"Is this really a proof?" is the exact question e-mailed to me today from an undergraduate mathematics student whom I know as a highly competent student. The one sentence question was accompanied with the following demo: I am looking for a down-to-earth, non-authoritative answer who one may gi...

Perhaps the "proofs" of ABC conjecture or newly released weak version of twin prime conjecture or alike readily come to your mind. These are not the proofs I am looking for. Indeed my question was inspired by some other posts seeking for a hint to understand a certain more or less well-establised...

the 2005 AMS article/survey on experimental mathematics[1] by Bailey/Borwein mentions many remarkable successes in the field including new formulas for $\pi$ that were discovered via the PSLQ algorithm as well as many other examples. however, it appears to glaringly leave out any description of t...

I do not know exactly how to characterize the class of proofs that interests me, so let me give some examples and say why I would be interested in more. Perhaps what the examples have in common is that a powerful and unexpected technique is introduced that comes to seem very natural once you are ...

I was wondering what role non-rigorous, heuristic type arguments play in rigorous math. Are there examples of rigorous, formal proofs in which a non-rigorous reasoning still plays a central part? Here is an example of what I am thinking of. You want to prove that some formula $f(n)$ holds, and y...

I'm reading the paper "the classification of algebras by dominant dimension" by Bruno J.Mueller, the link is here http://cms.math.ca/10.4153/CJM-1968-037-9. In the proof of lemma 3 on page 402, there is a place I can't understand. Who can tell me what $E_R \oplus * \cong \oplus X_R$ and $_AHom_...

I've been really trying to prove Ramanujan Partition theory, and different sources give me different explanations. Can someone please explain how Ramanujan (and Euler) found out the following equation for the number of partitions for a given integer? Any help is appreciated thank you so much! $...