# Sergey Orshanskiy

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 May1 comment Why do mathematicians sometimes assume famous conjectures in their research? These days a lot of mathematicians do research so they can publish their results, so they can get money and other benefits. The mathematical community considers it acceptable to publish interesting results relying on an assumption of a famous conjecture. Thus, this increases the set of potential topics one can do research on and then write about: you can prove a new theorem, or you can prove a new theorem while assuming a famous conjecture. Given the number of people who do research these days, many available niches end up being filled. Oct11 comment Probability of picking specific balls I may have a few more.But I hope you get the idea. Oct11 revised Probability of picking specific balls deleted 2 characters in body Oct11 awarded Editor Oct11 revised Probability of picking specific balls added 1 characters in body Oct11 comment Probability of picking specific balls I have a few mistakes, actually. Fixed Oct10 answered Probability of getting two black balls Oct10 awarded Supporter Oct10 answered Chance to pick 3 balls out of 6 (with replacement, order doesn't matter) Oct10 answered Probability of picking specific balls Oct10 comment Probability of picking specific balls This is my understanding of the question. There are 10 events. At each event you pick one red and one blue, and discard both. An event is "good" if both balls have stars. If we try 10 times, we can expect between 0 and 7 "good" events. What is the probability that there will be exactly five "good" events out of 10. Mar6 comment What is the best way to develop Mathematical intuition? Lastly, I don't see that much difference between the statement about a circle and the statement about A and B. I don't think that you really need to prove that a circle divides the plane into two parts. Maybe you do need it if you are building all geometry from scratch using a system of axioms - not Euclidean axioms, these will not be sufficient to prove this statement. Euclid did not define things like a point on a line lies between two other points. On the other hand, tautologies may still need a proof. (Well, it depends on which logic/model/proof system we are working with.) Mar6 comment What is the best way to develop Mathematical intuition? "One important property of a mathematical proof is that it does not use inductive reasoning (not to be confused, of course, with induction). I don't think this fact is obvious by any means." - well, I don't think that this fact is relevant. People who don't understand proofs, don't understand what is "inductive reasoning" either. My point is that you should not try to explain the theory behind proofs, unless you are teaching advanced mathematical logic. Just expose people to simple proofs, and they will pick it up. Feb18 answered What is the best way to develop Mathematical intuition? Feb17 awarded Teacher Feb17 comment Proving that a right (or left) inverse of a square matrix is unique using only basic matrix operations "...and thus there's only one B sufficing the equation." How did you conclude that? Why do you need to show that A is row equivalent to I? Focus on the question: uniqueness. Feb17 answered Is a good GRE score enough for a non-math graduate to be accepted in a decent pure mathematics graduate program?