Melvyn Bragg and guests discuss the problem of P versus NP, which has a bearing on online security. There is a $1,000,000 prize on offer from the Clay Mathematical Institute for the first person to come up with a complete solution. At its heart is the question "are there problems for which the answers can be checked by computers, but not found in a reasonable time?" If the answer to that is yes, then P does not equal NP. However, if all answers can be found easily as well as checked, if only we knew how, then P equals NP. The area has intrigued mathematicians and computer scientists since Alan Turing, in 1936, found that it's impossible to decide in general whether an algorithm will run forever on some problems. Resting on P versus NP is the security of all online transactions which are currently encrypted: if it transpires that P=NP, if answers could be found as easily as checked, computers could crack passwords in moments. With  Colva Roney-Dougal
Reader in Pure Mathematics at the University of St Andrews Timothy Gowers
Royal Society Research Professor in Mathematics at the University of Cambridge And  Leslie Ann Goldberg
Professor of Computer Science and Fellow of St Edmund Hall, University of Oxford Producer: Simon Tillotson.

P v NP

Scientific principles, theory, and the role of key figures in the advancement of science.

History

Society & Culture

Melvyn Bragg and guests discuss the German physicist who, at the age of 23 and while still a student, effectively created quantum mechanics for which he later won the Nobel Prize.  Werner Heisenberg made this breakthrough in a paper in 1925 when, rather than starting with an idea of where atomic particles were at any one time, he worked backwards from what he observed of atoms and their particles and the light they emitted, doing away with the idea of their continuous orbit of the nucleus and replacing this with equations. This was momentous and from this flowed what’s known as his Uncertainty Principle, the idea that, for example, you can accurately measure the position of an atomic particle or its momentum, but not both. With  Fay Dowker
Professor of Theoretical Physics at Imperial College London Harry Cliff
Research Fellow in Particle Physics at the University of Cambridge And  Frank Close
Professor Emeritus of Theoretical Physics and Fellow Emeritus at Exeter College at the University of Oxford Producer: Simon Tillotson Reading list: Philip Ball, Beyond Weird: Why Everything You Thought You Knew about Quantum Physics Is Different (Vintage, 2018) John Bell, ‘Against 'measurement'’ (Physics World, Vol 3, No 8, 1990) Mara Beller, Quantum Dialogue: The Making of a Revolution (University of Chicago Press, 2001) David C. Cassidy, Beyond Uncertainty: Heisenberg, Quantum Physics, And The Bomb (Bellevue Literary Press, 2010)  Werner Heisenberg, Physics and Philosophy (first published 1958; Penguin Classics, 2000) Carlo Rovelli, Helgoland: The Strange and Beautiful Story of Quantum Physics (Penguin, 2022)

Heisenberg's Uncertainty Principle

Melvyn Bragg and guests discuss some of the chemical signals coursing through our bodies throughout our lives, produced in separate areas and spreading via the bloodstream.  We call these 'hormones' and we produce more than 80 of them of which the best known are arguably oestrogen, testosterone, adrenalin, insulin and cortisol. On the whole hormones operate without us being immediately conscious of them as their goal is homeostasis, maintaining the levels of everything in the body as required without us having to think about them first.  Their actions are vital for our health and wellbeing and influence many different aspects of the way our bodies work. With Sadaf Farooqi
Professor of Metabolism and Medicine at the University of Cambridge Rebecca Reynolds
Professor of Metabolic Medicine at the University of Edinburgh And Andrew Bicknell
Associate Professor in the School of Biological Sciences at the University of Reading Produced by Victoria Brignell Reading list: Rachel Carson, Silent Spring (first published 1962; Penguin Classics, 2000) Stephen Nussey and Saffron Whitehead, Endocrinology: An Integrated Approach (BIOS Scientific Publishers; 2001) Aylinr Y. Yilmaz, Comprehensive Introduction to Endocrinology for Novices (Independently published, 2023)

Hormones

Melvyn Bragg and guests discuss the tiny drifting organisms in the oceans that sustain the food chain for all the lifeforms in the water and so for the billions of people who, in turn, depend on the seas for their diet.  In Earth's development, the plant-like ones among them, the phytoplankton, produced so much oxygen through photosynthesis that around half the oxygen we breathe today originated there. And each day as the sun rises, the animal ones, the zooplankton, sink to the depths of the seas to avoid predators in such density that they appear on ship sonars like a new seabed, only to rise again at night in the largest migration of life on this planet. With Carol Robinson
Professor of Marine Sciences at the University of East Anglia Abigail McQuatters-Gollop
Associate Professor of Marine Conservation at the University of Plymouth And Christopher Lowe
Lecturer in Marine Biology at Swansea University Producer: Simon Tillotson Reading list:  Juli Berwald, Spineless: The Science of Jellyfish and the Art of Growing a Backbone (Riverhead Books, 2018) Sir Alister Hardy, The Open Sea: The World of Plankton (first published 1959; Collins New Naturalist Library, 2009)  Richard Kirby, Ocean Drifters: A Secret World Beneath the Waves (Studio Cactus Ltd, 2010) Robert Kunzig, Mapping the Deep: The Extraordinary Story of Ocean Science (Sort Of Books, 2000) Christian Sardet, Plankton: Wonders of the Drifting World (University of Chicago Press, 2015)  Helen Scales, The Brilliant Abyss: True Tales of Exploring the Deep Sea, Discovering Hidden Life and Selling the Seabed (Bloomsbury Sigma, 2022)

