Julia Robinson's 100th birthday

the age of 65 on July 30, 1985).

So time for some facts about her

1) She got her PhD from Tarski on the undecidability of the theory of the rationals.

2) She is probably best known for her work on Hilbert's tenth problem (which we call H10)

In todays' terminology H10 would be stated as:

Find an algorithm that will, given p in Z[x_1,...,x_n] determine if it has an integer solution.

Hilbert posed it to inspire deep research in Number Theory. There are some cases that are

solvable (the topic of a later blog post) but the general problem is undecidable. This is not what Hilbert was aiming for. I wonder if he would be happy with the resolution.

The Davis-Putnam-Robinson paper showed that the decision problem for exponential diophantine equations was undecidable. It was published in 1961. The paper is here.  Martin Davis predicted that the proof that H10 was undecidable would be by a young Russian mathematician. He was proven correct when Yuri Maityasevich supplied the missing piece needed to complete the proof.  

I often read `H10 was resolved by Davis-Putnam-Robinson and Maityasevich' or sometimes they put all four names in alphabetical order. I like that--- it really was a joint effort.

3) She was inducted (a proof by induction?) into the National Academy of Sciences in 1975.

4) She was elected to be president of the American Math Society in 1982.  

5) She got a MacAuthor Fellowship prize in 1985 (Often called the MacAuthor Genius award.)

At the time it was worth $60,000.  Its now $625,000.

6) She also did work in Game Theory.

7) The Julia Robinson Math Festival is named in her honor (hmmm- is that a tautology?) Its purpose is to inspire K-12 students to get involved in math. For more on it see here.