I've done a lot of reading lately, and have bumped into one of my favourite subjects so much that I had to blog about it: Math. I've recently read Fortune's Formula, Twilight in the Desert, Against the Gods, the latest Walrus (Bird Flu edition), and the latest Business Week (Math edition). Guess what? Math is everywhere :) I smile when I hear my wife or parents say that...when I hear anyone say that...because I always knew it to be true.
I remember doing compound interest and figuring future account balances for my parent's accounts as a kid. I really got into Calculus when I started doing my Superconductor Propulsion research. After 4 years of Engineering Physics + 2 more of Industrial (Financial) Engineering....I've been math'd to death, and still am curious about areas I only touched on like Group Theory or forms like Elliptical Curves.
Math is everywhere, and in my opinion, your skill level in Maths will be a key determining factor in your success in business. I am not saying that everyone needs to be solving Fermat's Last Theorem, but if all you can do is figure out the area of your backyard (area=length x width) and how much sod you will need to cover it (area/8.5 sqft) so that your baby can crawl around on the grass....you are in trouble .
In the last 10 years I've met a few with excellent math skills, while the vast majority could hardly string together a geometric sequence or take the square root of 169 (even with a calculator). It's important, and the job market is valuing it more and more everyday. This is especially troubling in North America where our #math grads is being eclipsed by the number coming out of India, China....and close to home here in Toronto where the Ontario Education system is making math easier (read: dumbing it down) so more kids can graduate from high school. Infuriating.
Math is everywhere & here are some examples:
1. Buying Anything Online. Let's say you were going to go to Indigo.ca and buy a book from your home computer. At some point you will provide your credit card information and press "submit" to pay for your books. At that point, you will see a little security "key" icon in your browser status bar. That is supposed to mean that your connection is secure i.e. (usually) that all data transported is encrypted and (sometimes) that the party you are communicated with is trusted / authenticated.
How does this happen? A security protocol (SSL, TLS) or series of steps using MATH is being followed to encrypt your data. This typically starts with the generation of a "session key" which is just a random number. That random number is used at some point to encrypt your credit card number (and other data), to produce yet another number (ciphertext) with a mathematical forumla. Of course it is more complex than that, but I will tell you that this security is only as strong as your session key is random. How do I know this? Because the very first session keys in Netscape browsers 10 years ago where not 'very' random (see Claude Shannon, Information Theory) and as a part of my Physics Thesis I developed a random number generation protocol and of course the design for a Quantum Well device to act as a 'perfect' source. Netscape improved, and today key generation and public & private key cryptography implementations are significantly better & more accessible.
Math is "key" to electronic commerce. Without good Math, no buying books online securely. No buying anything online securely.
2. Investing in the Stock Market. This is such a general category, and there are so many examples that I won't bore you with all of the mathematical techniques that are used to value a stock (dcf etc...) which essentially consider the future earnings potential of a security. I also won't touch any of the statistical (technical) analysis or "quant" techniques that are used to predict where a stock will go next. I especially won't touch this as one of the things I've bumped into time and time again in financial engineering or AI work, is that in many/most systems it is not possible to predict future levels based on historical ones.
I will touch on how much to bet/invest on a stock. Let's say you are walking into a casino with $100 in your pocket and you sit down at the blackjack table and place your bet. How much of your bankroll do you bet? Well, what are the odds? Is there any information that you have that would give you an 'edge' over the odds? Now think of the stock market. You decide to buy some Apple Computer stock although it is probably overvalued today...How much of your investment dollars should you devote to it? What are the odds that you will get a 10% payback in 1 year? Is there any information that you have that would give you an 'edge'? This kind of edge/odds analysis (The Kelly Criterion) can help you decide the optimal proportional bet/investment to make. Gmax = R. All MATH.
I admit that prior to reading Fortune's Formula (Poundstone) I had not heard of the Kelly Criterion, but its simplicity / beauty (now I am talking like a physicist) and its connection to Information theory make it very compelling. I recommend googling it at the very least.
How much is a stock worth? What stocks should you invest in? How much should you invest? All questions that you can better answer with some MATH.
3. Forecasting. Today's cash flows, next quarter's revenues, the amount of oil left in the world....all things that get forecasted every day. A company's ability to forecast its revenues & expenses is often just as important to its success as the demand for its new products. Since crystal balls aren't used much in business (not since the dotcom boom) to do effective forecasting, we need MATH. Let me give you an example, and you tell me who you want working with you, person A or person B:
Me: How much revenue will we earn from selling Gizmos in 2006?
Person A: Hmmm. 10 Million? (guessing)
Person B: Based on a 5 Million dollar 2005, a 20% year over year growth rate, and a market growth rate of 40% year over year, we should be able to do between $6 - 7Million.
No brainer. Person B. Person B gets numbers, and can better answer a question that will impact how much money we spend doing sales, marketing, new engineering...etc.
Forecasting Tangent. How much oil is there left in the world? Check out Twilight in the Desert for an absolute dissertation based on SPE papers, concluding that Saudi Oil has peaked (or peaked 20 years ago) and we are all smoking good crack if we think daily production levels are going to rise by 1-2 million barrels / day for the next decade in order to meet global demand. Run on sentence, I know, but this is forecasting (MATH) used in a critical example.
As we know, wars get waged over energy (oil). The International Energy Agency, US DOE...all are projecting that demand for oil is going to rise at least 1 million barrels per day/per year. Why? We all use more of it. China needs more of it. Lot's more. These esteemed agencies in all of their forecasting, think that Saudi Arabia is going to satisfy that demand. Matt Simmons thinks we are in trouble, because the majority of Saudi oil comes from a handful (read 3-4) oil fields that are all very likely in decline.
Price of oil going up? Yeah. Unless we hit some major bird flu epidemic that causes prices to plummet for a few years, the price of oil is going up. Supply going down, Demand going up. Economics 101. If we are not careful, WW III.
Forecasting. MATH. Important stuff.
Enough for today. MATH is important, and becoming more so everyday. If you don't know it, either learn it, or surround yourself with people that know it. Hugely oversimplified, but I have to run to my daughter's music class.