There is a mystery at the heart of our universe a Puzzle that so far no one has been able to solve it can be weird. Welcome to the world If we can solve this mystery it will have profound consequences for all of us That mystery is why mathematical rules and patterns seem to infiltrate pretty much Everything in the world around us Many people have in fact described maths as the underlying language of the universe But how did it get there? Even after thousands of years this question causes controversy We still can't agree on what maths actually is or where it comes from Is it something that's invented like a language or is it something that we have merely discovered I think discovered Invented it's both. I have no idea Why does any of this matter well maths underpins just about everything in our modern world From computers and mobile phones to our understanding of human biology and our place in the universe My name is Hanna Frey and I'm a mathematician in this series I will explore how the greatest thinkers in history Have tried to explain the origins of maths extraordinary power Human is equation I'm going to look at how in ancient times our ancestors thought maths was a gift from the gods How in the 17th and 18th centuries we invented new? mathematical systems and use them to create the scientific and industrial revolutions and I'll reveal how in the 20th and 21st centuries Radical new theories are forcing us to question once again Everything we thought we knew about maths and the universe The unexpected should be expected because why would reality down there bear any resemblance to reality up here? In this episode I explore paradoxes within modern mathematics you shave the barber and I discovered the very weird world that math seems to be leading us into Maths is very much part of our modern world Even the images you are watching now are essentially numbers processed by computers Sorry guys Today maths is at the heart of big business in the development of new software such as facial recognition technology all of which from the mentally Is based on mathematical algorithms? And it matters because copyright issues and legal ownership can depend on where that maths comes from You can freeze the question. My guess is Matt's a genuine fundamental part of our universe something that we have discovered or is it merely Invented a language that we've created just to describe the world around us Mathematicians have argued over this idea for centuries. And even today this question is a thought-provoking and challenging dilemma So far I've explored how in ancient times maths was revered as a gift from the gods perfect complete and gratefully discovered by humans But through the ages new areas of mathematics Like algebra, and the concept of zero have quite simply been invented but for most of us we normally think of maths as just a series of Objective facts based in logic that someone somewhere has discovered Facts that we all start to learn at school Do anything like me you'll remember maths at school being taught as a series of rules was very logical It's very ordered. Very complete. Very black-and-white there were Right and wrong answers which you didn't necessarily get in other subjects like art or like music which were much more about preferences about opinions and about cultural differences It felt like the mathematical rules were intrinsically true, but why What are the fundamental mathematical laws? To answer that question You have to categorize everything you have to boil maths down into distinct groups of Objects in something called set theory Set theory is a language that talks about groups or sets of items So for example the set of odd numbers are all the whole numbers That cannot be neatly divided by two and the set of even numbers are those that can This reveals a basic rule adding an odd number to an even one produces an odd number From simple rules like these you can build up more and more complex rules and relations of maths But there's a problem with set theory a Paradox at the heart of mathematical rules which caused a bit of a crisis at the start of the 20th century you can discover this paradox yourself by going to your local hairdresser or Gentleman's barber and trying to define what you find in a concise and complete way The very definition of a bar I think I can help that mathematicians took the same approach to precisely define the laws of maths One sentence that defined what barber Wars what would you say it was? Cotton's hair cut men's hair, but that could be a hairdresser though, right hairdressing It needs to be a unique definition for barbers barbers and only barbers Yeah, that's a dress no Surroundings face the shame thing is something that only barbers do so someone who shaves men But Obama doesn't shave all men and I need a phrase that uniquely and completely identifies a barber and no one else See what garden so we've got the barber shades or men but only the men who shave but don't shape us We've agreed on a barber shaves all men and only those men who shave but do not shave themselves Right, I don't exactly roll off the tongue But how second there's bit of a paradox here Who shades the barber? When I shave himself, but if he does save himself then our definition here says they Doesn't shake