Category Archives: Math

Thompson and Tits share 2008 Abel Prize (Math)

Thompson and Tits share the Abel Prize for 2008

John Griggs Thompson, Graduate Research Professor, University of Florida, and Jacques Tits, Professor Emeritus, CollÃ¨ge de France, have been awarded the 2008 Abel Prize “for their profound achievements in algebra and in particular for shaping modern group theory.” In the prize citation, the Abel Committee writes that “Thompson revolutionized the theory of finite groups by proving extraordinarily deep theorems that laid the foundation for the complete classification of finite simple groups, one of the greatest achievements of twentieth century mathematics.”

In 1963, Thompson and Walter Feit proved that all nonabelian finite simple groups were of even order, work for which they both won the Frank Nelson Cole Prize in Algebra from the AMS in 1965. Thompson also won a Fields Medal in 1970. In the Abel citation for Tits, the committee writes that “Tits created a new and highly influential vision of groups as geometric objects. He introduced what is now known as a Tits building, which encodes in geometric terms the algebraic structure of linear groups.” The committee noted the link between the two winners’ work: “Tits’s geometric approach was essential in the study and realization of the sporadic groups, including the Monster.” Tits received the Grand Prix of the French Academy of Sciences in 1976, and the Wolf Prize in Mathematics in 1993.

The Abel Prize is awarded by the Norwegian Academy of Science and Letters for outstanding scientific work in the field of mathematics. The prize amount is 6,000,000 Norwegian kroner (over US$1,000,000).

Offering Residency to Foreign Engineers and Scientists

Rep. Lofgren wants residency for foreign engineers

Foreign-born engineering, science, and math students in the United States should be automatically granted legal residency when they get a job in this country, said California Congresswoman Zoe Lofgren.

Lofgren, a Democrat, spoke to an audience Friday at the Joint Venture: Silicon Valley conference about threats to innovation in the area. She said that about 56 percent of the Ph.D. candidates at the finest schools in the United States are immigrants, and because of the government’s current immigration policy, many of those people leave the country.

I support such legislation. I also think it is only one, of many measure to take to encourage science and engineering excellence (which will in turn help the economy). I have no doubt that other countries are going to be successful establishing their own global centers of excellence and attract scientists and engineers from around the world: including from the USA. The Curious Cat Science and Engineering Blog now includes a tag cloud on the right side of our home page, tags for this post include: government and economy.

The Mystery of the Voynich Manuscript

image from the Voynich manuscript

A fun read – The Mystery of the Voynich Manuscript:

Voynich asked the leading cryptographers of his day to decode the odd script, which did not match that of any known language. But despite 90 years of effort by some of the world’s best code breakers, no one has been able to decipher Voynichese, as the script has become known. The nature and origin of the manuscript remain a mystery. The failure of the code-breaking attempts has raised the suspicion that there may not be any cipher to crack. Voynichese may contain no message at all, and the manuscript may simply be an elaborate hoax.
…
This study yielded valuable insights into the process of reexamining difficult problems to determine whether any possible solutions have been overlooked. A good example of such a problem is the question of what causes Alzheimer’s disease. We plan to examine whether our approach could be used to reevaluate previous research into this brain disorder. Our questions will include: Have the investigators neglected any field of relevant expertise? Have the key assumptions been tested sufficiently?

Dr Gordon Rugg at the Department of Computer Science Keele University – Replicating the Voynich Manuscript

Related: Scientific Method Man – The medieval Voynich Manuscript – in the language of the angels…. or a hoax? – Ancient Greek Technology 1,000 Years Early – Prayer Book Reveals Lost Archimedes Work Studying Ideas at Heart of Calculus – Seeing Patterns Where None Exists

Who Killed the Software Engineer?

