Maths is often seen as a dusty old textbook subject. But it is actually the secret superhero behind countless modern marvels. From the apps on your phone to how we understand the universe, numbers, and equations are the hidden architects of our world.

Take the internet, for example. Most of us can’t do without it, even for a day. The network of systems and technologies that power the internet have underlying principles deeply rooted in maths. At its core, numbers form the invisible backbone of our digital world. The fundamental protocols, search engine algorithms, data transmission, and more – learning maths make it possible to use the internet as we know it.

And it doesn’t stop there. Mathematical breakthroughs have helped improve internet speed, security, and efficiency. Public-key cryptography essential to internet security is based on complex number theory. It shows us how abstract concepts help create tangible and revolutionary technologies.

Easy to relate with mathematical applications powering the internet? You might already know how physics, engineering, and finance also rely heavily on numbers and equations. Now, we’ll explore other fields and industries that use maths to innovate. Let’s start with an obvious one:

## #1 Artificial Intelligence (AI)

Self-driving cars to virtual assistants – anything that is powered by AI is essentially maths in action. You’ll find it even in image recognition and natural language processing.

Artificial neural networks at the core of many AI systems are loosely inspired by the structure of the human brain. These networks have interconnected nodes (artificial neurons) that process information. Math plays a crucial role in how these networks learn and function.

### The maths behind neural networks

Here’s a simple example. You are teaching an AI program to identify a ‘cat’ out of a collection of images. What do you think goes on in the system? It breaks down the image into thousands of numbers. Then, complex equations (like convolutional neural networks) are fired off rapidly to identify patterns that match a “cat.” So, the AI’s ability to learn and adapt relies heavily on several branches of maths like linear algebra, calculus, and statistics.

Linear Algebra matrices help represent the connections between neurons. Vector operations are used to perform calculations within the network. Eigenvalues and eigenvectors help analyse the network’s behaviour.

Gradient descent is a critical optimization algorithm that uses calculus to adjust the weights of connections between neurons to train the network. Understanding derivatives is essential for this process. Probability and statistics come into play when evaluating the performance of neural networks, identifying potential biases, and determining likely outcomes.

### Discrete Maths: Building Blocks of Algorithms

Discrete maths deals with objects that are distinct and separate, as opposed to continuous. Its concepts like sets, graphs, combinatorics, and logic are fundamental to AI algorithms. They build efficient systems and help solve discrete optimization problems.

Numerical methods are essential when dealing with large datasets and complex models. It is commonly applied to AI tasks like numerical integration, numerical optimization, and solving systems of linear equations.

Graph algorithms are used in pathfinding problems (like finding the shortest route), and combinatorial techniques are employed in optimization tasks (like finding the best combination of variables).

These are just some of the fundamental mathematical concepts that underpin AI. As AI evolves, we need even more advanced maths techniques to unlock its full potential. So, a solid foundation in mathematical concepts is essential for practitioners and researchers working in AI.

## #2 Cryptography & Cybersecurity

Cryptography is the art of secure communication and it’s all about number theory. But before you start thinking of secret codes and spy thrillers – today, cryptography is essential for online banking and digital payments. It even keeps your emails and chats safe by encrypting them.

Complex? Cryptography is basically advanced maths. Simple puzzles like the Caesar cipher to modern encryption form the foundation of cybersecurity with just numbers and patterns. Yes, prime numbers, modular arithmetic, and sophisticated algorithms are stopping cyber attacks right now. Here are a few cryptography and cybersecurity innovations using maths:

- Prime Numbers are the foundation of many cryptographic systems because they are ideal for key generation and encryption
- Arithmetic Operations within a specific range are crucial for algorithms like RSA and Diffie-Hellman.
- Discrete Logarithms are difficult to compute, making them perfect for cybersecurity.
- Finite Fields in algebra are used in algorithms like elliptic curve cryptography (ECC)
- Error Correction Codes are used to detect and correct errors in data transmission.
- Hash Functions, which produce fixed-size outputs (hash values) for any given input, are used for data integrity, authentication, and digital signatures.

Learning maths provides the theoretical underpinnings for much of modern cryptography and cybersecurity. As technology evolves and threats become more sophisticated, the role of mathematics in safeguarding digital information will only grow in importance.

Have you heard about The Enigma Machine? It’s an interesting case study on the power of maths that broke what was considered virtually unbreakable. If cryptography is still giving you spy vibes, here’s a quick story you may like:

### Bombe-ing the Enigma

The Germans used a complex cipher machine during World War II and it was such a big advantage to the Axis Powers. Because no one could crack this Enigma Code! Until, the tide turned thanks to the combined efforts of mathematicians, cryptologists, and linguists.

English mathematician Alan Turing (father of modern computer science), used statistical analysis, probability theory, and complex mathematical techniques to develop Bombe. It was a machine, which could test different Enigma settings at incredible speeds.

Bombe helped the Allies understand the underlying mathematical patterns of the Enigma code, which allowed them to decrypt German messages. The intelligence gathered was instrumental in turning the tide of the war and saving many lives. It is a remarkable example of how mathematics, often seen as abstract, can have a profound impact on the real world.

## #3 Supply Chain Management

So you ordered groceries or a new game online and delivered it to your doorstep. Ever wondered how it got there, from a factory or retailer? It’s not a simple pick-and-drop. Supply chain management is a complex process that is made easier by maths. How?

