We Must Know, We Will Know

Throughout the year we have seen that mathematics really has become part of our daily lives. From the paying our bills in the bank to driving our automobiles out of town, mathematical theories and principle has been incorporated in everything we do. Mathematics has truly become a part of us. But as we see the era of modernization, we can’t help but wonder of the future that mathematics holds for us. And if we wish to see the future of mathematics we have to look at the history of its past.
And this is what Marcus Du Sautoy has done in the fourth installment of the British television series, The Story of Maths, which outlines the history of mathematics. Entitled “To Infinity and Beyond”, writer and producer Marcus du Sautoy of the University of Oxford documents the 20th century mathematics. This final episode considers the great unsolved problems that confronted many great mathematicians during the 20th century. (Wikipedia, 2013)

Du Sautoy starts his journey in Europe by mentioning David Hilbert and his contribution that posed 23 unsolved problem in mathematics. As he st the agenda for the 20th century mathematics, he implied much importance on these 23 problems, believing that they were of the most immediate importance. Soon Hilbert’s first problem emerged as Georg Cantor was able to understand infinities. Before him no one really understood infinities. Cantor realized that infinities require mathematical precision. He was the one who showed the world that there were different infinities, some bigger than others. And through this Cantor has opened a door and an entirely new mathematics lay before us. (Wikipedia, 2013)

However there was a certain problem that Cantor was not able to solve: “Is there an infinity sitting between the smaller infinity of all the fractions and the larger infinity of the decimals?” And Cantor believed that there is no such set, and this in turn gave birth to what is now known as Continuum Hypothesis. And this would be the first problem listed by Hilbert. (Wikipedia, 2013)

Next Du Sautoy discusses the most famous mathematician of his time, Henri Poincare, and his work on the discipline of 'Bendy geometry'. This states that if two shapes can be molded or morphed to each other's shape then they must have the same topology. Poincare was able to identify all possible two-dimensional topological surfaces; however in 1904 he came up with a topological problem that he could not solve. This problem was also known as the Poincare conjecture that queries on what all the possible shapes for a 3D universe are. (Wikipedia, 2013)

However, this was solved by Grigori Perelman in 2002. Perelman linked the problem to a different area of mathematics. Perelman was able to find all the ways that 3D space could be wrapped up in higher dimensions. (Wikipedia, 2013)

Du Sautoy then goes back to the achievements of David Hilbert. Hilbert was already a star. Aside from his famous 23 unsolved problems, he was also famous for the Hilbert Space, Hilbert Classification and the Hilbert Inequality. And his early work on equations marked him out as a mathematician who was able to think in new ways.  Aside from this, Hilbert also showed that while there was infinity of equations, “these equations could be constructed from a finite number of building block like sets”. However Hilbert could not construct that list of sets. “He simply proved that it existed.” But because of this, Hilbert had created a new style of mathematics - a more abstract style of mathematics. (Wikipedia, 2013)

Du Sautoy also mentions that Hilbert believed that mathematics was a “universal language powerful enough to unlock all the truths and solve each of his 23 Problems.” Aside from this, Du Sautoy documents that Hilbert quotes that “we must know, we will know” for he believed that that if his 23 problems were to be solved, mathematics will be placed in an unshakable foundation. (Wikipedia, 2013)

However Kurt Godel had shattered Hilbert’s belief that mathematics was a universal language powerful enough to unlock all the truths and thus solve his 23 problems. Through Godel’s Incompleteness Theorem which was based on Hilbert’s second problem. Godel discovered that if a statement logically cannot be false, then the “existence of mathematical statements that were trues were but incapable of being proved.” (Wikipedia, 2013)

Du Sautoy then moves to America to introduce us to an American mathematician, Paul Cohen who took up the challenge of Cantor’s Continuum Hyphothesis which queries "is there is or isn't there an infinite set of number bigger than the set of whole numbers but smaller than the set of all decimals". Cohen discovered that there existed two equally consistent mathematical worlds. “In one world the Hypothesis was true and there did not exist such a set. Yet there existed a mutually exclusive but equally consistent mathematical proof that Hypothesis was false and there was such a set.” However this was without success. Cohen then worked on Hilbert’s eighth problem, the Riemann Hypothesis, which is also considered as the holy grail of mathematics. (Wikipedia, 2013)

Du Sautoy also tapped on the tenth problem of Hilbert which asks “if there was some universal method that could tell whether any equation had whole number solutions or not”. Many people believed that there was no such method possible, however, the question “how could you prove that no matter how ingenious you are you would never come up with such method?” still lingered. And Julia Robinson created the Robinson Hypothesis to answer this. Robinson Hypothesis states that” to show that there was no such method all you have to do was cook up one equation whose solutions were a very specific set of numbers: The set of numbers needed to grow exponentially yet still be captured by the equations at the heart of Hilbert's problem.” But it was not Robinson who was able to find this set, but rather Yuri Matiyasevich who saw how to capture the Fibonacci sequence through using the equations of Hilbert’s tenth problem. The set of numbers needed to grow exponentially yet still be captured by the equations at the heart of Hilbert's problem.

