Theoretical Computer Science

(A kind of professional confession, mini observations, not a scientific study.)

Is a math field I am fan of. It's a field where you can be an engineer and an artist at the same time. It is an excellent modern success story for the old business started by grandpas Euclides, Pythagoras, Archimedes and co. Let me explain briefly:

• One gets in touch with math behind computers every day: searches the web (freshmen linear algebra), listens to the mp3s (sophomore linear algebra inspired by some analysis and complex numbers), uses the DVDs with error correcting codes (advanced linear algebra again: finite fields and polynomials) or encrypts his bank orders (again, not so advanced algebra). I omit many many other occasions..
• "Computers" outpaced "physics" and competes with "fields around finances" in motivating the math research. My guess is they are number one.
• Unlike materialized computers themselves, the theory behind them is elegant and beautiful: It intersects most of the classical math fields (that were often developed without a slightest dream of computers, and advent of computers has given them a new meaning, what a postmodern art) and many of its important results exhibit diversity and freshness of ideas.
• I want to avoid researching in well established (and possibly important) fields of mathematics, where the state-of-the-art cannot be understood by anybody else than experts. I prefer spending half of my time searching for new coming questions, answering which is of higher relevance (namely because the answer can be understood). Theoretical computer science offers many such questions.
• There is the fabulous P versus NP problem in the heart of the theoretical computer science. It can be explained to high school students (unlike the Riemann hypothesis), has a huge importance (unlike the Fermat last theorem) and is the biggest frustration of the current mathematics: the state-of-the-art seems to be not much further than the "high school level of understanding". An interesting link (not for complete outsiders): http://www.cs.umd.edu/~gasarch/papers/poll.pdf

The previous might sound like TCS is a science utopia. Of course, I can share some negative impressions as well:

• The level of rigorousness of papers (and books) is rather poor compared to other math. As a consequence, there are serious mistakes in them very often or, at least, the papers are difficult to understand. This might be consequence of the fact that many (despite very clever) theoretical computer scientists were trained rather in programming than in general mathematics during their undergraduate studies. In addition, in TCS, publishing papers is rewarded with quite attractive travelling for conferences, (in other math the travelling is rather independent) so TCS people are more motivated to publish papers as frequently as possible at the expense of mathematical quality (that is time costly and its lack is not obvious at first glance).
• There is more hypocrisi in TCS than in other mathematics: often people just make up fake applications of their result in the introduction of their paper to make it look more attractive. Also they sometimes try to use fancy mathematics just because it is fancy mathematics.