The Math Behind AI and Its Relevance to Business Outcomes

Given the response to “Transformers: Understanding the Engine Behind Modern NLP and Generative AI”, it is clear that we have to peel back the layers even further. So sit back, relax, and let’s break down the fundamentals behind some of the more popular ways AI is being used today.

Imagine you're running a lemonade stand. Some days, you sell a ton of lemonade. Other days? Not so much. You start tracking the?temperature?and?how many cups?you sell each day. After a while, you notice a pattern:

• On?hot days (85°F or more), you sell?50 cups.
• On?cooler days (below 70°F), you sell?20 cups.

Now, imagine you had an?AI-powered lemonade stand. Don’t chuckle! It’s completely possible. Remember that AI-powered toaster from “Navigating the AI Revolution with Confidence”.?

Your AI-powered lemonade stand would not only recognize the temperature and sales pattern?faster than you?but also use?math?to predict exactly how much lemonade you need to make each day.

AI works like this for your business too.?It looks at?past data, finds patterns, predicts future trends, and?makes smart decisions. But how does it actually work?

It all comes down to?math.?And today, we're diving deep into?the formulas and logic behind the top common AI use cases; showing how businesses use it to?make better decisions, increase sales, and stay ahead of the competition. Let’s drive this example home and show the fundamentals.

Don't worry! You don't have to be good at math! You don't need fully understand the formulae. You just have to appreciate the concepts.

Word of caution: The math described here relates to standard statistics and supervised learning, but Large Language Models (LLMs) do not currently effectively leverage these techniques.

Project Lemonade Step 1: AI Learns from Data

The basics of AI learning boils down to Finding the Relationship.

AI is?obsessed with patterns.?But instead of guessing, it?uses math?to create?equations that explain the data.

Let’s say we want to figure out the relationship between?temperature?and?lemonade sales. We can use a simple?linear equation:

Where:

Finding the Perfect Equation with AI

AI doesn’t just assume a value for?mm?and?bb. It?calculates them?based on the data. This process is called?linear regression, and the formula looks like this:

Where:

Once AI calculates?m?and?b, it can predict?exactly?how many cups of lemonade you’ll sell based on tomorrow’s temperature.

Real-World Example: Netflix’s Recommendation System

Netflix uses a more advanced version of this math to?recommend movies and shows. It looks at:

• What you’ve watched before.
• How long you watched it.
• If you paused, rewound, or skipped.
• What similar users liked.

By applying?regression models?like the one above, Netflix?learns your taste?and predicts what you’ll want to watch next!

Project Lemonade Step 2: AI Finds Patterns Faster Than Humans

Imagine you have?100,000 lemonade sales records?and you need to analyze them?by hand. It would take?weeks! AI, on the other hand, can process that data in?seconds?using?statistics and probability theory.

One of the most powerful tools for this is?Bayes' Theorem, which helps AI figure out the?likelihood?of something happening based on prior events.

The Math: Bayes' Theorem for Decision-Making

Where:

Real-World Example: Amazon’s Product Recommendations

Amazon uses?Bayes' Theorem?to?predict what products you’ll buy next. It calculates:

• The probability of you buying a product if you’ve bought something similar before.
• How likely you are to buy based on your browsing history.
• Whether other customers like you also bought it.

This is how Amazon?suggests the perfect product?at just the right time!

Project Lemonade Step 3: AI Predicts the Future

AI can predict?future trends?using a technique called?multiple regression analysis, which looks at?many factors?at once.

The formula looks like this:

Where:

Real-World Example: Airlines and Ticket Prices

Airlines use?regression models?to?predict ticket demand?and adjust prices accordingly. AI constantly checks:

• How many people are booking flights.
• If there’s a holiday or big event coming up.
• Competitor prices.

If demand is high, AI?raises the price. If seats are still empty, AI?lowers it to attract more buyers. That’s how you sometimes find those?last-minute cheap tickets!

Project Lemonade Step 4: AI Keeps Learning and Improving

AI?doesn’t stop learning?after making one prediction. It continuously improves its accuracy using a method called?gradient descent, which adjusts the AI’s model every time it makes a mistake.

Where:

Real-World Example: Starbucks’ Seasonal Drinks

Starbucks uses AI to?test new flavors. If customers?love?a drink, AI?reinforces that recipe. If they?dislike?it, AI?adjusts ingredients?until it finds the perfect mix. This is why?Pumpkin Spice Lattes?became a worldwide hit! ???

Let’s Get Real: How About My Businesses?

