onsdag 15 februari 2012

The Death of Numerical Analysis

Archimedes 212 BC: Don't disturb my circles.

When I started my studies in the mid 1960's, Numerical Analysis NA was emerging as a new academic discipline developed by mathematicians attracted by the new capabilities of the electronic computer.

New departments of NA were formed outside departments of mathematics, as NADA at KTH by Germund Dahlquist, at Chalmers by Heinz-Otto Kreiss followed by Owe Axelsson, and in Uppsala again by Kreiss, while my former supervisor Vidar Thomee introduced mathematical NA at the mathematics department at Chalmers.

NA boomed and gave birth to new departments of computer science.

After finishing my Ph D with Vidar Thomee at the mathematics department and a post doc at the University of Chicago, I joined NA at Chalmers and when Owe Axelsson left in 1981 I had the chance to take over after him, but also a chance to return to the math department. I chose math and Axel Ruhe took over NA.

In the early 1990s NA was incorporated by math at Chalmers and when Axel Ruhe left Chalmers 10 years later, the life of NA at Chalmers was over. Today only a few residues of NA remain, and NA courses are no longer taught; they were simply assimilated into math courses without leaving any trace since the math courses are the same as before the computer. NA was born from math into a life outside math and now returned to math to die, as if nothing ever happened.

The development is similar at other universities in Sweden: NA first boomed but then lost momentum as we entered into the information age of 21st century ultimately based on NA.
It seemed as if NA became so widely used that there was no longer any need for any NA education.

The pillar of the old NA empire, NADA at KTH, is now meeting the same fate by being moved from its home at computer science to a mathematics department untouched by the computer.

Dahlquist managed to keep NADA outside mathematics, which allowed NADA to grow but when Dahlquist passed away the momentum was lost, and when now NA is being captured by mathematics, it has to face the same reality as NA at Chalmers (and Lund, Linköping, Umeå...).

The same is happening at the University of Chicago, where NA flourished within the math department in the 1970-80s under Jim Douglas Jr and Todd Dupont, while today NA faces extinction within computer science and math is again pure math without any NA.

Why is then NA dying when information science based on NA (like Googles search engine, imaging, simulation) is rocketing to the sky? If it is not eaten by math, computer science cleans the table.

When I look at the NA courses of today at NADA I see courses which are basically the same as those I met as an undergraduate almost 50 years ago: a bit of interpolation, Dahlquist stability and Gaussian elimination.

I see a petrified NA which is no longer fit for survival in the fierce competition of resources and students at the university of today, between math and computer science.

Old NA is dead and New NA is jet to be born, outside or inside mathematics departments.

Mathematics departments are in desperate need of revitalization by computational mathematics, but it seems that this hole cannot be filled with Old NA.

What may then New NA be? My (partial) answer is Mathematical Simulation Technology, but there are many other (possible) answers...

Test: Alive or Dead?

NA at KTH is in charge of the new Bachelors program in Simulation Technology scheduled to start in the Fall. This week NA will decide if this plan will be followed or the if the program will be shut down. Application opens March 15 and ends April 15. No publicity for the program has been made since the first announcement on Dec 1, 2011.

If NA is capable of upgrading to meet the requirements of the new program, then NA still has some life.

If NA decides to shut down the program, then NA is already dead.

I will report on the status as soon as the decision is made public.

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