Mathematical Magic, Magical Mathematics "Mathematics is like a beautiful garden. It is full of beautiful flowers, which, if we take care of them, we can witness wonderful magic." (Rózsa Péter) Ever since Euler, we have admired the relationship named after him: eiπ=-1 It seems almost mysterious how we can get an integer from the operation between two transcendental numbers: e and π, and the imaginary number i. It has long been known – to anyone fascinated by mathematics – that the above formula is the exponential form of -1 in the complex numbers. Paul J. Nahin has devoted a whole book1 to this fabulous formula of Euler. _______________________________ 1 Dr. Euler’s Fabulous Formula – Cures Mathematical Ills, Paul J. Nahin,…

My encounter with Open AI artificial intelligence „The real sign of intelligence is not knowledge, but imagination.” (Albert Einstein) As soon as the first news appeared that ChatGPT could be added as an extension to the Google Chrome browser, I took the chance, but the first attempts were poor. The chatbot had problems interpreting even the simplest question, so I stopped trying. Recently I read several positive reviews about ChatGPT - negative ones too, but that's natural - so I gave it another try and I'm very satisfied with the testing. I got a lot of good responses and one interesting erroneous response. After registration, you may ask for a translation of the full text by email.