People often think that if they're smart enough, they can beat the market. However, the math of trading is the easy part. Making the model line up with reality has always been the hard part. Even assuming you're the smartest guy in the room, getting the information and capital necessary to be able to exploit your smartness in the first place is the limiting factor.
The vast majority of active traders lose money compared to the market (basically the SP500). These are not amateurs - they are people who spend 9-5 (often much longer) trying to come up with intelligent trading strategies. So if you want to outsmart the vast majority of active traders, you'll say "I know math, the odds are drastically stacked against me," and you'll simply buy something like VOO, which tracks the SP500.
The traditional economic explanation for this is the Efficient Market Hypothesis - market prices already reflect all the available information out there, since people who know something will trade on it for an easy profit, so you can't beat it. In fact, this necessarily implies that any short term fluctuations outside the true value are random noise (so good luck "beating" that!). Couple this with Hayek's explanation for the failure of central planning - all of the information necessary for organizing society is scattered about the economy in individuals' behaviors and plans and reactions to changing incentives, and it is always changing; by the time you gather a big data set for the central planners, it's already out of date! Lenin ran into this exact problem and eventually stopped trying to plan. Guess who the central planner is in our situation? You!
However, the traditional explanation isn't entirely accurate. If markets are perfectly efficient, what incentive is there to gather and trade on information in the first place such that it is reflected in the market prices? Likewise, we have empirical evidence of a number of people and funds who have consistently beaten the market over time.
You might want to read Efficiently Inefficient by Lasse Pedersen, a prominent hedge fund academic. He argues that markets are efficiently inefficient. They're efficient only until it's no longer worth the investment to make them more efficient by exploiting pricing inefficiencies. For example, at the announcement of a corporate buyout, the stock price will not rise to the full level offered by the buyers, and the spread reflects the risk that the buyout will not go through. Event-driven specialists can trade on this "inefficiency" and make a profit over many such events. The cost of making potentially even more efficient trades will not be worth any additional profit.
The book also indirectly shows the requirements for being able to implement a smart money trading strategy in the first place. Quant strategies require lots of computing power and data. Event-driven funds have their own internal databases of how mergers and acquisitions panned out. Sometimes it's just about having a strong enough rolodex to be able to find shares you want to short in the first place, since you can't always just short a security because your model says you should.
Purely mathematical smarts are not the limiting factor for individual investors. Think about this question in any other field. "I'm good at chemistry, do you think I can make a new wonder drug?" Well, perhaps, but with what lab, what data sets, what funding for FDA trials? "I'm good at circuits, do you think I can make an improved GPU?" Well, perhaps, but with what what lab, software, analysis tools, and fab?
tl;dr: The Efficient Market Hypothesis is functionally true for individual investors, although funds with access to exceptional amounts of information, technical skill, and capital can beat the market (and even then most don't!).