Entrepreneurial activity requires a strong and strict methodical life-style, thus creative innovation and mathematical logic have to be combined for economic purposes, i.e. staying in the market means to creatively combine both mentioned sides of the same coin.

Entrepreneurial activity requires a strong and strict methodical life-style, thus creative innovation and mathematical logic have to be combined for economic purposes, i.e. staying in the market means to creatively combine both mentioned sides of the same coin.

This is really a nice question. I suggest that innovation and creativity are driven by a set of variables including intuition, luck and contingency. Mathematics and Logic are purely driven by formal rationality ....

@Stephen, i enjoy the point on process, method and systematics.

@Dieter, i would agree on intuition. I would also think that the intuition can be trained and advanced. I wonder whether mathematics and logic can contribute to this - developing intuition.

Entrepreneurship plain and simple is launching a new venture while taking on substantial risk of failure. Innovation on the other hand is developing something new, a product, a service, or a deploying a new business process.

Entrepreneurship requires being a risk-accepting person. Were entrepreneurs rational actors, entrepreneurship would not happen at the rate it does, because the likelihood of success is so low. Irrationality, i.e., gambling, or ignorance are what define the willing entrepreneur.

Creativity is not mutually exclusive with logic at all. Creativity is about making unexpected connections. Progress in the field of mathematics is predicated on creativity. You can make the case that physiology is the reason most mathematicians do their best work before 40 years old. Neuroplasticity is higher when younger. The ability to have creative insights is stronger when younger.

Now, in the business world, most innovation really isn't innovation in the sense of invention. It is about repurposing for finding a purpose for something that had been done before. I'll tell you a story:

Years ago I worked at Sendmail, Inc., a company founded by the inventor of the mail transfer agent, the program that moves an email from one network to another. The sendmail programming was (and is) part of the plumbing that made the Internet work, and why Eric Allman, its inventor while a graduate student at UC Berkeley, was recognized by the Smithsonian institution as a Hero of the Information Age. It was offering a version of the open source project of sendmail, the program, with a GUI and technical support for a license and support fee. Think the RedHat business model.

The market for MTAs was not great, but spam was becoming a big problem in the early 2000s. We did a licensing deal with another company called Cloudmark (neither of these companies exist anymore, having long since been acquired by competitors) in order to sell its product as an add-on to ours.

Cloudmark was founded by a guy who developed the razor open source anti-spam project. The two companies were having a party celebrating the partnership and I was talking with the founder of Cloudmark, Vipul Prakash, I said: "I think I know what you guys are doing with your SpamDNA (TM). You are defining a multidimensional space of features to detect spam, training it on samples of spam and good mail by incrementing each cell in the multidimensional space, then normalizing those frequencies by the sample size. The cells with the greatest proportion of spam get tagged as spam."

He says, "Oh, your read our patent."

I said, "No. It is something called a Skidmore-Turner classifier that has been around for 10 years."

I had applied a Skidmore-Turner classifier to the problem of ecological land classification (essentially what should grow where given equilibrium ecological conditions in a landscape) in a bit of research in 1992.

AI is really hot in industry right now. The thing is AI is mostly application of applied math research from the 1980s and 1990s that is only now finding applications to a broad range of problems. I was reading about research in unsupervised neural network classifiers applied to digital imagery back in the late 1980s.

It is the culmination of lots of very small advances in technology to make it viable for wide consumption. It is sort of like the essay I, Pencil. So many small operations go into making a pencil. Ditto, the computing infrastructures necessary to make the computations affordable and consumable on a large scale.

I can hardly coonect mathematics with creatvity...sorry

Good question. Maths is a language. The language is most effective when imagining a space as a subject of physics. Yet, we can imagine space under different subjects. A dominant and topical one is innovation.

We think about the right hemisphere for creativity, imagination and intuition and art and the left one for analysis, logics...

@Wassim, such thinking is of course limited and outdated. It is really about combining both. And creativity is not left side alone - there is right side to it too.

If we think of great mathematicians like Leibnitz (inventor of basic symbolic system of calculus), Euler and Poincaré (inaugurator and founder of topology), Galois (who demonstrated the impossibility of solution formula for algebraic equations of degree 5 or higher by introducing the concept of (algebraic) group), Gödel (who proved that axiomatic system of arithmetics is inevitably incomplete), and Hamilton and Pelerman (who solved 3-dimesion Poincaré conjecture by means of Ricci flow), many mathematicians were great entrepreneurs in mathematics. Hélas, it is very hard for mediocre mathematicians (like young me) to do an entrepreneurial research .

Yoshinori Shiozawa , i think these mathematicians were more innovative in solving problems experienced and observed, than innovative in mathematics per se. they mostly solved problems they encountered.

you find the same tendencies in mathematics as you see them in other disciplines too: The great universal scientists of former decades and centuries are not alive anymore. Instead, in recent times specialists dominate and govern the scenery who are strong in niches but who forget to discuss a general overwiew and the broader scenery, including innovative and entrepreneurial questions and answers.

Dieter Bögenhold Brian Barnard

In these days, it is inevitable that we are all specialists. The raison-d'être of academic SNS like ResearchGate may lie in the possibility to provides a forum open for all kind of specialists. We should try to do it.

Nevertheless you may distinguish between specialists being strong in details and generalists being strong in acknowledging the horizon, the historical development and interdisciplinary relations and other settings.

Dieter Bögenhold

Richard S. Hamilton is born in 1981. Grigori Y. Perelman was born in 1966. Both are alive now.

You may be wrong in thinking that generalists are strong in something. They are specialists in the width of our knowledge, history, or philosophy. Some people can be specialist in two or three fields, but is not a generalist.

i must say i believe in generalists, and the power of generalists too. i wonder if generalists are better problem solvers.

One thing seems be clear. A real entrepreneur must be a good manager of an enterprise and a good manager must be a synthetic artist. Here I means by synthetic art those arts like theatrical art and cinema production that requires all kind of talents and management skills. A mathematician is not required this kind of skills. This is one of the reasons that we find many gifted mathematicians who are poor manager of his or her ordinary life.