himself Let me clarify that if he doesn't shave himself then according to the definition He's one of the men shaved by the barber So he does shave himself Attempting to create a Mathematically precise definition creates a contradiction where the barber both shaves himself and doesn't shave himself This is known as the barbers paradox It is an illustration of the paradox at the heart of mathematics Which was discovered in 1901 by one of my favorite trouble makers Bertrand Russell The problem for maths was that Russell's paradox Undermines the logic of defining things like odd or even numbers by putting them into categories Or sets. Oh here. I have got a set of kippa attachments and in there I have got a set of things that aren't clip or attachments clipper attachment goes in there not a clipper attachment goes Clipper Not your clipper Now the question is Where does this bag belong it's clearly not a clipper attachment. Is it going to attach to? No, it's not which means it used to go in there But we've got a problem because this sink is supposed to only contain things that are not Clipper attachments Which means? That the contents of the bag can't go in the sink Since the bag or set is not in itself a clipper attachment but by its definition Contains clipper attachments. We can't easily categorize where the set belongs Similarly the barber can't in a logically consistent way be contained in a set of people that do shave themselves all the set of people who doped Russell's paradox shows that there is a logical problem with trying to categorize anything into coherent sets whether it's barbers clipper attachments or even numbers and This logical puzzle exposed a fault in the bedrock on which all the rest of maths is built If the foundations are shaky, how can we trust everything else? Bertrand Russell realized that Mathematics was a much Shaker ground when people had originally thought that turn at me much much harder to really lay a solid foundation for math that everybody agreed on and This is still wonderfully controversial this day. That's what you do in science in mathematics You take a sledgehammer You smash at whatever structure whatever edifice you've built you try to find the weaknesses and that allows you to figure out what needs to be shored up and that's really I think the legacy that that Russell left us I Think of it as In some ways the death knell or at least a major challenge of the attempt to ground my attics in logic and that's the thing That becomes really hard and lightest Russell's paradox Russell's paradox, cause the real crisis monks mathematicians suddenly maths was uncertain Fallible and if it has these fundamental problems How can it possibly be discovered so? Does that mean that maths has to be invented just a human language and all of the floors that come with it? If maths is merely an invention of the human mind, it's perhaps not that surprising that it's not perfect But I don't think I'm ready to accept the invention argument quite yet Math just seems to be too good at predicting the behavior of the world in ways We never could have imagined because just as Bertrand Russell was exposing the limitations of maths in one way Another Titan of the 20th century Albert Einstein was pulling it back in a completely different direction Take what is probably the most famous equation in the world with just five symbols, it looks so simple It's almost childish yet. It contains some incredibly powerful mathematical and Philosophical concepts I'm talking of course about e equals mc-squared So e Energy that is equal to M That's mass times by a constant C is the speed of light There is so much more to this equation than meets the eye It is Einsteins discovery that matter and energy are equivalent and that has profound consequences This equation gives us one of the immutable laws in the universe The reasoning is this Making something move requires More energy than keeping it at rest And because this C here is a constant If the energy goes up by accelerating something the mass also has to increase so that means that you or I Actually away a tiny bit more when we're moving in a car or eclaim The increase in mass only becomes significant when objects are moving at speeds close to the speed of light As an object approaches the speed of light its mass Rises faster and faster, which means it takes more energy to Accelerate it further It can't therefore weak the speed of light Because the mass becomes infinite and it would require an infinite amount of energy to get there The variant is equation As well as proving there's a cosmological speed limit this single equation also Explains how all the stars and the universe? Converts mass into energy as they burn brightly in the night sky Einstein's famous equation has proved itself to be a remarkable match for reality every time it's been put to the test Einstein had uncovered one of the essential mathematical rules underlying the cosmos It seems like clear evidence that that maths at least is discovered, but Einstein didn't stop there using the power of mathematics He brought about a fundamental shift In our understanding of space and of time and of how light travels through space To see that evidence of myself. I've come to an observatory to do some serious thinking About