Without a Proof, Mathematicians Wonder How Much Evidence Is Enough - quantamagazine.org

our researchers have recently come out with a model that upends the  conventional wisdom in their field. They have used intensive computational data  to suggest that for decades, if not longer, prevailing opinion about a fundamental  concept has been wrong.

What Is It Like to Have an Understanding of Very Advanced Mathematics? - forbes.com article

You can answer many seemingly difficult questions quickly. But you are not very impressed by what can look like magic, because you know the trick. The trick is that your brain can quickly decide if question is answerable by one of a few powerful general purpose "machines" (e.g., continuity arguments, the correspondences between geometric and algebraic objects, linear algebra, ways to reduce the infinite to the finite through various forms of compactness) combined with specific facts you have learned about your area.

Read the full article from forbes.com at this link. 

The article was brought to our attention by Prof. Kumaresan, MTTS Trust

Did Srinivasa Ramanujan fail in math?

Societies need myths to live by, and a mathematical genius failing in an exam is precisely the kind of myth that makes life alluring

How did Srinivasa Ramanujan (1887–1920), the mathematical genius, fare in his Intermediate examinations? Did he fail in mathematics? Or did he score a centum? Conflicting assertions float. Myths hover around geniuses and lend them an aura, and Ramanujan is no exception. 

Interestingly, the myth originated even during the mathematician’s lifetime. The Madras Times of April 6, 1919,published a profile titled ‘A Famous Madras Mathematician: Mr. S. Ramanujan, FRS’ on the occasion of his return to India from Cambridge. This contemporary sketch, notes for which the paper claimed were “chiefly collected from papers in the possession of the Madras Port Trust,” Ramanujan’s employer, stated that “In December 1907 … he appeared privately for the First Arts Examination and had the distinction of failing in all subjects, doubtless as a result of his illness.” (original emphasis) 

Read the full story from the "The Hindu" article here.

The sum of all positive integers

What do you think you get if you add 1+2+3+4+5+... all the way on up to infinity? Probably a massively huge number, right? Nope. You get a small negative number:

This is, by a wide margin, the most noodle-bending counterintuitive thing I have ever seen. Mathematician Leonard Euler actually proved this result in 1735, but the result was only made rigorous later and now physicists have been seeing this result actually show up in nature. Amazing. (thx, chris).

References:

Obtained from the webpage http://kottke.org/14/01/the-sum-of-all-positive-integers