Scott Aaronson who is quite outspoken on his blog , coined the term “certified organic theorems” and mentioned that the time for such things are over. It is clear that in these days it has become hard to distinguish mathematics that is AI generated (the analog of growing genetically engineered, …
The Math 1.0 and Math 2.0 transition in the terminology of Tao could also be seen as a distinction between a culture of “being” to to a culture of “having”. The dichotomy between “having or being” is a term coined by Erich Fromm, a German philosopher about whom I learned …
Math 2.0 as Terry Tao has called it, gives at first a rather depressive outlook onto the future of mathematics. There is no doubt that we currently experience an enormous shift in how mathematics will be done. This is not different in other parts of life like engineering, literature or …
A rather general positive entropy problem is that Baire generically, a volume preserving diffeomorphism T on a 2-dimensional manifold M has positive entropy. A much bolder conjecture is that every non-integrable volume preserving diffeomorphism on a compact Riemannian 2-manifold has positive entropy. It would mean that the Standard map had …
The September 8 event in mathematics was the solution to a millenium problem. Even more brutal (for me at least) is the October 6 announcement of the solution of hundreds of open mathematics problems. It is a slaughter house! One of them is the solution of a problem I had …
When we were teenagers, we were huge fans of Ruediger Nehberg. It is fascinating to have knowledge to survive outside without any technical tools. It is an art and Nehberg demonstrated such skill not only theoretically but also during his own adventures. Knowing some basic skills is still recommendable today, …
During our high school class reunion I took the following picture (bottom of the page). It shows the abbey of St Katharinental which goes back to the year 1242. The members of that convent collected and illustrated especially graduals, some of which go back even 1000 years from today. Monasteries …
The current crisis in mathematics is unparalleled. Not that there had not been challenges before: the Pythagoreans had to grapple with the existence of irrational numbers. The Galois drama illustrates the crisis, when the realization dawned that explicit solution formulas to polynomial equations do not exist for degree 5 or …
it is evident that we live in a time of extremely fast change with respect to epistemology, the way how we acquire known and gain new information. As a dinosaur, who has seen several “meteor impacts” (new math, math wars, the rise of the web, the moocs wars and now …
The September 8 event is comparable with the sputnik moment in the late 50ies. This was before I was born, but I felt the repercussions in my own education. We learned about set theory early in primary school. The “new math” revolution had come in the wake of the Sputnik …
In the legendary movie “The 13th worrior”, Helger of the Northmen reminds Ahmed Ibn Fahldlan in latin “propera, ut morti occurras”, which Melchisidek then translates as “Hurry to meet Death, before your place is taken.” I like that movie and mentioned it a couple of times We do not have …
Johann Wolfgang von Goethe wrote in 1797 the “Sourcerer’s apprentice” (der Zauberlehrling). This poem is one of the most famous allegories of all times, especially after being featured in the masterpiece “Fantasia” of Walt Disney in 2000. The story is is very relevant today, for obvious reasons. I got reminded …
A periodic Frenet curve in is up to isometry uniquely defined by a periodic curve in where the later describes the motion of the Frenet frame. Differentiation then defines a periodic curve in the Lie algebra . We can now reverse the story and start with a periodic curve in …
Update October 7, 2025: Kitsch is already produced by professional mathematicians . No problem if it is declared as such. I myself like some kitsch. It just has to be declared as fake. It feels a bit like climbing “action direct” with the help of the rope. No problem, if …