Then Du Sautoy covers a little on the concept of algebraic geometry. He mentions Evariste Galois who believes that mathematics should not be a study of number of numbers and shape rather it should be the study of structures. He also discovered that the key to tell whether certain equations could have solutions or not lies in the symmetry of certain geometric objects. And this idea inspired Andre Weil to create Algebraic Geometry which is a whole new language that connects number theory, algebra, topology and geometry all together.

Du Sautoy ends his four part British television series Story of Maths through a recap of the history of mathematics in different eras, civilizations, and nations. But as he ends this television series he leaves a mark of the beauty that mathematics hold – a beauty that can only be realized by understanding how mathematics seeks patterns, how mathematics solves the unsolved and how mathematics allows us to understand our world.

Mathematics that seeks patterns. In the first installment of the Story of Maths, we have seen that mathematics makes sense of patterns and this is strengthened by this fourth installment. We can see that mathematicians make sense of patterns because they are pattern searcher. This is what they do.  Mathematicians are curious people, they want to see pattern because they want to make sense of those patterns. There is beauty there. In the act of pattern seeking alone lays a beauty already. In turn mathematics has become a tool to search for patterns. Mathematics has somewhat become a mystery seeker. But to unravel the mystery, the mathematicians must seek clues in the form of patterns.

Mathematics that solves the unsolved. Mathematics is about solving problems. These unsolved problems are what bring mathematics to life. This is just like how Hilbert’s 23 problems would provide a strong and unshakable foundation to mathematics. Mathematicians aren’t motivated by money or material gain or even the application of their work, for them it’s in the glory of solving some of the great unsolved problems of the world and in the glory that they have outwitted previous generations of mathematicians. When one person tries to solve a puzzle, that person is motivated by the feeling afterwards once the puzzle is solved. This goes the same for mathematics. The adrenaline rush, the excitement and the glory you get after solving the unsolved is incomparable to any monetary or material gain. It is as if for a second there the world has stopped and has become a better place just because you are able to solve an unsolved problem. Just as Hilbert has once said, “we must know, we will know,” we will solve the unsolved.

Mathematics that allows us to understand. It is impossible to imagine modern life without mathematics. Even before mathematicians were driven to understand how numbers and space works. And not only did mathematics help us understand how numbers and space works, but it too has helped us understand our world. This is because mathematics has become the true language the universe has written; it is the key to understand the world around us. That’s the beauty to mathematics, not only is it a scientific discipline but through it we are able to understand the world, to look at the world and appreciate it for its beauty. If we understand something we are much able to appreciate it. And this is what mathematics is doing, it is helping us appreciate our world.

Through the Story of Maths, we were able to go back and look at the history of mathematics. Were able to travel to different time and nations, we were able to meet new people and we were able to learn mathematical principles, ideas and concepts. But what strikes us is not the mathematical history or concepts that we have learned through that journey but rather what strikes us is that we understand mathematics in a different level now, and by that we see the beauty of mathematics and not just its surface. And by seeing its beauty we are able to value it and appreciate it.

I end with Hilbert’s call, “we must know and we will know”, this does not only apply to the 23 unsolved problems or any mathematical problems, but rather this applies to everything. We must know more about anything first, for only then will we really know what that anything is. We have to understand first in order to fully appreciate it.

Reference:  The Story of Maths. (2014, January 21). In Wikipedia. Retrieved February 10, 2014, from http://en.wikipedia.org/wiki/The_Story_of_Maths

Mathematic's Past, Present and Future

When we think of math, we think of numbers. I guess that this concept is what normally is in our mind. We grew up thinking that math deals with numbers and only numbers. But can there be more to mathematics that what meets the eye? Can there be more to mathematics than the numbers and equations that it manifests? And can there be more to mathematics than a mere subject in school?

Well in fact, the answer is yes. Mathematics is not restricted to the infinite numbers or numerous equations, or even to the four corners of the classrooms where we have learned so much about mathematics. In fact mathematics has a relation to everything, a relation that exceeds not only to the world but to its past, present and future as well.

And mathematics in relation to the world can be evidently seen in the third instalment of the British television series that outlines the history of mathematics, The Story of Maths, Marcus du Sautoy ventures on an adventure to help us see the movement of mathematics from being part of the East to being an engine house of mathematical ideas in Europe. In this segment entitled “The Frontiers of Space”, Du Sautoy documents the discoveries that made Europe the new powerhouse of mathematics. Here Du Sautoy covers how the majestic mathematical boost in the East has ended. After their golden years of discoveries, Europe was now stepping forward, replacing the Middle East as the engine house of mathematical ideas. (Wikipedia, 2013)

Du Sautoy first tackled about the renaissance artist in Europe, especially in Italy, where masterpieces were not only of art but also masterpieces of mathematics. A famous mathematician and artist, Piero della Francesca caused a mathematical revolution by introducing the concept of perspective. This is seen in how Piero used mathematics to create depth in a two dimensional surface of a canvass. 

