Arsen Ivanov

It seems to me that the greatest problem with science and engineering is that of courage.

People seem to lack courage to achieve. To achieve often means to take calculated risk, to put yourself and your reputation on the line. So, many people choose not to achieve because they are more scared of being wrong than of being right and not saying it. Many avoid difficult problems in science, because they would rather fail at solving the problem by default rather than maybe, just maybe, solving it.

You have to wonder if Einstein would create Relativity if he would be afraid of being wrong. Actually, I think that because he was just a government clerk, he had nothing to loose, and that is why he came up with the idea in the first place. After all, when he became a sort of international science superstar, he never produced anything new again on the same scale. He solidified Relativity, sure, but no new groundbraking ideas came from him. Maybe it was because he tried and failed - like with Unified Field Theory - or maybe he did not try at all, because he was afraid of failing. I do not know. Unfortunately, I am not as familiar with his biography to give a conclusive opinion on this example.

The best analogy I can come up with is one of a good boxer, who knows he is good, who knows he has good chances to win championship, but who doesn’t compete for fear of being beaten. Can you be beaten? Sure! Can you win also? Yes! So, should the possibility of being beaten deter you from trying to win a difficult bout? Absolutely no!

The stereotype is that research is something very abstract, done by people not concerned with reality.

Maybe, research is a theoretical, abstract activity, but it is very reality-based. Research is a business — you compete with your peers in the field for money, for position of being 1st or 2nd or 3rd most-cited author in the field etc. You compete with the researchers who work on the same problem as you. You compete with them for the title of being the first to discover the new solution - with benefits not only being titular, but also monetary. The person who is the top dog, gets the top research-funding dollar.

In this way it is easy to see how researcher, or group of researchers, are essentially engaged in “idea” entrepreneurship. The goal is to:

1. find a problem that matters to people; If nobody cares about what you do, nobody will fund your work.

2. find solution that is useful to people; People want results.

3. be the first to do so. Only then the benefits come.

Let the most competetive win!

Is mathematics a consistent and rigorous system? Or is it an fundamentally intuitive system of abstract ideas describing the physical world?

According to Kurt Gödel’s Incompleteness Theorem, all “precise” knowledge is founded on at least one axiom — a fact accepted on faith, without logical proof. From this follows, that no matter how hard mathematicians might work, they will never achieve a perfect , logically consistent mathematical system. 19th Century has seen proliferation of various geometries — such as Lobachevsky-Bolyai-Gauss Geometry, Riemann Geometry, and Spherical Geometry, all proven to be as consistent well-founded in real world as the Geometry of Euclid. So, is there a true Geometry out there? Are all those mutually exclusive systems of geometry equally correct? I think so.

In my view, mathematics is not a precise science. Herman Weyl has, for instance, stated that perhaps mathematics might be as much a creative activity for man as “language or music.” Mathematics is a tool to understand the physical world, as much as painting or music are tools to understand the world of emotions.

The raw material of any useful activity is the fresh and ready mind. There is nothing you can do, when your mind is tired and heavy. Unfortunately, men are not machines, and everyone who is truly serious about doing serious work, have to grasp this concept.

I am not suggesting that people should work less. By no means, NO! My point is that work cannot be possible without rest, that to rest properly and efficiently should be viewed as preparation for productive work. One must prepare for work by resting sufficiently for work to be fruitful.