Nicolas Bourbaki

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spk_0 Hello, I'm Professor Marcus De Soutoi and this is a brief history of mathematics, which

spk_0 was first broadcast on BBC Radio 4.

spk_0 All ten episodes of the series are now available at bbc.co.uk for slash podcasts, for you

spk_0 to collect and keep and listen to whenever you wish.

spk_0 This podcast of the last episode is set in 20th century France.

spk_0 It's the story of a highly productive but elusive mathematical hero.

spk_0 I remember as a graduate student being quite terrified by the collected works of Nicholas

spk_0 Borbache.

spk_0 His work filled several shelves of the white head library in Oxford.

spk_0 Was this the kind of productivity that would be expected of me?

spk_0 It was several years before I learnt more about this prolific and elusive mathematician,

spk_0 and I started to feel a little less insecure.

spk_0 The collected works of Borbache represent one of the most ambitious enterprises in mathematical

spk_0 history, an attempt to reform and reinvigorate the whole discipline, to build a new way of

spk_0 thinking about mathematics that would unify two previously distinct areas of the subject,

spk_0 shapes and numbers.

spk_0 Already, this new way of mathematical thinking has paved the way for the solution to the

spk_0 notoriously difficult Fermat's last theorem, proved by the British mathematician Andrew

spk_0 Wiles in 1995.

spk_0 And I use it every day to navigate the complex modern world of mathematics.

spk_0 And I believe Borbache's mathematics will lead to many remarkable mathematical and scientific

spk_0 breakthroughs in the decades to come.

spk_0 A brief history of mathematics with markers to Sotoie.

spk_0 Throughout the 19th century, the Paris Academy of Science was no longer the mathematical

spk_0 powerhouse it had once been.

spk_0 It was overshadowed by Gertingen and the giants of German mathematics, Karl Friedrich

spk_0 Gauss and Bernhardt Riemann.

spk_0 World War I killed off most of the remaining mathematical talent.

spk_0 And at the beginning of the 20th century, the next generation of French mathematicians found

spk_0 themselves without a father figure to inspire and guide them.

spk_0 Until one such mathematician, Andre Vé, wrote to a member of the Academy of Science to introduce

spk_0 a new colleague.

spk_0 I'm sure you'll recall that Monsieur Borbache is the former professor of the Royal University

spk_0 of Besson-Poldivie, whom I met some time ago at a cafe, where he spends most of the day

spk_0 and even the night, having lost both his job and most of his fortune amid the troubles

spk_0 that caused the unfortunate Poldivian nation to disappear from Europe.

spk_0 Now he earns his living at the cafe by giving lessons in Bilott, the card game he plays

spk_0 so brilliantly.

spk_0 Borbache submitted countless papers to the Academy of Science in Paris, together with the

spk_0 expected biographical details.

spk_0 World War I interrupted Borbache's fruitful scientific work.

spk_0 He then found himself in the Caucasus during the revolution of 1917, working in a research

spk_0 institute in Poldivia.

spk_0 Civil War forced Borbache to emigrate to Iran in 1920.

spk_0 This was the beginning of a dark period in Borbache's life.

spk_0 He finally ended up in Paris, where no mathematician would acknowledge the originality of his ideas.

spk_0 It was all fiction.

spk_0 Monsieur Bulbache was a figment of Andre Vays' imagination.

spk_0 The pseudonym for a group of young French mathematicians.

spk_0 A character created to reinvigorate French mathematics, blow away all the assumptions,

spk_0 and create a bold new mathematics for the future.

spk_0 Nicholas Bulbache, the mathematician that never was, hence all those many shells in the

spk_0 Whitehead Library.

spk_0 They and his contemporaries would meet three times a year for a week or two at a time

spk_0 to brainstorm about mathematics.

spk_0 Normally, at a cafe on the left bank, no doubt the scene of Bulbache's card playing.

spk_0 But sometimes they would retreat to the countryside, so as not to be distracted from their goal,

spk_0 to rewrite mathematics from the bottom upwards, and put the whole subject on firm, rigorous foundations.

spk_0 Riga is to the mathematician.

spk_0 What mortality is to men.

spk_0 Bulbache was rigorous, but anarchic.