AI?isn’t magic - it’s just?math done at a large scale and at super speed.

Businesses exist to?make money, solve problems, and serve customers.?AI uses math to help you know:

• What to sell?
• When to sell it?
• How much to charge?
• Which customers to target?

Whether it’s a?small lemonade stand?or a?billion-dollar corporation, AI helps businesses?predict demand, cut costs, and grow faster?by making data-driven decisions.

Let’s delve into the real ways that AI-powered math?transforms business outcomes?in real life.

Demand Forecasting

AI analyzes past sales data and external factors (like social media trends, product reviews, and pre-orders) using formulas like:

(Looks familiar? ??)

Where:

???Real-World Example: Target’s Holiday Strategy

Target used AI-powered demand forecasting to stock the right toys ahead of Christmas. Instead of?guessing, they?analyzed past sales, Google searches, and social media mentions?to predict the hottest items - increasing holiday sales by 17%!

???Key Takeaway:?AI ensures businesses?stock the right products?at the right time,?maximizing profits?and?reducing missed opportunities.

Inventory Optimization

Think about a?grocery store. If they stock too much fresh produce, food spoils. If they don’t stock enough, customers leave disappointed. AI calculates the?perfect?amount of stock using the?Economic Order Quantity (EOQ)?formula:

Where:

• D?= Demand rate (how many apples are sold per week).
• S?= Ordering cost (cost to restock apples).
• H?= Holding cost per unit (cost of storing unsold apples).

???Real-World Example: Walmart’s AI-Powered Inventory System

Walmart used AI to?reduce food waste by 50%?by analyzing:

• Weather data?(hot days = more cold drinks, fewer soups).
• Local events?(Super Bowl weekend = more snacks and drinks).
• Purchase patterns?(Mondays = fewer shoppers, so less inventory).

???Key Takeaway:?AI helps businesses?save millions?by avoiding overstocking?or?running out of high-demand products.

Dynamic Pricing

Pricing?can make or break?a business. If a product is?too expensive, customers won’t buy it. If it’s?too cheap, the business loses profit. AI uses?Price Elasticity of Demand?to set the perfect price:

Where:

???Real-World Example: Uber’s Surge Pricing

Uber uses AI-powered pricing to?adjust fares in real time?based on:

• Supply (number of available drivers).
• Demand (number of people requesting rides).
• Weather, traffic, and event data.

During peak hours,?prices go up, encouraging more drivers to hit the road while maximizing profits.

???Key Takeaway:?AI?automatically adjusts prices?to?maximize revenue?without losing customers.

Customer Experience Improvement and Personalization

Customers expect businesses to?know what they like?before they even ask. AI-powered personalization makes this possible. AI uses?Collaborative Filtering?to make personalized suggestions:

Where:

???Real-World Example: Netflix’s AI-Powered Suggestions

Netflix analyzes:

• Movies and shows you’ve watched?before.
• Ratings and reviews?you’ve given.
• What other people with similar tastes like.

It then?predicts?what you’d enjoy next, increasing watch time and?keeping users subscribed.

???Key Takeaway:?AI?creates ultra-personalized experiences, keeping customers engaged?and boosting loyalty.

Smarter & Faster Decision Making

CEOs and business leaders?don’t have time?to analyze every piece of data. AI acts as a?real-time decision-making assistant. Businesses use?Decision Trees?to analyze?if-then scenarios:

Where:

???Real-World Example: Bank Loan Approvals

Banks use AI decision trees to?approve or reject loans, analyzing:

• Credit history
• Income level
• Debt-to-income ratio
• Loan repayment history

This allows banks to make?fast lending decisions, reducing fraud and boosting profits.

???Key Takeaway:?AI?removes guesswork, ensuring businesses?make the smartest choices.

As with all of these techniques, the output is only as good as that the data used. For the best results, you have to invest in your data system.

Final Thoughts

AI isn’t just for tech companies - it’s for EVERY business.?Whether you’re selling?lemonade, sneakers, flights, or Netflix subscriptions, AI helps businesses:

??Sell More?by predicting customer needs.

??Save Money?by reducing waste.

??Price Products Perfectly?using dynamic pricing.

??Keep Customers Happy?with personalized experiences.

??Make Smarter, Faster Decisions?to stay ahead of competitors.

The businesses that?embrace AI and math?will dominate the future. Those that?ignore it??They’ll get left behind.

So what’s your next move????

I recommend you start educating yourself so you can thrive in this AI Revolution.