O que é a matemática? | Os Mistérios da Matemática #2

amana's Primera's quizzes que hacemos con unos damos canta g kzc o mundo no ceodore teapots a discrete o entendido kampala breezy Simoes apparent our case precisamos nami ihara squeezes para que la sesión noses para que pasa officer pardner suniverse patrol cuando causes circumstances experiences a sentiment sense a balloon on Allis police organisms Pacifica's a processes no jockey Nintendo me no existen a mop or so no suspicion literal mentioned SP Chili's anonymous message enter a documento pasa necessary met Luke reviewed Canseco Jose de Almeida X ETA SP Tiago in on Harvard a Akiva Cardozo Thiago Alves

de Stars Deadpool importation or sano-sama service PDS prevent or anonymity motto avoid a acusó de la palabra despair inverse a according centimeter strain in confused OTC Devon Pacheco here Perez says momento de Cali Bharati song EFX our sauce into a Travis this is possible [Music] [Applause] [Music] [Music] [Music] Mia prossimo de matemáticas I'm Antonio brunet odd okra magic ang effects upon pod appeal appropriate occasion today's problems Jeff wait Rob asada Pelosi Saddam menudo hasta see no logic oh I pray Terry develop outage easily dodging his over case platicas wrote a mockery of dodging funky decay

adentro Mysterio's Marvel Universe's a Bible is a significant Yvonne todrick a diseases appropriate oh no Vegeta de pensar tipo de premature Penta Sasha Dora's the hustle yeah perplexing dodgy G&G de grandes a geography simplest men to fast to power up solutes in chill submerges process things because some para privileged leading to carpet drawings you goes to Jupiter in contract his post a second - Parris a cigar magnetism the silver has seen use the simplest Michiko a circus or set a background for please listen as la estrogen and the potential in the fair system em convey

Jesus Shiva oranges and Michael origin solicitor Muhammad ranges community can focus on my specialty made in Dagestan when Tokyo Japan Tamaki much what is mathematics both considered a mathematical democracy you know a trivial no another series por que cada pasado medium pocket range he touch kamesh karma does the desk isn't she solution a place to the place i mean i verificar consequences Raj fights Kubrick a cigar won't be the excess idle problemo Sergey concepts it's interesting that a subject that's as careful of precision as it is can be the hard to define Sumati match edge

efficacy definite constant agile threw shade cereal - who is spongy and also no song stops wearing jeans so the cheapest it grazes para spies Ella famous because [Music] you have to say wise it's going on and why is that going on why what and you you seek deeper and deeper explanations just like when children want to know more all the time children are so wonderfully curious unfortunately we kind of squash the curiosity out of them and by a time people are adults mostly they have squashed all that curiosity out of them and that all that

I mean you have responsibilities as an adult and especially if you're struggling and you don't have a lot of leisure time or you have to work very hard in order to earn enough money those kinds of things don't allow you to stop and go why why did this happen why did that happen but that's where math comes from so a lot of times you think of mathematics are simply being about numbers of our formulas but it's so much more it's about finding patterns and relationships between things and between ideas and so in addition to studying

numbers you might be studying things like objects you might be studying things like I study knots so you take you take some string and you tie it up into a knot and you might wonder what is a mathematician doing thinking about knots you know that's not a number but it turns out that mathematics is a powerful tool a way of thinking that enables you to find structures and patterns and and think about the various properties as you transform a lot of what's going on inside of it now this seems like some esoteric activity right like

like why are we doing this these are just people like you know thinking about nonsense that has no applicability in the world and that was the history of knot theory for a long time it seemed to have no applicability but then we discovered that in fact your DNA inside of you gets knotted up and you have little enzymes that come through and are not your DNA and so somehow the mathematicians thinking about and figuring out the properties of knots prepared us to better the biology to better understand the human body and the DNA inside of

