A Brief History of Mathematics (podcast)
Subject: Mathematics
Type: Podcast
Host: Marcus du Sautoy, Professor of Mathematics
How long is it?
There are ten episodes. The average episode length is 13 minutes and 42 seconds.
Is it easy to understand?
It is down-to-earth and digestible, with analogies for consolidation.
Who is it for?
It is aimed at anyone with an interest in mathematics or history.
How recent is it?
BBC Radio 4 released the last episode in 2010.
What to expect
Episode 1: Newton and Leibniz (the mathematician, not the biscuits!)
- A brief introduction to calculus
- The history of two late 17th century mathematicians who were working on calculus at the same time – and the controversy that arose
- Which of them we eventually recognised as the inventor of calculus
- How calculus has aided our understanding of other concepts
- The applications of calculus in today’s world
Episode 2: Leonhard Euler
- The ways in which Euler turned anything he could into mathematics
- How Euler rebuilt calculus
- How the mathematics that Euler invented two hundred years ago has transformed the internet
“Read Euler. Read Euler. He is master in everything.”
(Pierre-Simon, marquis de Laplace)
Episode 3: Joseph Fourier
- The role of mathematics in the French Revolution
- Fourier’s fascination with heat
- The opposition to Fourier’s work
- How the mathematics of Joseph Fourier contributes to physics and modern technology
- The mathematics behind sound waves
Episode 4: Evariste Galois
- Galois as a French revolutionary
- Why symmetry intrigued Galois
- How Galois transformed our understanding of symmetry
- Why statistics are so powerful
- How Galois’s mathematics is used by particle physicists to determine what the universe is made of
Episode 5: Carl Friedrich Gauss
- How Gauss predicted the movement of stars
- The Gaussian or normal distribution as the lifeblood of statistics
- How Gauss’s mathematics underpins modern medicine
- How Gauss’s story is a valuable tool in the fight against prejudice
- Why Gauss didn’t show his working
Episode 6: The Mathematicians Who Helped Einstein
- Jonas Bolyai, Nicolas Loachevski and Bernhard Riemann
- Why Einstein sometimes struggled with mathematics
- The mathematics to describe curved space and multiple dimensions which were necessary for Einstein’s theory of relativity to work
- Why Einstein receives so much attention
Episode 7: Georg Cantor
- How Cantor showed us how to carry on counting when the numbers run out
- Why infinity is a number – or rather, infinitely many numbers
- Why some infinities are bigger than others and why there are infinite infities
- Why Cantor was a century ahead of his time
- How the nature of infinity explains why the human brain will always be more clever than artificial intelligence
Episode 8: Henri Poincaré
- How Poincaré’s work proved that there are certain problems that mathematics will never be able to answer and how this insight gave rise to chaos theory
- Why mathematics is unpredictable
- Why a butterfly flapping its wings in West Africa makes tiny changes in the atmosphere that could cause a tornado in Tokyo
- The implications of chaos theory for the stability of the solar system
Episode 9: Hardy (not the actor!) and Ramunajan
- Why prime numbers are a “diabolical malice” and arguably, the most important numbers in mathematics
- How computer scientists encrypt websites using prime numbers and why it works
- Why Hardy and Ramanujan both attempted suicide
“His originality had been a constant source of suggestion to me”
(Hardy, talking about Ramunajan)
Episode 10: Nicolas Bourbaki
- The power of shapes and numbers
- The birth of algebraic geometry
- How a group of French mathematicians transformed their discipline and paved the way for several mathematical breakthroughs in the 21st century, such as the solution to Fermat’s Last Theorem
- The application of the mathematics of these French mathematicians to phones and smart cars.
- Why geneticists are also interested by this mathematics
My thoughts…
The relationship between mathematics and science
In A Brief History of Mathematics, Marcus du Sautoy argues that mathematics is the driving force behind modern science. After learning about the history of mathematics, I can see how a mathematical breakthrough tends to lead to a scientific one, whether this occurs immediately or after a few centuries. This also makes sense because of the fact that we use mathematics as a ‘language’ in science. For example, in physics, mathematical equations and models are used to describe the behaviour of particles, forces, and the laws of motion. So, as our mathematical vocabulary increases, we find practical applications for these discoveries through science.
However, I am not denying that science can inspire mathematics. Science provides the real-word problems and questions that mathematicians can research. It is also important to note that we cannot analyse the complete histories of mathematics and science simply because they are still being written, so we have not seen the full potential of either field. Ultimately, I would say that mathematics most definitely is a driving force of scientific progress.
Is the value of mathematics its usefulness or should we pursue it for its own sake?
I would argue that the value of maths is partially dependant on its benefit to us, however, this does not contradict my belief that we should pursue maths for its own sake. The history of mathematics demonstrates that regardless of whether or not a mathematician is solely interested in mathematics for its own sake, their work is eventually applied or built upon in a way that is useful. In addition, I see no reason why mathematics should not be treated as an art, with utility being a by-product of its evolution. Perhaps the value of mathematics is unimportant as long as the field continues to develop.
One last thing
Finally, it’s worth noting whether you thought anything was missing in the brief history of mathematics? What I’m hinting is that none of the personalities in the podcast were female. Unfortunately, women are still outnumbered in STEM fields today and this issue isn’t exclusive to maths-based subjects. If you are interested, you should also learn about female mathematicians in history here, because they deserve more recognition.