what we actually see when we look at stars in the sky such as our Sun If things were happening right now We wouldn't be able to see it until eight and a half minutes later because that's how long it takes the light to travel to The earth so when you're looking at the Sun you're seeing how it was eight and a half minutes ago. Exactly and Objects that are further away we see them as they were further back in time So for instance, there are other stars in our galaxy, there are Thousands of light-years away. So we see them as they were thousands of years ago So when you look in a telescope and you're you're seeing them how they were When people were building pyramids and Pythagoras was discovering his rules on earth Exactly and and we can see things that are even further away than that. So galaxies outside our own galaxy And we see many of them that as they were a billion years ago or more gosh goodness Did this one got smaller scales then they say is there like a limit to how big? something has to be before this works if you I mean I'm looking at you now right like Presumably is taking time to bounce off you and for me to see you. Yes, it is but light travels at any credibly fast speed 300,000 kilometers per second, roughly so the time it takes to travel from me to you is it's very very tiny fraction of a second but in theory I am seeing You in the very yes, you're absolutely seeing me in the past All of this shows that we can never know what the universe is like at this very instant the universe is Remarkably not a thing that extends just in space but in time as well This is fundamental to Einstein's revolutionary Insights about our universe. He realized that the very concept of time is relative That is to say it depends on the position and movement of the observer He worked it out by thinking about events that appear to be simultaneous So let's imagine that you're in a hot air balloon looking above the observatory here and you're high enough that you can see a flash of light in London and say and another one in Portsmouth and Let's assume that these flashes of light go off such that You see both of them happening exactly Simultaneously so from where I am. It looks like the best flashing the highs enter at exactly the same time but if I were in an aircraft that was flying very fast Towards London I would see the flash of light in London before and a flash of light from Portsmouth Using the inescapable logic of mathematics Einstein realized that if an observer is moving Towards one of the flashes they would see that flash before the other one caught up with them So for them, the flashes are not simultaneous But whose okay, but I mean they did go off together. Who's wrong. Am I right in the hot air balloon? In fact, there is no way of saying that you are right and I am wrong in How we observe these events? This is called relativity So our whole concept of time my whole concept of timings. What happens first? What happens second? Comes down to where we are and how we're moving Exactly. So the concept of time is now inextricably linked to the positions in space and your movement through space So this is why we can't describe space and time separately, but we have to put them together in space-time You can't separate the two. I can't separate the two and that all comes down to this idea that Einstein Managed to prove via thought experiments. Yeah, that's the amazing thing about it purely through thought experiments and And a good bit laughs and a good bit of math. Yeah, very good bit of mice I'm Stein were using the mathematics to make sense of the universe and Claiming that the universe was nothing like what anyone thought it was His concept of relativity flew in the face of what people had believed about space and about time for centuries Whether that was the Greeks thinking that the universe was eternal and unchanging or Isaac Newton's more mobile and mechanistic descriptions Einstein took his thoughts even further attempting to wrestle gravity into a neat mathematical law he believed it was all down to the strange behavior of Space-time and if he was right as he laid out in the theory of general relativity in 1916 Then gravity will even affect light If you've got a star shining light from over here Then you the observer over there will receive it in a straight line But if there's a massive object in the way You might think you won't be able to see the star However Einstein predicted that the mass of an object will distort the space-time around it and anything Moving through that warped space-time will have to follow the curves This warping of space-time Einstein said is what we usually describe as gravity We think of gravity as keeping the planet in orbit around our Sun in fact, he said it's the result of the distortion of space-time near massive objects and Einstein calculated the precise effect it would have on light so the Starlight while still technically traveling in a straight line will follow the curves of space and appear around the object Einstein predicted that in exactly this way we should be able to observe light from distant Stars getting bent as the Stars pass behind our Sun But a theory is just a theory an invention of the mind it only becomes a discovery when proven by practical measurement or experiment