I am sorry if I am posting this question here; I thought that since I am looking for historical evidences of successful people in mathematics, so may not this question be an opinion-based one. And also not duplicate as it is not about getting PhD at later age or the like.    I am 30 years old; I have studied physics to masters degree, even though I liked physics but I left it mostly because I didn't find any strong talent to do a great thing in physics and I thought that I can achieve it in mathematics. It's been a few months that I have started mathematics from scratch and I am spending average 14 hours a day learning maths. Though I have found mathematics more fascinating than any other things but my strong stimulus to go ahead especially as a self-learner is hope to do a ground-breaking research and be successful in that.   My questions are:  1- Will my mind be biologically too old to do comparable to what Fields medalists or other brilliant people have done or maybe more (like Perelman's work)?   2- Would you let me know even one person in history who started or turned to maths at their 30s or late 20s, but did famous works?  Some notes:    My question is not about getting a PhD in late ages or be successful in finding an academic position (including research), although soon or late I have to get a PhD in math as well, especially because of being in math community and other advantages. BTW, works that are not considered breakthrough or even writing books in math for students are as invaluable as e.g. Perelman's work, I believe. Please consider that my questions are not about comparisons.      There were some people in history who got their academic degrees at old ages but they were 'in' mathematics from theirs youth or even childhood; so examples of these people aren't relevant since by starting math now I mean that I am 30, and I am just starting undergraduate books in maths.  Physics is not math or even close! For example, I learnt differential forms in general relativity texts but it was just about 10 pages in 430-page physics text. And now I see that almost everything in a simple topology text is new for me.    Thanks to everyone for reading and taking the time for the great responses. Really appreciate it!
I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could.  This is a question I've been asking myself now for some time. In most areas, there's a "cut off age" to be good at something. For example, you're not going to make the NHL if you start playing hockey at 20. It just won't happen.  So my question then, how late is too late to start studying math and make a career out of it? By "start studying math" I mean, to really try to understand and comprehend the material (as opposed to just being able to do well in a formal, intuitional environment).   I don't mean this from a "do what you love, its not too late" motivational perspective. I mean this from a purely biological perspective; at approximately what age has your brain's capacity to learn effectively and be influenced by your learning stop? When does the biological clock for learning new math run out?  My reasoning for asking this question is (for those who care): I love math. Really I do. But , having spent the first 21 years of my life in sports/video games/obtaining a degree in a scientific field which I care nothing of/etc, despite all my best attempts at trying to learn math, am I just too late starting to ever actually be good enough at it to make it a career? I've almost completed my second degree (in Math), but find that in many cases, despite how I look at a problem, I lack the intuition to comprehend it. I'm going to single him out (sorry), only as an example, but Qiaochu Yuan is my age.   Note 1: If this question isn't a suitable post, I won't be offended at all if you vote to close - I know this question borders what's acceptable to ask.  Note 2: Thanks to everyone for reading and taking the time for the great responses. Really appreciate it!
I'm trying to solve this problem from Hatcher 3.3.24.  Let $M$ be a closed connected 3-manifold, and write $H_1(M, \mathbb{Z})$ as $\mathbb{Z^r} \oplus T$ where $T$ is torsion. Show that $H_2(M, \mathbb{Z})$ is $\mathbb{Z^r}$ if $M$ is orientable or $\mathbb{Z^{r-1}} \oplus \mathbb{Z_2}$ if $M$ is not orientable. In particular $r \geq 1$ if $M$ is not orientable. Using exercise 6 construct examples showing there are no other restrictions on the homology groups of closed 3-manifolds. (In the nonorientable case consider the manifold $N$ obtained from $S^2 \times I$ by identifying $S^2 \times \{0\}$ with $S^2 \times \{1\}$ via a reflection of $S^2$.)  I think I've solved the first part, here's my proof:   First note the following theorem: If $M$ is a closed connected and orientable n-manifold then $H_n(M, \mathbb{Z}) = \mathbb{Z}$ and $Tors(H_{n-1}(M, \mathbb{Z})) = 0$. If nonorientable, then $H_n(M, \mathbb{Z}) = 0$, $Tors(H_{n-1}(M, \mathbb{Z})) = \mathbb{Z_2}$.  Now note by Poincare duality and UCT we have that $H_2(M) \cong H^1(M) \cong \mathbb{Z^r} \oplus T_0 \cong \mathbb{Z^r}$.   In the nonorientable case consider the exact sequence:  $0 \longrightarrow H_2(M) \longrightarrow H_1(M) \longrightarrow H_0(M) \longrightarrow 0$  But we know $H_1(M) = \mathbb{Z^r} \oplus Z_2$ from the earlier theorem and $H_0(M) = \mathbb{Z}$.   Therefore $H_2(M) \cong ker(\mathbb{Z^r} \oplus Z_2 \rightarrow \mathbb{Z}) \cong \mathbb{Z^{r-1}} \oplus \mathbb{Z_2}$.   For the rest of the question I'm quite lost. How can I get a complete list of fields for a standard object? I am writing my CV using moderncv package, everythig is nice but I have a problem with \cventry command. I have something like this:   (it means 2010 - now)  I would want to have this in one line, rather than in two lines. I tried looking into the moderncv style files but with no success. What can I do to achieve the effect I want? 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