Math Family Tree
The Math Family Tree highlights the major discoveries, events, and mathematicians from the content covered in Mathematics Illuminatedand maps it on a timeline starting as early as 25,000 B.C.E., with the discovery of the Isango Bone, to present day with the Fields Medal winner, Grigori Perelman, who solved the Poincare Conjecture.
Orange lines illustrate the connections between how earlier mathematical developments influenced those that came later, spanning both units and decades.
Unit 1 The Primes
It is often said that Mathematics is a universal language. No matter one's culture, country, gender, race, or even religion, certain mathematical principles remain true. The fundamental letters of the mathematical alphabet are known as the primes.
Unit 2 Combinatorics Counts
Counting things seems so simple. Children do it intuitively, connecting a thing with fingers to say how many. Finding efficient and interesting ways to organize things and information is what the field of mathematics, known as Combinatorics, is all about.
Unit 3 How Big Is Infinity?
It takes courage to push beyond the boundaries of understanding, to both explore and explain the boundlessness of the infinite. Numbers and counting are real — intrinsic to our everyday life. But acknowledging their existence ties us to the existence of the infinitude.
Unit 4 Topology’s Twists and Turns
Can you imagine the shape of the universe? That's where Topology comes in: a branch of mathematics concerned with the study of spatial relationships that don't depend on measurement, and is more concerned with concepts like 'between' or 'inside,' and how things are connected.
Unit 5 Other Dimensions
Is there such a thing as a higher dimension, a parallel universe where otherworldly things can happen? Over the years, artists, writers and filmmakers have tried to answer that question, creating some dazzling works of science fiction in the process. But are the higher dimensions we see in sci-fi really fiction?
Unit 6 The Beauty of Symmetry
They say, beauty is in the eye of the beholder. What we consider to be beautiful in nature, art, or music often differs from culture to culture. But somehow, there seem to be constants — commonalities in how we as human beings "see" beauty. Where does that "sense" of beauty and order come from? And what does algebra or geometry have to do with it?
Unit 7 Making Sense of Randomness
How can we make sense out of the seemingly random results of throwing a pair of dice or even the haphazard flow of heavy traffic in the city? How can we talk meaningfully about any situation that is unpredictable or has an uncertain outcome? Well, welcome to the mathematics of probability.
Unit 8 Geometries Beyond Euclid
We live in a world — a reality — ruled by straight lines. Our streets, houses, cubicles — virtually all of our space is parceled into rectilinear grids. Mathematicians were also ruled by straight lines — some would say imprisoned by them — for two thousand years. But what is a straight line? And when is a straight line not "straight"?
Unit 9 Game Theory
We've all heard it said that life is like a game. Most games have well defined rules, with clear benefits for winning and costs for losing. And that makes them something we can think about logically and mathematically. But what about life? Can mathematics tell us anything about the competitions and collaborations that happen every day? From the social sciences to biology, robotics and beyond, the answer is yes.
Unit 10 Harmonious Math
Waves — lightwaves washing against our eyes creating a vision of the world around us, sound waves crashing against our ears — sometimes jarring and other times, beautiful, cosmic waves bathing the Universe. All of it explained, illuminated, and connected via mathematics.
Unit 11 Connecting with Networks
Virtually everything we experience — in nature as well as human activity — involves a series of connections that link one thing to another. Networks, you might say, make the world go 'round.
Unit 12 In Sync
Many things in the universe behave in a synchronized way — whether manmade, or natural. We see synchronization as an emergence of spontaneous order in systems that most naturally should be disorganized. And when it emerges, there is a beauty and a mystery to it, qualities that often can be understood through the power of mathematics.
Unit 13 The Concepts of Chaos
Most of us learned at an early age how an apple falling from a tree... inspired Isaac Newton to describe how the universe behaves by certain predictable rules. But what about when the universe doesn't behave so... predictably? Can mathematics explain the often unpredictable behavior of the physical world?
interactive 14 Math Family Tree
The Math Family Tree highlights the major discoveries, events, and mathematicians from the content covered in Mathematics Illuminated and maps it on a timeline starting as early as 25,000 B.C.E., with the discovery of the Isango Bone, to present day with the Fields Medal winner, Grigori Perelman, who solved the Poincare Conjecture.