in the decade after Einstein's prediction Solar eclipses around the globe gave scientists the chance to repeatedly test his theory The darkness of the eclipse allowed them to actually see stars passing close to the Sun When scientists took the measurements, they discovered that light from a distant star was bending around the Sun in exactly the way that Einstein had predicted the Mathematics of general relativity was correct With general relativity Einstein completely upended our understanding of space time matter and energy and kind of what else is there to the nature of reality? All of a sudden we learned that mass and energy can warp the fabric of space and time this beautiful interconnected dance Where the motion of matter affects the warping of space in time? Which affects the motion of other matter we used to think of space as this boring static stage upon which events? unfolded Then Hightstown told us that space Is itself an active player in this game? Like you stretch your rubber sheet and yet a substance perfectly described by beautiful Mathematical equations. I mean, how did you think of that? How did you think of something like this? Einstein's description of gravity the warping of space-time Accurately explains why objects stay in orbit, whether they're satellites around the earth or galaxies around black holes His equations are being tested and re proven every day and without Einstein's general theory of relativity Mon communication gps or satellite TV systems couldn't even function Although this theory came from his mind from thinking about the problem rather than from real-world experiments It's still so good at predicting so perfectly capable of describing what happened in the universe that it must be reflecting some underlying Mathematical truth and this lends quite a lot of weight to the argument that mathematics is discovered Which is something that matches up with my own experience because when you're toying around with mathematics? It really does feel as though you're exploring something that already exists But if we accept that maths does already exist and is an intrinsic part of nature Then surely all the rules are out there waiting to be discovered In some ways There's quite a lot like a game of chess So you have these very strict rules that you're not allowed to break But within those rules there are all kinds of opportunities to play around and be creative The only problem is that in manners. No one tells you what those rules are. We have to work them out for ourselves Most Mathematicians like a challenge, but this idea got blown apart a maths conference in 1930 in the Prussian city of Colonels burg when two great mathematicians and their conclusions Collided on the one side You have got David Hilbert a mathematical King in every possible sense of the word This is an enormous ly well respected man who laid down the gauntlet? Asking people to come up with a fundamental set of rules on which every mathematical proof could be based on The other side was a young academic called Kurt girdle In contrast to Hilbert's who thought that mathematics should be built from the ground up by humans GERD or thought that mathematics was discovered He believed that mathematical truths exist outside of us and that we have very little say in what we can find that summit in königsberg can be seen as a clash between those who thought that Mathematics is part of our fabric of reality to be discovered and those who saw it as a language Under our control Hilbert's was confident that humanity would soon know all there is to know in maths But girdle who had also been trying to find the rules of maths had come to the opposite conclusion in a side room of the summoners girdle quietly announces that in fact however hard you try There are always going to be some things that are unknowable they are always going to be parts of the Mathematical game that can't be fully explained and if you can't know all the rules, how can you play in a game? according together any rule based math system is always gonna have some things that are either unknowable or Unprovable and what's more? He could prove it. It's kind of ironic if you think about it This was quickly accepted and became known as girdled incompleteness theorem and if it's an interesting twist on our key question, it shows that even if Mathematical rules truly are part of the universe and we're simply discovering them We are nevertheless going to have to accept some of those rules Without knowing how or why they are true Normally people think that there's some intrinsic difference between science and math on one hand and Faith based belief systems from the other and yet what curdles theorem tells us Is that's not true that there are things in mathematics that you have to take on faith or you can't do the mathematics To me. This was an astounding thing to realize we're going to have to accept that we can't give massive foundation in formal rules or in logic in the way that we thought we could I think it's enormously exciting That math in some sense is open-ended. So in a sense it puts an end to one way of thinking about Mathematics but I think it actually adds color and richness to the subject because it's just gonna keep on going So what does girdle's incompleteness