spk_0 Indeed, the only thing that wasn't allowed in meetings was to remain silent.

spk_0 Bulbache was about creating a new mathematics, one that everyone was expected to take part in molding.

spk_0 Certain foreigners, invited as spectators to Bulbache meetings,

spk_0 always come out with the impression that it is a gathering of madmen.

spk_0 They could not imagine how these people shouting sometimes three or four at the same time

spk_0 could ever come up with something intelligent.

spk_0 But for the members of the Bulbache collective, it was all part of the process.

spk_0 The guiding ethos of this group was based on the very thing that makes mathematics so unique amongst the solences.

spk_0 In physics, chemistry or biology, theories live or die based on their ability to account for experimental data.

spk_0 Mathematics is different.

spk_0 Once a theorem is proved, it will hold true forever.

spk_0 Each generation of mathematicians builds on the work of its predecessors.

spk_0 But Bulbache felt that the mathematical edifice had become rather rambling and with too many disconnected wings.

spk_0 They believed in the inherent unity of mathematics.

spk_0 They wanted to present the whole of mathematics in its purest, simplest form,

spk_0 to reclassify and reform the entire discipline.

spk_0 They wanted to strip mathematics back to its deepest foundations.

spk_0 The maths they did was highly abstract and very ambitious.

spk_0 The invention of Bulbache did reinvigorate French mathematics just as they had hoped.

spk_0 But then the specter of another war began to loom over Europe.

spk_0 They fled to Finland, hoping to keep Bulbache alive from there.

spk_0 But soon ended up in prison on suspicion of being a Soviet spy.

spk_0 His calling cards belonging to Nicholas Bulbache and pages of incomprehensible equations

spk_0 all looked very suspicious to the Finnish authorities.

spk_0 He narrowly avoided execution, but escaped one prison in Finland only to be thrown into another

spk_0 in Rua in France, where he was charged with desertion from the army.

spk_0 Mathematics had always been a comfort to vey when the going got tough in the real world.

spk_0 Once when I took a painful fall, my sister Simone could think of nothing for it but to run

spk_0 and fetch my algebra book to comfort me. And as vey waited trial in prison, it was mathematics again

spk_0 that brought him comfort. One of the joys of mathematics is that it requires little equipment

spk_0 beyond pen, paper and imagination. The prison provided the first two of these,

spk_0 they had plenty of the third. In April 1940, he wrote to his wife Eveline,

spk_0 my mathematics work is proceeding beyond my wildest hopes, and I'm even a bit worried.

spk_0 If it is only in prison that I work so well, will I have to arrange to spend two or three months

spk_0 locked up a year? Usually, they was very cautious about publishing his work too soon,

spk_0 preferring to check every detail of his proof. But on this occasion he felt that the future was

spk_0 too uncertain to risk delay. He wrote to the editor of the prestigious French journal

spk_0 Contreau du. I'm very pleased with it, especially because of where it was written. It must be the

spk_0 very first in the history of mathematics, and because it is a fine way of letting all my friends

spk_0 around the world know that I exist. And I am thrilled by the beauty of my theorems.

spk_0 To which the editor's son, a friend and colleague of theirs, wrote back,

spk_0 embarsly, we're not all lucky enough to sit and work undisturbed like you.

spk_0 In prison in Rourne, they began to develop a whole new approach to mathematics,

spk_0 building on the work of Bourbon-Bacquille, an approach that would allow him to change the algebra

spk_0 of equations into something much more tangible. In the beginning of the 17th century,

spk_0 the French philosopher and mathematician René Descartes invented a way to convert lines,

spk_0 shapes and places into numbers and equations. Any position in space, he realised, could be described

spk_0 as a set of coordinates. I'm standing outside Broadcasting House in central London,

spk_0 and I've got a global positioning system here on my phone. Now, the phone is telling me that my

spk_0 latitude is 51.5 degrees north, and my longitude is 0.14 degrees west. Now, these numbers

spk_0 identify my north-south and east-west location, as measured from the place where the equator

spk_0 meets the line of longitude running north-south through Greenwich, the so-called Meridian line,

spk_0 and they allow you to locate my precise geometric location on the earth's surface.

spk_0 In school today, most children learn about two distinct areas of maths, shapes and numbers.