us I like to say that mathematics is formalized common sense we have certain type of ideas we say that well they should happen this is true well let's let's let's analyze that using the tools of logic and make it more precise you know uhm way to describe this is that let me give you an abstraction we abstract a lot and that scares the heck out of everybody just the word abstract so let me give you a simple example of abstraction now I have I'm gonna give you two completely different problems problem one I'm going to

have three apples here and two apples here problem how many apples do you have I got five hours now I'm going to give you a completely different problem my grandchildren I have three grandsons and I have two granddaughters how many grandchildren two ahead well one two three you said five but how did you know you see that's what mathematics does is says it doesn't matter if they're grandchildren or apples or books or whatever you're talking about that doesn't matter in the analysis so that's the abstraction we say there's certain properties that are not important that

are not necessary and so we dismiss them and when we dismiss them we're getting down to really what's what's what's necessary and by getting it down to the fundamentals it applies more and more things but children are not encouraged to think of mathematics that way that's definitely true and so I wish that starting from a very early age math could be presented as an exploration rather than a set of rules and methods for achieving particular outcomes because math shouldn't be about the outcomes it should be about the process and about the possibilities and about all

the different things that can happen and it should be about the circumstances in which different things are possible one definition that mathematicians have used in recent years which I think to me makes a lot of sense is that mathematics is a study of patterns it's simple but that's really what it is it's a study of patterns and and that to my mind is a connection with God because God as creator has made a world in which there is finiteness in which there are patterns many of those are beautiful and all of that is what mathematics

is about sight I think of math as looking at patterns and structures so some people love to find structures and patterns of numbers and so if you have a hundred chairs in a room you say oh there's a hundred right that's like a way of quantifying it 38 students a hundred shares 15 pieces of chalk 75 candy bars some people love to find structure and patterns in in functions you know if the stock market is going up or down or that the way bacteria grows is exponential or there's a music function you know with a

beat of like that sinusoidal curve I love to study patterns and structures of pictures and and so math assists a goal of just studying patterns and structures of things and you could do it in numerically you could do it algorithmically you can do it algebraically and I like to do it geometrically mathematics is in some sense a sort of a language if you it it is based on a certain set of definitions we define things like we define a point we define a line we define a circle and then we discover all kinds of relations

among those things that we have defined and so it is an intricate combination of inventions and discoveries but which at the end creates a language that for reasons that not everybody understands actually it turned out that this language is a very very adequate for describing phenomena in the universe and in fact the universe as a whole is this team Montes pursuers kimijima Mathematica comes first my language in college in Kumasi a Piazza Hesperides identificado sentido NHANES Pergamos la symbol O's play represent our quasis Fatima's cuantas veces symbol O's aprendemos Harrah's pradana see symbols dimensional Paris

: Oaxaca mathematical allegory Oberon khadija message to Dharma's kesava na verdade nova sentido perkier give a para siempre que cuando diferentes pause natera xiv of aaron cohen cements do Mathematica s de volver a suspense immense apart Sergey quasis pratik a scales possessive Oh president militares says Alcantara courses compasses for example suja to determine our dog over lunch places have whom tell farmer ji Quan Chi fickas meritorious LZ over a linguist price yes linguist Oh todos differentö mas de Soto's my Zetas are to Pontos represent a sensor metas mesmo es por SI no NOS lo Paris's

comedy sonar as squeezes so he presented as poor pause difference con symbols difference or a quantity of systemic Ferengi represent a certain symbols differences in human language in French yet what I call the sizzling versions there Mathematica a mathematica evolved umberto comp audio describer universe essa como para fazendo GGC mathematical astronomy taliano Galileo Galilee Kino sacra Jesus's ascent was bars Parkington demos conciencia otra vez de Mathematica episode earlier umas fast set as the Haley - my sumati much gone away a Pinot smelling regime yella Anthem almani da fuq Brando's poco spell experiencia con mathematica kiichi