therein mean for our view of the universe and the part that maths plays in it Well, it depends on what you're trying to use maths or if your goal is use it to describe What's around you then it still offers a very detailed picture enough to navigate your way through the universe and to explain its features Sure, the map is not gonna be the same as the terrain but even if maths is a bit incomplete around the edges you could Argue, it doesn't really matter Although girdle proves it's not possible to formalize all of maths It is possible to formalize all the mathematics. We actually need to use Take flying as an example. Now. I did my PhD in the mathematics of aerodynamics and that means I spent four years Poring over equations for wing sections and winds the stuff that I know like the back of my hand But does that qualify me for going up in one of these on my own? Absolutely? Not and on the other hand, these guys don't really need to know any of this stuff to make them graceful acrobats in the air Not having a complete understanding doesn't always matter We've still phone successfully for over a hundred years and now it's my turn And then this is your diagonals rap that comes across this will dig in a little bit on takeoff when you're leaning forwards and running down the hill I can help I Can handle it? And do you have quite a good feel for where the thermals are you have to have the right weather conditions? So if you imagine a hill that faces totally in the wind that's well-drained Maybe darker and it will create its kind of pool of warm air and then it will Want to kind of reaches a decent temperature difference it bubbles up through the air. It's almost like we've got kind of opposing skills Yeah, and like this sort of about the same thing, but they you don't need my skills. Do you do what you do? And I couldn't do what you do. Mm-hmm. I guess they're the ground spirit element. There's a bit of mass Yeah, I start the lesson with a bit of math to begin with how where's the wind coming from? How strong is? But you're not solving navier-stokes equations are you Before the theoretical analysis of aviation came along the practical side of flying was mere trial and error Now we have a much more reliable understanding of what keeps us aloft And it doesn't really matter if the mass behind it is Ultimately a bit fuzzy around the edges In the real world the best that we can do is just accept gales incompleteness theorem and get on with life Yeah We have to put a sign for the moment the question of whether maths is invented or discovered Because it now looks like we may have to determine which part of maths we are asking about You see for me girdles work highlights the distinction between pure theoretical maths and practical Appointment so here is how I see things with mathematics There's a split down the middle of the subjects because the story Changes depending on what world you start with whether it's the real one or one that exists in our imaginations And right now when we're flying this is very much in the realm of applied mathematics where everything is tangible and practical And a little bit imprecise But alongside that is where the more theoretical pure mathematics lives that's where you have your proofs your paradoxes and incompleteness theorems a realm which doesn't match up with a physical reality sort of imperfect perfection Even though I instinctively feel that Max is discovered I like that there is this pure theoretical part of maths that isn't found in reality And since the mass there doesn't need to match reality it's a convenient place where we can leave all the weird contradictory bits that we come across However, I might have it the wrong way around Although pure theoretical math seems rather divorced from reality that might merely reflect the fact that reality is not quite what we think it is and It's a reality that we can uncover through the strange maths of quantum physics the Weirdest world that most of us have come across are likely to be in fiction such as this Alice's Adventures in Wonderland now the author Lewis Carroll real name Charles Dodgson was actually a mathematics dawn at Oxford and a staunch traditionalist It's generally believed that much of this surreal story is a thinly veiled satire on the new avant-garde math that was flourishing when he was writing in the 1860s Still feels relevant today and applies equally well to the new weird kid on the block contin physics Take a close look at the physical world around us and you can reduce it all to maths The solid bricks of our houses or the blood cells in our veins can all be reduced down into chemicals Which comprise elements? Which themselves are made up of atoms? Comprising a tiny nucleus of protons and neutrons and electrons buzzing around in a cloud of mostly emptiness The protons and neutrons in turn are built from smaller subatomic particles that we can't directly observe We can only verify their existence using experiments and mathematics as We delve deeper into this world Scientists have discovered something very strange indeed We can never actually know the precise location of most particles in this sub atomic or quantum realm all we can know is the likelihood of them being somewhere a mathematical formula that describes the probability