Mathematician solves algebra's oldest problem using intriguing new number sequences

[Jim__]

Is anyone familiar with Prof Norman Wildberger? He is a UNSW Honorary Professor. He used to produce math videos for the internet, for example, his History of Mathematics. Wildberger was well-known for his opposition to the use of infinity in mathematics. This paper is written by him and Dr Dean Rubine.

The problem is the solution of higher order polynomials.

An excerpt from phys.org

...

Prof. Wildberger's rejection of radicals inspired his best-known contributions to mathematics, rational trigonometry and universal hyperbolic geometry. Both approaches rely on mathematical functions like squaring, adding, or multiplying, rather than irrational numbers, radicals, or functions like sine and cosine.

His new method to solve polynomials also avoids radicals and irrational numbers, relying instead on special extensions of polynomials called "power series," which can have an infinite number of terms with the powers of x.

By truncating the power series, Prof. Wildberger says they were able to extract approximate numerical answers to check that the method worked.

"One of the equations we tested was a famous cubic equation used by Wallis in the 17th century to demonstrate Newton's method. Our solution worked beautifully," he said.

more ...

The full paper is open source and available here

[murielm99]

1. Why is he opposed to the use of infinity?

[Jim__]

2. I think he objects to the use of the actual infinite. My best attempt at a short answer to your question is that ...

... he doesn't believe that any actual infinite exists, and assuming the existence of actual infinities can lead to problems. He defends his position in this 42 minute video of a debate with another mathematician - it's been a long time since I watched this so I may have misstated his position..

[xocetaceans]

4. I am not sure that you have misstated his position. I am not sure that he ever specifies it exactly, but it seems...

...that his reasons have to do with the ability to carry out computations when dealing with "infinite" objects: e.g., transcendental numbers like pi and e.

Anyway, he is actually a great teacher and has put a lot of work into his online videos. I think that he tries and succeeds in meeting the students where they are and because of that his explanations succeed. His other online lectures that contextualize math and its history are also very nice.

It is great to see him and his coauthor succeed in this way.

Also, thanks for posting this. It is always nice to read good news.

[erronis]

3. Thank you. This will be a fascinating read. Mathematics - the language of the gods.

[BadgerKid]

5. Infinity is a concept though.

I don’t see why that’s a problem. I will have to look at the paper.

[Jim__]

6. I don't think this paper talks about infinity. It's about a generalized solution to polynomial equations.

In post #2 above there is a video where he talks about his objections to math's use of infinity.

[SCantiGOP]

7. Excuse me while I go to the Registrar's office

I’m dropping this thread for an easier one that I can understand.