On the power of a clear vision

“Are you sure you wanna do this?….” crushed into my head while I was sitting in the small and dark office of Mr. P. It was a warm und sunny day in July of 2000. I knew everybody else was outside enjoying the summer and the remainder was founding New-Economy startups and becoming both famous and millionaire over night.

It is more than 15 years ago now and still feels like yesterday. Actually I can see the scene right in front of me when I close my eyes. I am more the visual type of guy, but we will come to that later on.

“Yes” I pushed back boldly, “I’ll find Max O. – son of the incredible Dedekind and provide you with evidence proving his existence by end of this summer!” I committed myself to this quest, an endeavor of two months through dark, cold and stony fields while every body else was having fun. What the hell made me do that?

OK, if you didn’t get it by now, I am talking about my PhD thesis. And I committed myself to bring a detailed proof and an algorithm to provide maximal orders over Dedekind domains. Which is a topic from algorithmic algebraic number theory, it is mathematics. I promised my PhD advisor to submit my PhD thesis by the end of the summer break, which meant within the next two months. The question is still waiting to be answered: Why did I commit to this?

Usually it is uncommon within natural science to sell the result before you know a detailed proof. After all the answer is simple: It just felt right! I had a clear vision. It was my gut feeling telling me this is the result I can show. This will be the PhD thesis I will be able to submit. It will be a result I will be proud of because it has some beauty built into it. But how can this work out? My gut feeling presenting a crazy idea which I call vision? Shouldn’t a vision be based on structured deductive analysis? Fact based reasoning ad decently thought through?

Going back in time to July of 2000. It was a strange feeling. After months of research in the dark and outmoded academic library, reading through dusted books, reading back and forth concepts in different environments, old and new, the idea bloomed by itself. Today I know that this was not a coincidence. Studying the field in different environments allowed me to view this topic from different angles, to take different perspectives. This helped me to understand the commonality as well as the specialties of the various situations. This was the fundament of my understanding of the topic.

Allow you brain – you imagination to play with it and it will create ideas. In my case it was a picture. I literally saw how all the bits and pieces fit together and build up a huge colorful mosaic. This proves as well that I am a visual guy. Remember that I promised you also to deliver this proof.

With a vision you have the most powerful tool in your hands, it can be the ultimate turbo boost to achieve your goal. I had the vision for my PhD thesis. I saw it. I saw how the orders and the ideals, the radicals and the modules played together over the quotient field of their underlying Dedekind domain. – Sorry for that, I could not resist to put in these technical mathematical terms.

They formed such a beautiful picture that this must have been a vision. It was probably not the first vision I had in my life. But it was definitely the first one I realized. This vision gave me the strength to commit myself, to work hard on the details and submit my PhD by the end of the summer of 2000.

Was it a brainy vision or just a crazy gut feeling? Regardless of what you call it, it was not inductively derived, it was not a reasoned approach, I hadn’t had the proof for it all. Nevertheless – and this is my main point – it was based on extreme research and experience in the field. I did not come out of the blue.

A gut feeling or intuition is always based on strong experience and knowledge and created by your brain and not by your gut. If you are able to realize these feelings, to use your intuition that is a great skill.

Let your intuition build a vision. Visions are strong. If you have one your should use it. Share it with others and get them engaged. Try it out and enjoy.