1,617 reputation
521
bio website
location
age
visits member for 2 years, 8 months
seen 11 hours ago

Oct
14
awarded  Good Question
Oct
14
accepted What did Rolle prove when he proved Rolle's theorem?
Oct
14
awarded  Popular Question
Oct
14
awarded  Nice Question
Oct
14
revised What did Rolle prove when he proved Rolle's theorem?
deleted 7 characters in body
Oct
14
asked What did Rolle prove when he proved Rolle's theorem?
Oct
6
comment The distribution of the shortest path through $n$ points
Maybe I'm just dense, but I don't understand what you mean by the shortest path through a set of points.
Oct
4
awarded  Popular Question
Oct
3
comment Why do roots of polynomials tend to have absolute value close to 1?
Here's a different way of stating the heuristic. Say the coefficients $a_i$ are IID with mean 1 and variance $\sigma^2$. Then for fixed $z$, $P(z)$ has a (complex) variance given by a geometric sum. For large $n$ and $|z|\gtrsim1$ this variance has real and imaginary parts that grow approximately like $|z|^{2n}$, and therefore the distribution gets too wide, and the probability of $|P|<\epsilon$ falls like $|z|^{-2n}$. This drops off so fast that the prob. of having $|z|$ significantly greater than 1 is small. But the problem is isomorphic under circle inversion, so the same holds for $|z|<1$.
Oct
2
comment Why have mathematicians used differential equations to model nature instead of difference equations
I want to know what units the $10^{-10}$ is expressed in.
Oct
1
comment Has philosophy ever clarified mathematics?
It's hard to imagine why ultrafinitism would exist except that its originators were philosophically allergic to infinities. Similar deal for nonaristotelian logic.
Sep
30
comment Why have mathematicians used differential equations to model nature instead of difference equations
Furthermore, difference equations don't require complicated epsilon-delta definitions. Nor do differential equations require epsilon-delta definitions. Newton and Leibniz solved differential equations about 150 years before epsilontics came along.
Sep
22
awarded  Good Question
Sep
22
awarded  Popular Question
Sep
21
accepted Did Leibniz really get the Leibniz rule wrong?
Sep
21
comment Did Leibniz really get the Leibniz rule wrong?
KConrad's comment says that on Nov 11, 1675, "He asked himself if (uv)′=u′v′ and quickly dismissed it by the example you gave: u=v=x." Is that correct? Your answer makes it sound like the dates are all much fuzzier, perhaps by years, and we have no way of knowing whether it took Leibniz five minutes or a year to discard the hypothesis. Am I correct in understanding that this was all material from an unpublished personal notebook?
Sep
21
awarded  Nice Question
Sep
21
asked Did Leibniz really get the Leibniz rule wrong?
Sep
21
comment Did differential geometry undergo a notation change?
related: mathoverflow.net/a/175956/21349
Sep
6
awarded  Curious