Computer Science Education: Where Are the Software Engineers of Tomorrow? by Dr. Robert B.K. Dewar and Dr. Edmond Schonberg

Over the last few years we have noticed worrisome trends in CS education. The following represents a summary of those trends:
1. Mathematics requirements in CS programs are shrinking.
2. The development of programming skills in several languages is giving way to cookbook approaches using large libraries and special-purpose packages.
3. The resulting set of skills is insufficient for today’s software industry (in particular for safety and security purposes) and, unfortunately, matches well what the outsourcing industry can offer. We are training easily replaceable professionals.
…
As faculty members at New York University for decades, we have regretted the introduction of Java as a first language of instruction for most computer science majors. We have seen how this choice has weakened the formation of our students, as reflected in their performance in systems and architecture courses.
…
Every programmer must be comfortable with functional programming and with the important notion of referential transparency. Even though most programmers find imperative programming more intuitive, they must recognize that in many contexts that a functional, stateless style is clear, natural, easy to understand, and efficient to boot.

An additional benefit of the practice of Lisp is that the program is written in what amounts to abstract syntax, namely the internal representation that most compilers use between parsing and code generation. Knowing Lisp is thus an excellent preparation for any software work that involves language processing.

This is an excellent article: any CS students or those considering careers as programmers definitely should read this. Also read: Computer Science Education.

via: Who Killed the Software Engineer?

Dewar, a professor emeritus of computer science at New York University, believes that U.S. colleges are turning out programmers who are – there’s no nice way to say this – essentially incompetent.

Bigger Impact: 15 to 18 mpg or 50 to 100 mpg?

This is a pretty counter-intuitive statement, I believe:

You save more fuel switching from a 15 to 18 mpg car than switching from a 50 to 100 mpg car.

But some simple math shows it is true. If you drive 10,000 miles you would use: 667 gallons, 556 gallons, 200 gallons and 100 gallons. Amazing. I must admit, when I first read the quote I thought that it must be an wrong. But there is the math. You save 111 gallons improving from 15 mpg to 18 mpg and just 100 improving from 50 to 100 mpg. Other than those of you who automatically guess that whatever seems wrong must be the answer when you see a title like this I can’t believe anyone thinks 15 to 18 mpg is the change that has the bigger impact. It is great how a little understanding of math can help you see the errors in your initial beliefs. Via: 18 Is Enough.

It also illustrates that the way the data is presented makes a difference. You can also view 100 mpg as 1/100 gallon per mile, 2/100 gallons per mile, 5.6/100 gpm and 6.7 gpm. That way most everyone sees that the 6.7 to 5.6 gpm saves more fuel than 2 to 1 gpm does. Mathematics and scientific thinking are great – if you are willing to think you can learn to better understand the world we live in every day.

Playing Dice and Children’s Numeracy

My father, Willaim Hunter, a professor of statistics and of Chemical Engineering at the University of Wisconsin, was a guest speaker for my second grade class (I think it was 2nd) to teach us about numbers – using dice. He gave every kid a die. I remember he asked all the kids what number do you think will show up when you roll the die. 6 was the answer from about 80% of them (which I knew was wrong – so I was feeling very smart).

Then he had the kids roll the die and he stood up at the front to create a frequency distribution of what was actually rolled. He was all ready for them to see how wrong they were and learn it was just as likely for any of the numbers on the die to be rolled. But as he asked each kid about what they rolled something like 5 out of the first 6 said they rolled a 6. He then modified the exercise a bit and had the kid come up to the front and roll the die on the teachers desk. Then my Dad read the number off the die and wrote on the chart 🙂

This nice blog post, reminded me of that story: Kids’ misconceptions about numbers — and how they fix them

in the real study, conducted by John Opfer and Rober Siegler, the kids used lines with just 0 and 1000 labeled. They were then given numbers within that range and asked to draw a vertical line through the number line where each number fell (they used a new, blank number line each time). The figure above represents (in red) the average results for a few of the numbers used in the study. As you can see, the second graders are way off, especially for lower numbers. They typically placed the number 150 almost halfway across the number line! Fourth graders perform nearly as well as adults on the task, putting all the numbers in just about the right spot.