of their position All of this means we are Fundamentally at a quantum level just a great fuzz of energy and probabilities Much more Lewis. Carroll would have liked that And the only way to explore this ill-defined quantum world Is through mathematics perfectly equipped to handle strange probabilities It seems like there's quite a lot of uncertainty in quantum physics, does that bother you Um, no when I heard that things were you know? Uncertain and also against our common sense in quantum physics. Then I felt like oh, wow, that sounds interesting. I wouldn't know more about that the palatal maths behind the quantum world was first laid out by Austrian physicist Erwin Schrodinger in 1926 his equations accurately described the unusual behavior of subatomic particles Okay. All right. Tell me what then quantum physics lesson 101 Where where do we start? Give me? Okay, I would say we have to start with superposition So let's talk about electrons. So there's a very small particle and they can be in two space They have a state with spin and the spin can be pointing up or down So if we were in the classical world the spin could only be either up or down But in the quantum world the spin is in a superposition Which means it can be up and down at the same time. Let me see if I understand it. So superposition is where something is An isn't something at the same time. Yes, we can think about some examples so let's say that we have a cup and the cup is full of water or That's one state. Another possible state is that the cup is empty So if we were bringing the quantum ideas to the classical world We would say that the state one possible state of the cup would be two being empty and full at the same time Okay, which you never see in in in the world that we're living in never see a cutlass full and empty. Yes, we we don't But you see this in laws in the quantum world. Yes super positions are Essential part of the quantum world like a light being on and off at the same time Exactly or the cake being eaten or not eaten at the same time? Okay. It's a very tough idea to get around given two possible outcomes in the quantum world We now have to allow for a third one the combination of both outcomes But the quantum scale you can have your cake and eat it This is such a weird idea How do we know it's real? Well, because we've done many experiments to prove it that show exactly that behavior What does that experiment look like? Well, if we put it say in terms of things we have here in the table we could think about let's say that I wanted this piece of sugar to come into my cup, but there's This pot in the middle so then if the sugar is going to come from here to my cup it could either go this way or That way in the classical world but in a quantum experiment It can take both fruits at the same time and I would be able to distinguish that it did that if I did a quantum Experiment. Okay weird Welcome to my world so you go through this whole transition from first the ideas in the mathematics and Then up to showing it in the experiment What came out of schrödinger's mass was a prediction of something even stranger but can sometimes be produced when particles interact in the quantum world a phenomenon called entanglement All right. Tell me about entanglement Okay, so take two electrons if the electrons are entangled and I do something to one of the electrons for example change the direction of the spin that will Instantaneously affect the state of the other electron, even if they're separated long distances. How far away away from each other? Well, they can be a few centimeters. But now the latest experiments using satellites show entanglement across 1,200 kilometers Once yes, you've got something over here and you do and something 1,200 kilometers away you do something to one an Instantly the other one incident he knows what's happened. Yes it you affect the state of the other one instantly Apparently there is no causal link. The only thing we can say is that the two particles are synchronized How does one know what the other ones doing? Well got that we're still trying to understand because that's what mathematics tells us and then we can show it in the experiment but we're still struggling to understand what that means and one of the reasons why we don't Understand it and you know it like you're asking is because we don't see it in our everyday life. So let's say it's not part of our Experience and in common sense, but that doesn't mean it doesn't happen So quantum mathematics has made predictions which have been discovered to be true But despite that the quantum world is so weird it suggests to me that the math behind it is just invented It feels like what we're seeing is evidence of a man-made system being pushed too far These are the absurdities that appear when it's applied to situations it wasn't designed for But my quest to find the truth about Mars Takes me back to nature There is amazing new evidence that quantum processes might actually be crucial to our own existence and much of life on Earth a Vant would strengthen the arguments that mathematical processes are Intrinsic to our world, but maths is discovered It all comes down to Photosynthesis the process that converts sunlight into chemical energy used in life It takes place