folkways a la Concha going Roger Bacon presumption on sacral Tracy Ellington Giamatti much commotion do I stutter Adagio Adagio is Irma Thomas caprara delicacy drama tamarkan Kunis and Oprah's tuturro de la da de na verdade cnty cell he grows essentially a conclusion in mathematica now a definite you near Paseo de venir Mathematica porque es que la fundamental demise Ella simplest men cheat Venice does oh hey horses Prada Finnick Odair out by the ella misma no take was a definite well of course one of the questions about mathematics is is whether it actually exists in an

ideal form out there and we're just discovering it or whether we're actually creating it I think most mathematicians believe that it's out there and to a large extent were simply discovering what's out there the universe is is built on patterns and very subtle patterns patterns within patterns and things they're never simple and yet they're never more complicated than they need to be paraphrasing I'm stunned here make it as simple as you possibly can but no simpler and and that's that's the essence of Mattox [Music] mice coma Percival per se beerus i street - Dada hailey

- JK a fatal conceit reduce America's a Contessa knows about eh consecutive arrows and numerous I would concede he room to the Queen cement plant money Polaris experimenters as initial mathematic which is normally normally peso doesn't matter much case institutional factors mathematical non home corner cases leave the community so trash no sewing from prison Panasonic former no sounds in distance yeah if you have a very so Trish a key name to others policy reduce the doesn't know music Adam Adela at at other Parramatta much the directive is to clearances the adult blinken cuckoo magic Mathematica

Korea a no Sancta portrays no animal a group I would consider reaching out didn't know some reform in distance the original geometry at apologia to do is some some very notion education she keeps her Mano Menezes fov oh come off a momenta sprinting the octopanda synonymous of altercation residue second cycle non so intend eran creevy area tap Revere kick veo cómo contest [Music] my serial sequence Mentos Sonos syria algo que vamos commodity fabric our para la sierra no Seguros Adagio para cenar noses necesidades seremos nose us create or esto significa Bo's o cerium a tomas

my evidences kzc sentido universe ooh a Posadas atta boy so i confirm moses nurses desk abiertas creosote experiences come por que debemos adentro send o de Mathematica yeah Keesha compassion oh so far [Music] the way everyone in the world I think gets involved with the need the desire the fundamental longing for meaning one wants to understand the meaning of one's life the meaning of life and this and that offered hope history science art music but there was always a limit that came up very quickly you would have to become an expert in order to get

the first inkling of meaning a friend of mine wanted to study the piano and his teacher said to him this is wonderful you're going to study the piano practice scales for ten years and then we'll start playing a piece of music what is that how are you going that drives you away from music practicing practicing practicing memorizing without any meaning instead mathematics offers instant access to the deepest the endlessly deep meaning of things because the meaning of things is form structure is what art is about and mathematics is the deepest and the most personal of

the arts yeah see if you went to the if you walked as a math department here at Calvin or almost any place and you went up to a mathematician and said why do you do this why do you do what you do and some people would say well they must think that well it's because of this this is the basis of science and technology it's very practical sort of thing that's not what a mathematician said they would say I do it because of you and where do you find that building mathematics found an order and

symmetry and structure in simplicity in finding that something that looks incredibly complicated when you somehow cut to the heart of it you can see that there's a very simple ordinary structure that ties everything together and that's just enormous ly satisfied I mean when you can say I I puzzled over this problem for a long time and I've gotten this insight that brings everything together there's just a delight and a joy in that that's that's that's wonderful and so it's that sense of order of joy of harmony and pattern you know and if you if you

were just talk to a visual artist and you say well what are the things that make are beautiful for you one of the things they would say is color but almost everything else they would say is the same thing the mathematician is about what makes mathematics beautiful for him or her so I don't think there's a great deal of difference in our concept of beauty between [Music] Mozza service UGK Asteria toda Sibelius app racism is universally significant [Music] periquito do is a katana Mathematica confit are very porky elephants Jana [Music] so gh Hardy are well-known

atheists in mathematics he has these criteria for what make good mathematics economy of expression sort of sort of standards that would you would apply to what make it makes a good poem what makes a good poem economy of expression depth seriousness elegance those kinds of things maybe a bit of a surprise there's something in the poem that wow I hadn't thought of that and that's sort of like a beautiful mathematical proof where you pull out an idea where you go wow that's really neat so those are the criteria for mathematics why do those theories wind

