BBC
By the seventeenth century Europe had taken over from the Middle East as the world’s power house of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was now on to discover the mathematics that describes objects in motion.
In this programme, Marcus du Sautoy visits France to look at the work of René Descartes, an outstanding mathematician and theoretical physicist as well as one of the great philosophers, who realised that it was possible to link algebra and geometry.
His vital insight - that it was possible for curved lines to be described as equations - would change the course of the discipline forever.
Marcus also examines the amazing properties of prime numbers discovered by Pierre Fermat, whose famous Last Theorem would puzzle mathematicians for more than 350 years. He shows how one of Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet.
In England he looks at Isaac Newton’s development of calculus, a great breakthrough which is crucial to understanding the behaviour of moving objects and is used today by every engineer. He also goes in search of mathematical greats such as Leonard Euler, the father of topology or ‘bendy geometry’ and Carl Friedrich Gauss, who at the age of 24 was responsible for inventing modular arithmetic (a new way of handling equations).
Gauss made major breakthroughs in our understanding of how prime numbers are distributed. This made a crucial contribution to the work of Bernhard Riemann, who developed important theories on prime numbers and had important insights into the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.
First broadcast: Monday 13 Oct 2008 on BBC FOUR. For further broadcast details, and to watch online where available, visit bbc.co.uk
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Comments on: "The Frontiers of Space"
nacram has started a thread discussing The Frontiers of Space.
i love the old stories about ancient bulding &i'm in the faculity of engineering in egypt (civil department)
Regarding Marcus' comment that the English wouldn't name a town after Newton, as the French have done for Descartes, I live in the suburbs of Chester just off Newton Lane, and five minutes walk from a place called Newton. My guess is that it was new town some time between the Romans and the industrial revolution (well obviously!). So in other words, Isaac Newton was probably named after a town.
I LOVE this series. The host really makes the subject come alive. So when I missed last week's episode (#3), I was frustrated not to be able to download it from the website. Isn't there a way to make that available, as you do with "Click" episodes?
I dont know if I missed a part of it, but it seems that there wasn't a part about Evariste's Galois contribution.It just turns out that he's one of my heroe's, I hope there would be another programme that will take up the life and contribution of this titan.
Re: Comments on: "The Frontiers of Space"
Hello, I'm Fred.
I'm not sure if this is the best place to start this conversation but I belive that here I can find somebody to talk about a book wich I've been reading.
Its name is EMPIRE OF THE STARS and is about the entire period of the discovery of black holes, so as far as I can undertand when a star gets old, it can not produce so much ligth anymore and the gravitational force of the star starts to compact itself. According to Chandra, if a star is smaller than a certain limit it became a cold rock, If not something incredable happen, the star keeps contracting until gravitational force finds its limit. Now my question is, for fact mass deformes space and as much mass you add to it more deformation you will cause so the reason that you can not see the star wich became a black hole is not only because it captures light but is also due to the stong deformation of the space. Is that right?
Thanks
Re: Comments on: "The Frontiers of Space"
Hi Fred,
You've got a few things on the go at the same time there. Deformation of space is just another way of looking at gravity, and that is what makes a black hole black. Any body (like a planet or a star) has mass, and that mass applies a gravitational attraction to anything else that is proportional to that mass and inversely proportional to the square of its distance from that body's centre. That means for us standing on the Earth's surface, nearly 4000 miles from its centre, we feel a certain attraction. If we jump up, we go so far before falling back down. We can throw a stone in the air at a higher speed and it will take a few seconds to come back down. We could shoot a bullet into the air and it might take a minute or two to come down. Now if we fired a projectile at a high enough speed, it would never come back, as the gravitational force pulling it back will diminish as it recedes. This velocity is called the 'escape velocity', and for Earth it is about 7 miles per second. For the moon it is considerably lower, and on a very small asteroid it really would be possible for an astronaut to jump right off.
Now if we extrapolate in the opposite direction, with greater mass and a smaller radius, the escape velocity needs to be much higher, but the universe has a speed limit - the speed of light. If you get a dense enough object, the escape velocity can exceed that limit and not even light can get out. This is a black hole.
For a very long time they were only theorised, but now there is overwhelming evidence for their existence, both as individual stellar ones (a star of at least 8-10 times the mass of the sun is required to form one), or as supermassive ones at the centres of most galaxies (you may have read recently they have measured the one at the centre of our own galaxy to be at a distance of 27,000 light years and a mass of around 4,000,000 times the mass of the sun.
Here's one last sound bite: if you wanted to compress the Earth to make it into a black hole, it would need to be reduced in size to a diameter of about 2 centimetres!
Re: Comments on: "The Frontiers of Space"
All this cold star compacting stuff is pure science fiction, according to what I learned. Not one ounce of truth to it, at least according to actual provable accounts. I have never seen one. And neither has anyone else.
I think we should keep that in mind. The Universe can still function without this theory.
Sincerely,
William McCormick
Re: Comments on: "The Frontiers of Space"
Sorry, I forgot to sign in when I replied. Post #3 was me.