On question is: why? The examples in differential geometry can be difficult and time-consuming , unlike simple calculus, and are best done with computer, not by hand. A single tensor, as found in general relativity, may have dozens of components...writing them out would be taxing. My question is, what do want to do with this knowledge. There is value in learning complicated, abstract math to signal intellect and thus become more popular online, and maybe get consulting work. But in terms to practical applications, a lot of it is done by software programmed by large teams (not just one person), although learning the rules is always helpful. If you want to be a professional researcher who makes original findings in pure mathematics, it will presumably require full dedication, and one can't be both a quant trader and pure researcher at the same time (even someone as smart as James Simmons, founder of Renaissance Capital, was forced to choose between one or the other; he chose the former).
It seems as of late ,especially since 2013, there is huge demand for learning complicated mathematics, coding, and trading algorithms. It's like the AP-math class of high school, but as of 2013 expanded to include almost everyone, not just a dozen students lol. This recent obsession with math and finance is described in more detail in . People observe, read headlines about high-IQ founders, venture capitalists, and coders making tons of money in Web 2.0 (Uber, Pinterest, Snaphat, Dropbox, etc.); STEM people getting tons of prestige, status, and global notoriety for their finding (Arxiv physics and math papers frequently go viral); and how the economy, especially as of 2008, rewards intellectualism and STEM in terms of higher wages and surging asset prices (like stocks (the S&P 500 has nearly tripled since the 2009 bottom), web 2.0 valuations (Snapchat is worth $15 billion, on its way to $50 billion), and real estate (Palo Also home prices have doubled since 2011)), and, understandably, many people want a piece of the wealth pie. They see that intellect - which includes STEM, finance, and also quantitative finance - is the path to both riches and social status (as embodied by wealthy geniuses like Musk, Thiel, Zuckerberg, Shkreli), which is why there is so much interest in these technical, difficult subjects, unlike decades ago when only a handful of people were interested.
But another question is: Does algorithmic trading work? I don't know for sure, but I think a lot money is made in market making (Citadel Capital comes to mind), which tends to full under the umbrella of algorithmic trading - the two are closely related. And the math in involved has much less to do with differential geometry and number theory and more to to do with statistics and linear algebra (such as analyzing correlations between data). This involves a lot of trading and paying constant attention to order books - it's a full time job. I don't think it's as glamorous as many think it is, and I'm not sure if the returns are worth the effort. There are simpler methods, based on mathematics such as the ETF decay, that an also generate very good returns and don't require full-time trading. Here is one http://greyenlightenment.com/post-2008-wealth-creation-guide...