequent response is that it is 'boring'. And, while I disagree to the utmost, I understand where they are coming from. The fact is mathematics is perhaps the most poorly understood subject by its teachers and the population at large. I was lucky to have a father who cultivated my interest in mathematics at a young age, but even so, as I left high-school I had become convinced that math is boring, a dull subject populated by endless formulae that are applied in an arcane seemingly random manner.


But mathematics is far far greater than I was led to believe from how terrible my teachers were. Mathematics, the study of relationships between objects truly is the queen of the sciences.  As I started college and realized that Electrical Engineering, my chosen major, would give me no chances to take any non engineering classes, distraught over this prospect, I decided I needed to change majors, but I had no clue what to change to, then my father gave me two books to read, The Man who Knew Infinity and The Man Who Loved Only Numbers, Reading these, my eyes were opened to the true beauty of mathematics, I saw what my high-school teachers so failed at imparting, what mathematics is. It is the study of how objects relate to one another, regardless of what the object is. It is indeed the language of the universe, the noblest science.


And this, this is what they were able to make boring. I was dumbfounded, how could people in good conscience make such a beautiful and interesting subject boring. I could not understand, perhaps it was from laziness, or misunderstanding, or tiredness, but still, to take such a subject and make it boring should be a crime. The mathematical training of American high schools is downright criminal. Not only does it not grant the students even a shred of mathematical literacy and maturity, it makes them distrust and hate the subject. A subject full of beauty and wonder, a subject where even the most simple rules will lead you into bizarre worlds full of things to explore, and they, these villains that teach the subject have turned it into a cesspit of boredom for most of their students. How is this not a crime? If anything should be a crime should not turning something interesting and beautiful into something ugly and boring be a crime?

Best use of Lego's in the History of Mankind.

yes, its a Lego Turing machine, how sweet is that? and yet, more proof that lego are the most awesome toys.

I really don't have anything else to say, if you don't think this is totally awesome and sweet, well, I'm not sure if you are in the right place then.

Early computer to be brought back online.

The Harwell computer, the UK's third oldest computer is about to head down to bletchley park to be rebooted after 36 years idle.

Mr Barnes said the prospect of seeing the Harwell computer up and running after more than 36 years was "very exciting

indeed it is, computers have become so ubiquitous to modern life, tha it is easy for us to forget how modern they are, and we often forget those early pioneers into computing technology that has created the modern era. its nice to see these great early computers starting up again to remind us how far we have come, now that we seem to be sitting on the cusp of the quantum computing revolution.

read more here

Crypto-Human Interest.

So I wanted to share a fun story with Two Centuries On, a Cryptologist Cracks a Presidential Code

However, I think this article really misses a opportunity to explain the importance and nature of cryptography and misses some very important points of how cryptography matters to our daily life as opposed to being just the playthings of presidents and friends as a exercise for the mind.

the very nature of our modern lives is build on a foundation of cryptography. all modern financial systems rely on the strength of modern cryptography. and modern cryptography is very goddamn strong. and quantum cryptography is unbreakable.

The code-breaking effort the allies unleashed in WWII is one of the greatest stories of ingenuity, hard work and very possibly more than any other factor, defeated the axis powers.


All online purchases rely on the modern public-key system for encryption, one that cannot be attacked like we would attack enigma, we know how the system works, without the key to find what you needed to decrypt the message would take all of the computers on earth working non-stop for thousands of years. I think to sell cryptography short is to fail in your responsibility to educate the public, and the fact that they spent time talking about simple substitution cyphers but don't mention the massive impact crypto plays in our day to day life is intellectually disingenuous.

None-the-less, by the current standard of media and what sort of job we can expect the 4th estate to do on our behalf(a terrible one) it is a fun article, that you should read.

Great Quantum Turing Machine Batman!

Ah, dear reader, It has been a while, not that time particularly matters to you, what with the whole not-existing thing you got going on, not that I blame, you, its not like I update this thing with any regularity, although I would like to change that... and with that note, lets get down to the entry....