But there’s a pattern to the second-graders’ responses. Nearly all the kids (93 were tested) understood that 750 was a larger number than 366; they just squeezed too many large numbers on the far-right side of the number line. In fact, their results show more of a logarithmic pattern than the proper linear pattern.

New Theory of Everything

Surfer dude stuns physicists with theory of everything

An impoverished surfer has drawn up a new theory of the universe, seen by some as the Holy Grail of physics, which as received rave reviews from scientists. Garrett Lisi, 39, has a doctorate but no university affiliation and spends most of the year surfing in Hawaii, where he has also been a hiking guide and bridge builder (when he slept in a jungle yurt).
…
Despite this unusual career path, his proposal is remarkable because, by the arcane standards of particle physics, it does not require highly complex mathematics. Even better, it does not require more than one dimension of time and three of space, when some rival theories need ten or even more spatial dimensions and other bizarre concepts. And it may even be possible to test his theory, which predicts a host of new particles, perhaps even using the new Large Hadron Collider atom smasher that will go into action near Geneva next year.
…
Although the work of 39 year old Garrett Lisi still has a way to go to convince the establishment, let alone match the achievements of Albert Einstein, the two do have one thing in common: Einstein also began his great adventure in theoretical physics while outside the mainstream scientific establishment, working as a patent officer, though failed to achieve the Holy Grail, an overarching explanation to unite all the particles and forces of the cosmos.

Now Lisi, currently in Nevada, has come up with a proposal to do this. Lee Smolin at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada, describes Lisi’s work as “fabulous”. “It is one of the most compelling unification models I’ve seen in many, many years,” he says.

Actual open access paper: An Exceptionally Simple Theory of Everything by A. Garrett Lisi
Reactions: A Theoretically Simple Exception of Everything – Upon further review, surfer’s new Theory of Everything severely deficient
Related: String Theory – CERN Pressure Test Failure – Webcasts by Chemistry and Physics Nobel Laureates

Math and Science Education Assessment

Science Friday podcast (NPR radio programming) on the urban institute study mentioned a few weeks ago in: The Importance of Science Education.

Conventional wisdom says that U.S. students don’t measure up well against students in many foreign countries when it comes to math and science skills. But is that really true? A team of researchers have re-assessed the results of several common measures of science education success, and they say the true picture may not be as gloomy as some analysts have said.

“When it comes to math and science, American students are no worse, and often score better, than students from many leading countries,” said Harold Salzman, one of the authors of the new Urban Institute report “Into the Eye of the Storm: Assessing the Evidence on Science and Engineering Education, Quality, and Workforce Demand.” The researchers argue that some of the rankings produced by measures such as the Trends in International Mathematics and Science Study (TIMSS) are due to statistically insignificant differences in scoring.

Read the actual report – Into the Eye of the Storm, Assessing the Evidence on Science and Engineering Education, Quality, and Workforce Demand by B. Lindsay Lowell, Harold Salzman.

The Simplest Universal Turing Machine Is Proved

The Prize Is Won; The Simplest Universal Turing Machine Is Proved:

And so as part of commemorating the fifth anniversary of A New Kind of Science on May 14 this year, we announced a $25,000 prize for determining whether or not that Turing machine is in fact universal. I had no idea how long it would take before the prize was won. A month? A year? A decade? A century? Perhaps the question was even formally undecidable (say from the usual axioms of mathematics).

But today I am thrilled to be able to announce that after only five months the prize is won–and we have answer: the Turing machine is in fact universal! Alex Smith–a 20-year-old undergraduate from Birmingham, UK–has produced a 40-page proof.

Vaughan Pratt Standford CS professor, disputes the proofs validity.

Computational Science and Engineering by Gilbert Strang

New book, Computational Science and Engineering by Gilbert Strang, is available. The website includes some sections of the book. Video Lectures of Gilbert Strang on Linear Algebra, Spring 2005.