- Network optimization techniques find the most efficient truck routes or cost-efficient ways to ship goods by considering distance, fuel costs, and delivery time.
- Linear programming helps in optimal resource allocation to minimise costs by balancing demand and supply.
- Statistical models are used by companies to analyse historical sales data and predict future demands. It helps plan production, inventory levels, and transportation.
- Time Series Analysis helps forecast seasonal variations in demand by identifying patterns in data.
- Economic Order Quantity (EOQ) is useful in minimising total inventory costs.
- Simulation models, statistics, and probability can be used to assess risk scenarios and develop contingency plans.

Supply chain management is a complex system with many interconnected parts. Learning maths provides the tools to analyse this system, make informed decisions, and improve efficiency. Like finance, the innovations using maths in business and trade are limitless.

## #4 Biology & Medicine

The study of life might seem far removed from numbers. But from genetics to epidemiology, maths is used to analyse biological data and develop new treatments. The world of medicine is also increasingly data-driven. Medical imaging, clinical trials, and drug development rely heavily on mathematical models. Maths is also the language scientists use to communicate the intricacies of life.

Here are some examples of how maths is applied in some key areas in bioinformatics, computational biology, medical imaging, etc.

- Bioinformatics is a field that applies computer science and mathematics to analyse biological data. DNA Sequencing, for instance, uses maths algorithms to assemble, analyse, and interpret massive amounts of data. It helps us understand gene function and variation.
- 3D maths modelling and geometric formulas help predict and analyse protein (building blocks of life) structures from their amino acid sequences.
- Maths models are also used to study and understand various aspects of health and disease. Epidemiologists, who study the spread of diseases like COVID-19, use statistical models to track outbreaks, predict future trends, and evaluate the effectiveness of interventions.
- Physiology, the study of how the body functions, uses maths models to simulate blood flow, heart function, and the nervous system.
- Psychology, the study of the mind and soul, also involves a lot of statistics and data analysis to understand how the brain works.
- Medical imaging (X-rays, CT scans, and MRIs) uses maths algorithms to analyse and extract relevant information for diagnosis.

The advanced use of maths in biology and healthcare shows that mathematical understanding is vital to evolve with the times. Building a strong foundation in maths helps you grasp the intricacies of any industry or profession.

## #5 Agriculture

Modern agriculture is more than just planting seeds and harvesting crops. Farmers now rely on maths to optimise crop yields, manage resources efficiently, and predict crop patterns. Remote sensing and data analysis are two main agriculture innovations using maths.

Precision farming, crop modelling, irrigation management, supply chain optimization, and financial analysis are the key areas of maths innovation in agriculture. Here are some examples:

- Statistical analysis helps in yield mapping to identify areas of high and low productivity, guiding decisions on fertilisation, irrigation, and seeding. Farmers use GPS and sensors to create detailed maps of crop yields across their fields.
- Variable Rate Application (VRA) helps farmers optimise resource use. This requires precise calculations and mapping.
- Mathematical models simulate crop growth based on temperature, rainfall, and nutrient availability. It can also help farmers predict the outbreak of diseases and pests, by analysing historical data and weather patterns.
- Sensors in the soil and atmosphere collect data on moisture levels, temperature, and other factors. Statistical analysis helps optimise irrigation schedules.
- Farmers can use mathematical and statistical models to evaluate profitability and financial risks.

The potential for maths innovations in agriculture is exponential. AI/Robotics, climate change adaptation, genetic engineering, and more open up the potential for new-age farming to put numbers to work and yield bigger numbers in profitability and sustainability.

Bringing together all innovations using maths in diverse fields is no one-time read. The more you look, the more you’ll find. What we discussed above is only the tip of the iceberg. So, here are some more fields where maths is revolutionising the way things are done better and quicker:

### Climate Science

Climate change is one of the biggest challenges of our time. Scientists use maths models to simulate the Earth’s climate, predict temperature changes, and analyse the impact of human activities. It’s like running a giant computer game that simulates our planet.

### Gaming

Character movement, virtual explosions, and even the random drops of loot are calculated using maths formulas. Game developers use geometry to create 3D worlds, physics to simulate real-world interactions, and probability to determine the odds of winning.

### Music

Maths and music are closely related. The harmony of a chord, the rhythm of a beat, and even the design of musical instruments involve maths principles. Sound waves are analysed using maths techniques, and composers often use patterns and sequences inspired by numbers.

### Fashion Design

Fashion might seem like an art form, but it’s also a science that involves maths. Pattern making, draping, and predicting fashion trends rely on numbers. For example, understanding the proportions of the human body is essential for creating well-fitting clothes.

### Archaeology

Uncovering the past might seem like detective work, but it involves a lot of maths too. Archaeologists use statistical methods to analyse artefacts, carbon dating to determine the age of objects, and geometric techniques to map out ancient sites.

Math’s influence extends far beyond the classroom. The next time you look at a complex problem, remember that maths is the key to unlocking the solution. From the natural world to the digital age, numbers are the language of innovation. It is the invisible thread that connects diverse fields and drives innovation.

On that note, we’ll leave you with one more story about how maths saved one of the most important missions that the world has ever seen.

#### Apollo 11 Moon Landing: A Maths Miracle

The one big step for mankind would have been doomed, if not for precise mathematical calculations. Even the slightest error in calculating Apollo 11’s trajectory could have sent it off course. But getting to the moon was only half the battle won, identifying a safe landing site involved topographical mapping and gravitational calculations. And, the spacecraft’s guidance system relied on complex mathematical algorithms.

**A famous incident during the Apollo 11 mission highlighted the critical role of maths: **

A computer glitch almost caused the landing module to overshoot the intended landing site. Quick thinking of the astronauts and the accurate calculations of the engineers on Earth, decided on a manual takeover using calculations to ensure a safe landing.

So, maths is not just numbers. It’s the language through which we understand and control our world, especially in high-stakes scenarios like space exploration.