in molecules called chlorophyll which can be found in plants algae and bacteria In bacteria, we have something that similar to what we have in plants So this is the stuff that the the captures the sunrise exactly each of these molecules Which of these little blue things here that I'm showing is a bacterial chlorophyll and if we take it apart it will capture light the chlorophyll captures by absorbing particles of light or photons So our photon is absorbed and it's absorbed by all of them So energy is shared by all of these bacteria chlorophylls and that sharing we call it is in a quantum superposition because it's coming in and hitting one of these but all of them and somehow in a ways as if each of the electrons of the chlorophyll are talking to each other and sharing the energy around the subatomic particles in the chlorophyll are synchronized in a way that can only be described by quantum Mechanics does it do a good job? I mean, is it efficient that is part of why photosynthesis is efficient because By sharing the energy among all of them is easier to transfer the energy to another molecule Imagine if you have to share the energy one by one you have to splode each part separately But if you share the energy all together just plot all the parts at the same time Every leaf on every plant on the planet has been following these quantum rules For millions of years and we still don't fully understand how they do it Without quantum physics despite all the mathematical uncertainties and ambiguities Plants wouldn't produce oxygen so efficiently and with our oxygen we wouldn't exist The systems are amazing because they are Effectively at the interface between using a little bit of classical mechanics and a little bit of quantum mechanics to operate in a wonderful way ultimately quantum mechanics is at the heart of photosynthesis and well I guess all of life on earth it is it is we can say life is nothing but quantum mechanics giving us energy So what does all this mean for our key question about the origins of maths There is no shortage of evidence that mathematical rules are intrinsic to the world We keep discovering them everywhere however we now know we have to take some of that maths on faith and believing in the numbers is taking us to a very strange world with crazy notions like superposition and entanglement at the core of it quantum mathematics is Inextricably linked to the world as we know it all as we knew it because the world is actually a whole lot weirder than we thought what quantum mechanics does do is force us to Question what is real? Then what is reality? anyway Just how much light can mathematics shed on reality with the world stripped bare Exposing the nuts and bolts of existence. What does math tell us about this realm of subatomic particles? The math that underlies it isn't particularly pretty but it can all be written out in just one equation This is the formula that describes the constituents of the universe It has become well enough accepted to be called the standard model of subatomic physics I told you it wasn't pretty Now you're just gonna have to take my word for it on this one this equation encapsulate all of the fundamental properties of the subatomic world But there are a couple of sticking points for one thing no one has ever satisfactorily explained how our common-sense day-to-day version of the world emerges from this kind of subatomic Reality all of that fuzziness all of that uncertainty in the quantum world Just how does it end up giving us that comfortable familiar solidity of the normal world? At the other end of the spectrum the solar system and Beyond is Beautifully and accurately described by a different equation Einstein's general relativity This remarkable equation tells you about gravity about the warping of space-time about general relative And when you take these two together these two single mathematical Sentences they're enough to tell you everything you need About the fundamental behavior of the universe and everything in it There is nothing more articulate than mathematics Maths seems to be written into the physical universe So on the one hand a teeny tiny scale the standard model of particle physics does its amazing job and In the ginormous scale general relativity. I mean you you couldn't ask for anything more There's just one problem when you try and put these two together They're incompatible The problem is that general relativity breaks down in the quantum world gravity simply doesn't apply to particles at the subatomic scale Meanwhile quantum effects are virtually never seen at the scale of humans and planets where gravity rules you and I are never in a superposition of Existing and not existing at the same time. So what does this mean for us? Are there two different worlds each of aying their own set of mathematical laws? Solving this conundrum is one of the biggest problems that puzzle Scientists today will we ever reconcile the two? I think it's perfectly plausible that within our lifetime Somebody maybe somebody watching this program will discover the mathematical structure which unifies Einstein's theory of relativity with quantum mechanics and just provides a perfect description of This world and that would be really exciting Will we have one? How do I know? we