So, while i was living in that terrible cess-pit known as the world sans internet I had time to read Programming the Universe by Seth Lloyd. This book is a must read for anyone who is interested in computability and the world as we understand it. Following up in the tradition of Wolfram's A New Kind of Science and Rucker's The Lifebox, the Seashell, and the Soul(which i cant recommend highly enough) Programming the Universe is an exploration of what information science and the mathematical underpinnings of computation mean to how the world works and how to explain the universe in terms of a new physical entity (information) that must be considered when trying to understand what base forces and rules control and manage the universe.

However, Lloyd, a leading researcher in quantum computing, takes an interesting approach viewing the universe as not merely something that can be imitated by any old Universal Turing Machine, but rather, the universe is a giant quantum supercomputer that is constantly computing itself.

This is a elegant way around dealing with the problem of Chaos theory and quantum interaction that plagues most attempts at determinism by Universality of Turing machines. Chaos theory showing that if our measurements are even just a tiny bit off from the real value of the event we are measuring it would be impossible to predict its course, and the quantum interference that puts a minimum bound on how precise our measurements or even any measurements can be.

Lloyd also makes a very interesting point about entropy, viewing entropy as an increase in information, an increase in all those bits, that make up the universe as a complete and wonderful whole. is i think particularly thrilling,

Furthermore, Like Rucker's Work, Lloyd's work reads like a great lecture, anticipating questions and givng a phenomenal overview of the theory and its consequences. I give this book my highest recommendation. It is a fascinating read and has shaped the way I personally, understand the fundamental forces and interactions of the universe.

Solution to Problem 2 of Project Euler

My solution to problem 2 was done shortly after solving problem 1, so you can see the progression of my Scheme programming, still not as sharp as it could be, (and I didn't even try to explore the interesting mathematical attacks on the problem, I'm still using the problems as exercises in coding and not yet looking at them as math problems, something I imagine I wont be able to keep up for long...

(define (fib n)
  (fib-iter 1 0 n))
(define (fib-iter a b count)
  (if (= count 0)
      b
      (fib-iter (+ a b) a (- count 1))))
(define (fib< n)
  (fib<-iter n 1 empty))
(define (fib<-iter n count l)
  (cond ((> n (fib count)) (fib<-iter n (+ count 1) (cons (fib count) l)))
        (else l)))
(define (euler2 n)
  (euler2-iter (fib< n) 0))
(define (euler2-iter l sum)
  (cond ((not (empty? l))
      (cond ((even? (car l)) (euler2-iter (cdr l) (+ (car l) sum)))
            (else (euler2-iter (cdr l) sum))))
        (else sum)))

then I call the function by (euler2 4000000)

Code for My Solution the the First Euler Problem

This was basically the first scheme program I have ever written and the first program i have written in about 4 years, so yes, I know the code is very sloppy...

(define (testdiv n f)
  (cond ((= (remainder n f) 0) 1)
        (else 0)))
(define (buildlist n m)
  (cond ((> n 0) (buildlist (- n 1) (cons n m)))
        ((= n 0) m)))
(define (test2div n f1 f2)
  (cond ((= (testdiv n f1) 1) n)
        ((= (testdiv n f2) 1) n)
        (else 0)))
(define (euler1 n f1 f2)
  (cond ((not (empty? (cdr n))) (+ (test2div (car n) f1 f2) (euler1 (cdr n) f1 f2)))
        (else (test2div (car n) f1 f2))))

It worked but due to the fact that its been 2 weeks since I wrote it and the code is ugly as hell I cant for the life of me remember how I call it. sure, I could probably figure out how, but if I had any desire to go back to this problem I would almost certainly scrap this and rewrite the code entirely..

A bit of a change of pace...

Well its been a while, a while since you, oh non-existent reader and i sat down here on this masturbatory exercise of a blog and had a catch up and the obligatory change of pace.

So, to start, lets get caught up. I am enjoying myself in Oakland, have a nice new apartment and a job that while is not great affords me time to think, Time to study, Time to relax. In that time i have started working on getting my math up to par, to this end I have begun some slight work on the Project Euler problems. to accomplish this I have begun to learn the programming language SCHEME. I have started this by working my way though MIT's "Structure and Interpretation of Computer Programs".To that end i will be posting here my solutions to both the exercises of that book and the Project Euler problems.