spk_0 But Descartes showed us how to turn shapes into numbers using his idea of coordinates.

spk_0 Andre Vé wondered if you could do a similar thing, but in the opposite direction.

spk_0 Could you use intuitive ideas about geometry and shapes to solve problems in the world of numbers

spk_0 and equations? He showed us how to think about equations as shapes. Yes, it's a tricky idea,

spk_0 and it was complicated even for the mathematicians of the time. It's a giant mathematical leap forward.

spk_0 Absolutely the product of Bourbacchi's extreme ambition, and it moved the entire discipline of

spk_0 mathematics onto a totally new level. They created the mathematically beautiful concept of what is

spk_0 now called algebraic geometry. This concept has since enabled mathematicians to solve equations

spk_0 that for centuries had seemed quite impossible. Most famously, it paved the way for a solution in

spk_0 1995, a Fermat's last theorem. The British mathematician Andrew Wiles may have played the final

spk_0 chord in this much celebrated proof, but it was the whole idea of algebraic geometry that made this

spk_0 possible. Now, as you may have heard me argue more than once in this brief history of mathematics,

spk_0 I believe mathematics is the driving force behind modern science. So I can anticipate your next

spk_0 question. What has this highly abstract concept of algebraic geometry done for the real world of

spk_0 science and technology? And I'm going to say that it's too early to judge. Mathematics is often

spk_0 ahead of the game. It can take two or three hundred years for the full power of mathematical insights

spk_0 to be appreciated by scientists. But already there are promising signs that algebraic geometry

spk_0 will prove itself in the real world of science and technology. It's used in codes on mobile phones

spk_0 and smart cards. Some biologists believe it sheds light on the evolution of genes, and robot

spk_0 designers are interested in it too. They, himself, however, was never that bothered by how his mathematics

spk_0 would be applied. They was released from prison in May 1940, and rather than sticking around in

spk_0 France, he did what many European mathematicians were doing at the time, move to America.

spk_0 The Institute for Advanced Study in Princeton had opened its doors in 1933, but the end of the

spk_0 war was a well-funded research centre with many superstars in the faculty, Einstein and Gurdle

spk_0 and countless other scientific emigrates. With Europe ravished by war and Gertengen destroyed by

spk_0 Hitler, Princeton quickly became the place to study mathematics. And to this day, it continues to

spk_0 attract mathematical talent from across Europe, including Britain's very own mathematical superstar

spk_0 Andrew Wiles. Although this autumn, Andrew Wiles is due to arrive in Oxford where I work. Could this

spk_0 be a good omen for where might be the happening place for mathematics in the 21st century? I hope so.

spk_0 At the start of this brief history of mathematics, I set out my stall. Mathematics, I said,

spk_0 is the Queen of Science. Of course, microscopes and telescopes and countless key experiments have

spk_0 played a hugely important role in the history of science. But I believe that the main driving force

spk_0 behind scientific discovery is mathematics. Of course, I'm a mathematician and of course I'm biased

spk_0 in favour of my own discipline. But time and again in this brief history of mathematics, I hope I've

spk_0 shown just how powerful mathematics can be in the scientific quest to understand the world.

spk_0 Galileo said that the universe is written in a mathematical language. And until we understand

spk_0 that language, we have no hope of reading it. Without mathematical insight, scientists are

spk_0 wandering around in a dark labyrinth. Mathematics is the Queen of Science. But here's the final twist.

spk_0 It achieves this status, not because it sets out to answer scientific questions,

spk_0 but because mathematicians pursue mathematics for its own sake.

spk_0 Mathematicians deal in abstract problems. Their equations have a life of their own detached from

spk_0 reality. But it is the solutions to these abstract problems that have had amazing and often

spk_0 unintended consequences for the world of science. It is the mathematicians who focus solely on

spk_0 mathematics who have changed the course of modern science.

spk_0 Thanks for listening to this podcast from BBC Radio 4 with me, Marcus De Sotoi.

spk_0 And if you enjoyed this episode, don't forget you can collect the whole set. All 10 episodes

spk_0 of a brief history of mathematics, as well as the terms and conditions can be found at

spk_0 bbc.co.uk forward slash podcasts.

Nicolas Bourbaki

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