would all like to have one but You know, maybe we are not smart enough to formulate a theory that combines everything It's it's hard. I do believe that there are good ideas out there and that eventually It might take a long time, but eventually humans will work this out. I'm confident about that So we make it all the way to include all possible forces at all possible scales with all possible forms of matter It's a hope I have our species and that's all I can say The incompatibility of these two great theories general relativity and quantum mechanics creates a serious obstacle for believing that math is really discovered and There's a bigger hurdle to come many of the best proposals to unify general relativity and the quantum world Have consequences that are even weirder than the problems. They're trying to solve They predict the existence of multiple universes This idea is rooted any mathematical explanations of the quantum world and the work of its founding father Erwin Schrodinger the mathematics in Schrodinger's equation insists that particles can exist not for states at the same domain and Training it himself says that these possibilities aren't just alternatives but really happens simultaneously This can leads to multiple Universes and a maths also suggests. There's an infinite number of them each slightly different from the others Everything that's possible Yep, that's right everything possible happens Somewhere even Schrodinger acknowledged that the consequences of his equation describing the quantum world Might see me lunatic. But if there's one thing I've learned is that you should trust the maths So maybe our experience isn't special Maybe our reality isn't unique after all There are so many distinct avenues of Investigation That lead to the possibility of a multiverse From our studies of unification and string theory from our studies of quantum mechanics even from the study of Space going on infinitely far even that gives rise to a version of the multiverse if we're going to reject everything That just seems weird We're almost guaranteed to reject the true theories in the view of the future when they get discovered. I think we should just chill out accept that the world is weird and that's just part of the charm and Trust the math So why does all of this matter Well, if maths really is discovered, then there is an intrinsic truth behind the mass we uncover however, weird that truth seems to be If math is invented then how do we know what is true or false? Is it true purely because we define it so and how does it relate to the real world that we will experience? In this series we've seen that maths can explain so much of our world from aerodynamics to planetary orbits from the subatomic world to processes crucial to life on earth and That is something I just can't accept as a coincidence So here's my take on things for me. It's almost as there you have this alternate parallel Mathematical worlds that hides just beneath our own you can't see it. You can't touch it The only way that you can explore it is by using the language that we've invented All of those symbols and equations and conventions are our only tools of navigation And they are undoubtedly man-made But once you're inside that world once you're exploring the landscape that mathematics is laid out in front of you I am Absolutely convinced that you are on a voyage of discovery It is a world without a human designer So ultimately, I think it's both Mathematics is a little bit of invention and a lot of discovery Mathematicians will probably never all agree and maybe we will never find a definitive answer But the consequences of having that debate is why it really matters we have used mathematics for a much deeper understanding of nature and of the universe in general We know about the universe now Thinks that a few hundred years ago people didn't even know what to ask Searching for the truth about maths has over 2,000 years of history transformed the human experience Discovering patterns everywhere in nature has given us structure beauty and inspiration Inventing new areas of maths has led to an explosion of technology that Ultimately underpins modern trade and computing We have discovered powerful rules that we continue to use to explore Enhance and explain the world around us and we have had a Tantalizing glimpse of what could be to come? it's quite possible that what we have been doing in science for all these centuries is in some sense looking for our keys under the lamppost we have been able to use Mathematics to describe what happens out there? but that could be the tip of an iceberg of reality that we as yet don't have any understanding of haven't yet had any contact with But most of all I think that asking questions about the origins and truth of maths has given us a purpose It's given us understanding Ultimately math has given us meaning What is it that makes our world work the way that it does explore more about the magic and mystery of mathematics and how it impacts our everyday lives by going to the web address below and following links to the Open University Tomorrow Brian Cox wonders if we will ever find aliens human universes here at 8:00 next tonight on BBC four David Livingstone and the missionaries who changed the face of empire