up explaining how the universe works so well they're just random human notions from a naturalistic worldview of symmetry and preference that shouldn't have any special status if everything is just random I questioned that math missions wrestled with is why does mathematics work why does it describe the world around us Eugene Wigner put it best he wrote a paper called the unreasonable effectiveness of mathematics and in it he said that mathematics is like a miracle he uses this language it's miraculous and on a number of different levels the first is that we do mathematics and we

don't run into contradiction you know if the human brain is just the result of some unguided process of natural selection it doesn't make sense why we should trust the brain to be able to reason and do mathematics if we're just made to survive then how we able to know truth right if the process that brought us here was just about making creatures that could reproduce well then why are we able to think these incredible mathematical and bring together these different lines of thought without them running into contradiction and so one of the questions big nerd

asked is is why I wasn't able to do mathematics why are we able to access and reason in this deep way but then big nerd went on to ask me says but then why is it the mathematics we create is useful to describe the world around us in particular he noted that in recent history math officials don't try to describe the world mathematicians are in their offices in the basement working on the blackboards doing their mathematics and they're not thinking about physics they're just thinking about the math they're saying this looks beautiful I'm going to

pursue this idea this is elegant this seems to be true but then once they develop the mathematics generations later it turns out that's the very mathematics needed to describe the world around us a beautifully beautiful example is the mathematics of the vibrating string and being able to understand the overtones and then okay so we understand overtones but then to discover that understanding how overtones are created actually gives us insight into other physical phenomenon that was the great surprise of the 19th century and and it has something to do with the fact that the universe makes

more sense as more patterned to it than we can ever imagine and yet these are very subtle patterns when I look at my own mathematics and I look at the mathematics of the people that I know there's a lot of creation involved in that we create the tools that we use to study these matters we create the procedures that we're going to use those are those are human-made what's often surprising is how effective they can be given that they're human-made but we never fully understand the real essence of the patterns that are out there but

we're constantly playing and trying to get at them and we create the mathematical structures than use to try to understand those atoms we never fully grasp them but and we grasp them well enough to be able to to use these insights how can you explain the effectiveness of mathematics there's a Christian view of that that I'm very much drawn to and it's sort of a view that CS Lewis had when he said in Miracles the disorderly or complex world which we cannot believe in is the same disorderly or complex world that God refused to create

so you talk to any scientist and ask what drives your thinking Brian Greene for instance I don't know what his religious views are but he's the author of the book called the elegant universe and he says that physical theories use symmetry as their basis for being created in other words they use symmetry symmetry as the basis for an effective explanation so unpacking that if you have two two competing mathematical theories to explain something the simplest the most elegant one will be the one that mathematicians go with and why is it then that those kind of

things wind up explaining how the universe works there's a philosopher named Marc Steiner he's at last I knew he's at Hebrew University in Israel he got his PhD at Harvard and wrote a book called the applicability of mathematics as a philosophical problem and in that he says look you have an if you think that humans evolved with a blind chance model of evolution it's just time plus chance with no oversight of an intelligent being then why is it that humans would have a privileged status in the universe to the extent that their ideas of beauty

and symmetry wind up explaining how the universe works and he says it makes it look like the universe was created with us in mind fine-tuned for us because if we're just sort of a random happenstance why would we have any special privilege why would our notions of beauty and symmetry help explain how the universe works well Lewis is common I think is relevant here the disorderly or complex world that we cannot believe in is the same disorderly or complex world that God refused to create so this idea that we're created in God's image have a

rational capacity reflective of his and his intent is that we were created with to know and enjoy his creation and enjoy him I think that explains why mathematics works you can of course come up with naturalistic explanations and I'm not ruling those out and people who are atheist might what have a well worked out worldview on that but for me it's just much much more satisfying it creates a better it helps me to see things whole as you were if you will it gives a better perspective yes this seems to fit very very well [Music]

[Music]