It's kind of humbling to know that I can't understand any of that. I barely passed mathematics in British high school - but for some reason took to quadratic equations and other slightly more advanced maths in college, I enjoyed it back then - but simply cannot read nor understand just about all of the topics in that thread.<p>I'd have to look up what the "/" in "M/L" means in the 5th reply (I didn't)<p>There are so many _symbols_ used in mathematics. It's all as if they're spells written by wizened greybeard wizards and passed down to apprentices throughout the centuries.
I wonder what’s going on with the passive aggressive edit war in this answer: <a href="https://mathoverflow.net/a/23521" rel="nofollow">https://mathoverflow.net/a/23521</a><p>It’s about whether Euclid’s proof that there’s no finite set of primes is a proof by contradiction or not. The fact that this is disputed at all shows a certain unwillingness to use original sources — maybe each of them only looked at a different textbook’s restatement of the proof. Because no matter whether a proof of the theorem <i>can</i> be stated without contradiction, it took me all of 30 seconds to find a translation of the original proof to show that Euclid did in fact use one:<p>> I say that G is not the same with any of the numbers A, B, and C.<p>> If possible, let it be so. Now A, B, and C measure DE, therefore G also measures DE. But it also measures EF. Therefore G, being a number, measures the remainder, the unit DF, which is absurd.<p>(<a href="http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html" rel="nofollow">http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX...</a>)
It's things like this that help me to remember how very little I know about mathematics. I looked about halfway down and saw that I didn't have the slightest idea what any of them were talking about. I console myself with the thought that there are other subject matters that I am an expert in that they are not. Probably.
The weight of the names in this thread is really something. I'm constantly amazed at the quality of what is posted on Mathoverflow. Kudos to them for harbouring such a community.
I guess the probability theory and statistics is the field with most false beliefs. It's because human intuition doesn't really work, but everyone is trying to use it anyway.<p>For example, the answers mention the belief that if 3 distributions are pairwise independent then they're jointly independent. Another false belief is that if 2 distributions are independent then they are conditionally independent. Also, people might think that you can pick a real number from R uniformly.
The most common false belief I met during the years is that people think you can use math as-is in software. Reality is that you almost always need knowledge about numerical methods and for easier things you need to understand how floating-point arithmetic works.
Can someone give a counterexample for this one? I read the comments but I still don't see how it's false:<p>> If <i>f</i> is a smooth function with <i>df</i> = 0, then <i>f</i> is constant.<p>I assume the smoothness and <i>df</i> = 0 criteria are said to hold on the <i>whole</i> domain, right? Yet the claim is that <i>f</i> fails to be constant over the same domain?
Got a degree in math. For me, the repeated act of rigorously proving counter-intuitive results put me into a state of mind where I tried to avoid having "beliefs" until they were proven results.
This article's posting on HN is possibly inspired by the recent post about the unreasonable uses of bubble sort [0] as it is a counterintuitive belief in CS that an inefficient algorithm could ever be useful. I am pretty sure that there are other beliefs in the computing world that are also common and completely false, such as "Deleting a file removes the data from the drive" or "Twice the number of cores working on a task means the process will finish twice as quickly."<p>[0]: <a href="https://news.ycombinator.com/item?id=30112906" rel="nofollow">https://news.ycombinator.com/item?id=30112906</a>
Here's an interesting one: "this set is open, hence it is not closed".
Apparently this is wrong, and R is both open and closed. Does anyone have a clear explanation as to why this is or what this means? I can't quite understand the comment explaining it.
I'm currently reading (almost finished, in fact), Roger Penrose's <i>The Road to Reality</i>. Despite having most of a master's in mathematics, I found his comment early on about trying to keep the mathematics accessible to be a bit laughable. Modern mathematics can get abstruse very quickly. It's likely that a typical HN reader could read the abstract of a PhD dissertation in just about any field <i>except mathematics</i> and have an idea of what the dissertation is doing. For mathematics, it's possible that even with a PhD if the dissertation is outside their specialty they might not know what it's about.
> Many student believe that 1 plus the product of the first n primes is always a prime number.<p>Wow, pretty sure I read this in New Scientist magazine in the early 2000s, quoting some "cryptography expert". Guess he wasn't such an expert.
I’m getting re-asked cookie preferences every time I go to sites like SO. Is it OK for sites to ask for cookie preferences on return visits to their sites after preferences have been set and “saved”? Or maybe I’ve turned off the Cookie that would have saved preferences…
> If f is a smooth function with df=0, then f is constant.<p>Why would this be wrong? If the derivative is zero everywhere, how would the function not be constant? Or does this mean something completely different?
These seem fairly advanced, so I don’t know if I would call them “common”. But maybe I am out of the loop. Are these concepts and very specific sounding beliefs actually widely known to math majors or CS majors?