Plankton

Melvyn Bragg and guests discuss the man who, in 1905, produced several papers that were to change the world of physics and whose name went on to become a byword for genius. This was Albert Einstein, then still a technical expert at a Swiss patent office, and that year of 1905 became known as his annus mirabilis ('miraculous year').  While Einstein came from outside the academic world, some such as Max Planck championed his theory of special relativity, his principle of mass-energy equivalence that followed, and his explanations of Brownian Motion and the photoelectric effect.  Yet it was not until 1919, when a solar eclipse proved his theory that gravity would bend light, that Einstein became an international celebrity and developed into an almost mythical figure. With  Richard Staley
Professor in History and Philosophy of Science at the University of Cambridge and Professor in History of Science at the University of Copenhagen Diana Kormos Buchwald
Robert M. Abbey Professor of History and Director and General Editor of The Einstein Papers Project at the California Institute of Technology And John Heilbron 
Professor Emeritus at the University of California, Berkeley Producer: Simon Tillotson Reading list:  Ronald W. Clark, Einstein: The Life and Times (first published 1971; HarperPaperbacks, 2011) Albert Einstein (eds. Jurgen Renn and Hanoch Gutfreund), Relativity: The Special and the General Theory - 100th Anniversary Edition (Princeton University Press, 2019) Albert Einstein, Out of My Later Years (first published 1950; Citadel Press, 1974) Albert Einstein (ed. Paul A. Schilpp), Albert Einstein: Philosopher-Scientist: The Library of Living Philosophers Volume VII (first published 1949; Open Court, 1970) Albert Einstein (eds. Otto Nathan and Heinz Norden), Einstein on Peace (first published 1981; Literary Licensing, 2011) Albrecht Folsing, Albert Einstein: A Biography (Viking, 1997) J. L. Heilbron, Niels Bohr: A Very Short Introduction (Oxford University Press, 2020) Walter Isaacson, Einstein: His Life and Universe (Simon & Schuster, 2008) Max Jammer, Einstein and Religion (Princeton University Press, 2002) Michel Janssen and Christoph Lehner (eds.), The Cambridge Companion to Einstein (Cambridge University Press, 2014) Dennis Overbye, Einstein in Love: A Scientific Romance (Viking, 2000) Abraham Pais, Subtle Is the Lord: The Science and the Life of Albert Einstein (Oxford University Press, 1982) David E. Rowe and Robert Schulmann (eds.), Einstein on Politics: His Private Thoughts and Public Stands on Nationalism, Zionism, War, Peace, and the Bomb (Princeton University Press, 2007) Matthew Stanley, Einstein's War: How Relativity Triumphed Amid the Vicious Nationalism of World War I (Dutton, 2019) Fritz Stern, Einstein’s German World (Princeton University Press, 1999) A. Douglas Stone, Einstein and the Quantum: The Quest of the Valiant Swabian (Princeton University Press, 2013) Milena Wazeck (trans. Geoffrey S. Koby), Einstein's Opponents: The Public Controversy About the Theory of Relativity in the 1920s (Cambridge University Press, 2014)

Albert Einstein

Jupiter is the largest planet in our solar system, and it’s hard to imagine a world more alien and different from Earth. It’s known as a Gas Giant, and its diameter is eleven times the size of Earth’s: our planet would fit inside it one thousand three hundred times. But its mass is only three hundred and twenty times greater, suggesting that although Jupiter is much bigger than Earth, the stuff it’s made of is much, much lighter. When you look at it through a powerful telescope you see a mass of colourful bands and stripes: these are the tops of ferocious weather systems that tear around the planet, including the great Red Spot, probably the longest-lasting storm in the solar system. Jupiter is so enormous that it’s thought to have played an essential role in the distribution of matter as the solar system formed – and it plays an important role in hoovering up astral debris that might otherwise rain down on Earth. It’s almost a mini solar system in its own right, with 95 moons orbiting around it. At least two of these are places life might possibly be found.   With Michele Dougherty, Professor of Space Physics and Head of the Department of Physics at Imperial College London, and principle investigator of the magnetometer instrument on the JUICE spacecraft (JUICE is the Jupiter Icy Moons Explorer, a mission launched by the European Space Agency in April 2023) Leigh Fletcher, Professor of Planetary Science at the University of Leicester, and interdisciplinary scientist for JUICE Carolin Crawford, Emeritus Fellow of Emmanuel College, University of Cambridge, and Emeritus Member of the Institute of Astronomy, Cambridge

P v NP

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