The French Mathematician Who Changed Our Understanding of Investing. By Robin Powell.

The early work of mathematician Louis Bachelier was barely recognized in his lifetime. But his doctoral thesis, The Theory of Speculation, influenced at least five Nobel Prize winners and is now acknowledged as one of the foundational works in the field of financial economics.

Even if you aren't interested in the stock market, it's impossible to escape it. Market movements are reported daily in newspapers, and hourly in the broadcast media. There are whole TV channels devoted to relaying the latest ups and downs, and which particular stocks are either beating or lagging the rest of the market. There are also thousands of commentators on social media trying to make sense of what's going on.

But what if I told you that the daily movements of markets and of individual stocks are completely irrelevant and tell us nothing of any value? What if prices move up and down in a totally random fashion? Extraordinary as it might seem given all the attention paid to the markets every day, both of those things are true.

We've known for a very long time that, unless you were privy to inside information, market movements were very hard to predict. "Even in the late 1800s," writes the financial historian Mark Higgins in his new book, Investing in U.S. Financial History, "market efficiency was a formidable obstacle to outperformance. The famed stock operator Daniel Drew captured this sentiment when he reportedly commented, "To speckilate [sic] in Wall Street when you are no longer an insider, is like buying cows by candlelight."

Then, in 1900, a French mathematical student named Louis Bachelier presented a PhD thesis that explained why, for all intents and purposes, it's impossible to know in advance which stocks are going to go up or down from one day to the next.

Prices follow a random path

Bachelier proposed that the price of a stock or bond follows a random path, influenced by countless tiny, unpredictable factors.

"The influences which determine the movements of the stock exchange are innumerable," he wrote. "Events past, present or even anticipated, often showing no apparent connection with its fluctuations, yet have repercussions on its course…The determination of these fluctuations is subject to an infinite number of factors (and) contradictory opinions in regard to these fluctuations are so divided that at the same instant buyers believe the market is rising and sellers that it is falling."

To illustrate the randomness of price movements, Bachelier borrowed the concept of Brownian motion, a physical phenomenon observed in fluids. In essence, he equated the erratic movement of pollen particles in water, as observed under a microscope, to the seemingly erratic movement of asset prices.

"There is no useful information contained in historical price movements of securities," he concluded, and, therefore, "the mathematical expectation of the speculator is zero."

Strangely enough, Bachelier's paper, The Theory of Speculation, attracted very little attention at the time. The story goes that a statistician named L.J. Savage, discovered Bachelier's work in the 1950s and thought that his economist friends ought to know about it. So he sent postcards suggesting they read it.

One of the recipients of those postcards was Paul Samuelson, who later became the first American Nobel Laureate in Economic Sciences. Samuelson realized how ahead of his time Bachelier was, and he was instrumental in having the paper translated into English and published. He also wrote the foreword.

Samuelson's recognition of Bachelier's contributions was significant, as it helped to bring the Frenchman's work to the attention of the wider academic and financial community. As well as Samuelson, several other leading financial economists were influenced by Bachelier's ideas, including Robert Merton, Fisher Black, Myron Scholes and Eugene Fama — all of whom also went on to receive the Nobel Prize.

Someone else who was influenced by Louis Bachelier was the Princeton economist Burton Malkiel. The title of Malkiel's best-selling book, A Random Walk Down Wall Street, is inspired by Bachelier's famous statement that market prices are "no more predictable than the steps of a drunkard."

So, if stock prices really are a random walk, what are the key takeaways for investors? For me, these are the four most important ones.

1. Stock markets are efficient

As Mark Hebner explains in his book, Index Funds, The 12-Step Program for Active Investors, the stock market is like a giant super-computer, or collective brain, aggregating the opinions of traders everywhere. "Think about it from a purely logical perspective," writes Hebner. "Is it realistic to presume that an individual investor or a stockbroker can know more than the combined knowledge of ten million traders?"

2. Profiting from mispricings is very difficult

No, they don't always get it right, but, in the words of Burton Malkiel, markets are efficient enough to make them "extraordinarily hard to beat." As Hebner puts it: "Tenets of market efficiency do not state that prices are perfect, or that at any given time there are no mispriced securities in the marketplace. Rather, these tenets assert that because prices reflect all known information, mispriced securities cannot be identified in advance."

3. Investing beats speculation

Speculation, as Bachelier showed, is a zero-sum game. In fact, when you factor in the costs of trading or investment management fees, it's a negative-sum game. Picking stocks or bonds — whether you do it yourself or pay an active manager to — is, in the words of Mark Hebner, "an ill-fated strategy that wastes time, energy, and money. The better solution is to trust the collective brain… and maintain risk-appropriate exposures in low-cost globally diversified index portfolios."

4. Your biggest challenge is you

Bachelier's description of market prices staggering around like a drunkard is a very appropriate one. As an investor, there's no way of telling what to expect next. Inevitably, prices will fall repeatedly, often out of the blue and very sharply. "What is hard," writes Burton Malkiel, "is having the discipline to save on a regular basis and to keep it up when news reports suggest that the sky is falling and economic disaster is sure to follow." All investors are prone to what Malkiel calls "behavioural foibles." Having a financial advisor to help you identify those foibles and keep you rational is a huge advantage.