My third meeting with Cris …
- The Way of Discovery Math: Cris highlighted again that it is important to distinguish the following two aspects in mathematics, i.e. presenting mathematical results and actually discovering mathematical results. He said, if I want to really understand mathematical practice, I need to follow and analyse the second aspect. In his lectures, Cris is trying to teach his students how to discover math, but this is indeed difficult, he says. For example, he is intentionally presenting them several wrong definitions before finally concluding with the correct definition. Even in one of his paper, Cris et al. successfully published several wrong definitions (before introducing the correct one) of a non-deterministic automata, although the reviewers first wanted them to “remove the rubbish”: C. S. Calude, Elena Calude, B. Khoussainov. Finite nondeterministic automata: Simulation and minimality, Theoret. Comput. Sci. 242, 1-2 (2000), 219-235. He also pointed me to the books of George Polyá, in particular, Mathematics and Plausible Reasoning. Further Cris said that if we train (young) researchers we have to teach them “to have the guts to not be afraid to be wrong“. And then he said: “The productivity of a PhD is 5%, 95% is failure” and this is almost the same situation for professional mathematicians (besides some genius), who do not continuously produce correct and beauty proofs and theorems.
- An assessment system for mathematical knowledge: Cris said that my proposal is still to vague and abstract to be understood by other scientists. He made an example to illustrate that I should work on my presentation of new ideas (freely cited, not his actual words): “When I present my view to solve a mathematical problem I need to include to things: (1) I need to provide a number of concrete steps towards the solution, i.e. first I proof this, then I proof this, … and I have to point to the basic methods I will be using, e.g. I’ll use graph theory rather then topology. (2) I need to point to my previous accomplishments, i.e. some steps I have already addressed. Then people will accept it more likely.” Cris also said, that for the existing achievements, I do not necessarily have to provide my own work, but I can point to existing research and that will increase my acceptance. So what I will do for my seminar talk is, to put more emphasis on the methods and related work part. And I will use many examples to illustrate my approach. I will have a look at Cris GoogleTalk again. However, in general, Cris thinks that this could be interesting. Actually he believes that 90% of all published mathematical proofs are either incorrect, incomplete, or uninteresting. “Having over 100.000 published a year, how are can you still find your way without any guidance? You have the expertise in your small community, but as soon as you have to rely on work outside your field, you have to trust the expert.“
I also met interesting people today, I am eager to talk to further. And I’ll get a chance tomorrow, as there is the “end of the lecture party”.
- Emilia Mendes expert is web development.
- André Nies mathematician
- Brian Carpenter (haven’t met him, but will soon). Cris recommended me to read his A Dialogue on the Internet, published in Bulletin of the European Association for Theoretical Computer Science (2008)