Du Sautoy then proceeds to Rene Descartes of France, whose discovery to link algebra and geometry unlocked the possibilities of looking at secrets that would help future mathematicians and physicists. Du Sautoy also talks about Pierre de Fermat invention of modern number theory, and that his contributions is now used as the basis for codes that protects our credit card transactions on the internet. (Wikipedia, 2013)

After these, Britain boomed into the mathematical picture.  It was currently Britain, the new world power, which gave boost to mathematics. One of the most famous British who influenced the boost of mathematics was Sir Isaac Newton. His development of maths and physics was crucial to understanding the behaviour of moving objects in engineering, therefore giving us a glimpse of how to describe and understand the moving world we are in.

Du Sautoy also covers the Leibniz and Newton calculus controversy, the Bernoulli family, Leonhard Euler. He also mentions Gauss, whose mathematics touched many parts of the world. One of which was the invention of a new way of handling equations, modular arithmetic. Aside from this, Gauss also created new direction of numbers through the contribution of understanding of how prime numbers are distributed, and this in turn provided platform for Reimanns’s theories on prime numbers.  (Wikipedia, 2013)

What is evident in this third series is not only the discoveries made by the European counterpart, but on how amazing mathematics really is. Through their discoveries we can see the relation that mathematics holds to the world. We can see the relation it has to our past, our present and to some extent our future.

Mathematical relation to the world’s past. Through the radical discoveries contributed by these people, we can trace mathematics back to our history. Even to the extent that the technologies that we greatly depend upon today were in fact just mere scribbling of mathematicians in the 17th century. Mathematicians before saw mathematics as either a hobby or a way of life. They scribbled problems, ideas, and imagination in their parchments hoping to prove and make sense of patterns. They saw mathematics in all different areas of life such as art, where masterpieces of arts became masterpieces of mathematics. To them, the world was a reflection of a much more amazing mathematical world. It really is amazing that a rich history was contained from the scribbling of the 17th century, and that these scribbling would be the one to paint the present and the future of mathematics and of us. 

Mathematical relation to the world’s present. The past paints the future. That is universally accepted truth. And we should be thankful for the creative minds, the vast imagination and the perseverance of mathematicians before for they were the ones responsible for bringing mathematics into the modern day mathematics we have today. We are dependent on so many things that actually was based on mathematics such as mentioned above, our credit card transactions online are protected by mathematics. Mathematics became a way for us to understand and make sense of the things we take for granted so much. It has become a way to describe and understand the changing world. Through the power of mathematics, we can understand the complex and ever changing world. We were able to solve equations that could not be solved any other way only because the result of mathematics is everywhere. For us, they no longer are mathematical fictions, rather they are mathematical facts.

Mathematical relation to the world’s future. The past paints the present and the present will color the future. The discoveries made in the past and used in the present have given us a new perspective to look at mathematics and the world. The past and the present gave us magnifying lenses to clearly see the world for what it really is. And these mathematical lenses can be used to explore what mathematics holds for us, to explore what the world holds for us and to explore what the futures holds for us. The past moulded our present. And because of these, we are able to see the world for what it really is and what it can become.

When we think of mathematics, we think of numbers or formulas or equations or the hardest subject we had faced since preschool. But the truth is that mathematics is not restricted to only those. Mathematics is much more than those. It lends itself to us, to our world and to our lives - whether it be past, present or future. Mathematics was, is and will always be a part of us. There is more to mathematics than meets the eye, we have to remember that mathematics lies hidden beneath our lives, our world and our journey for it was, is and will always be a part of us.

Reference:  The Story of Maths. (2014, January 21). In Wikipedia. Retrieved January 26, 2014,                from http://en.wikipedia.org/wiki/The_Story_of_Maths

Getting to know

*Individual Report: Algebra (Group presentation)

               

Algebra here, algebra everywhere, we have been collaring it since high school, but do we really know what algebra really is? We are only confined to the knowledge of the term “Algebra”.  Have you ever wondered of digging deeper into algebra? We started our discussion of getting to know more algebra.

 Simple, we introduced algebra as an easy discipline. I myself think that algebra is not a hard nor an easy subject. Some of it, I like and some are not. We first define algebra: a generalized arithmetic, a representation, a generalization of what is in the real world. We relate it in life, (love life), work, studies, agriculture and a lot more that involves generalization and computations.

There are a lot of topics that cling into algebra: functions, relations, practical applications, economics and many more to mention. Algebra makes everything flow smoothly.

As we go through our discussion, we prepared some questions in our game. Our game is like a quiz show of the different topics in algebra and how far we remember it.  Say for instance, getting the area of the isle surrounding a pool given the other measurements. It may sounds complicated but it only needs a comprehension of the problem and the aid of algebra, we can able to get the area without even really measuring manually the isle.

We had a debate on whether algebra is used in daily life. I stand as pro. Well, for me, I consider it as part of my whole thing and that follows of my daily living. There are people who stand contradicting to what I believe because for them, practicality in life no need for any algebra. I respect their notion of algebra. What I’m upto is not just the notion of "practicality", "simple and basic living", I wanted more than that.

Great example of representing algebra is the money game by our group mate. In this game the other students were given some equations then they have to see a generalization from it of how does the equations make true. Example: violet * gold = yellow; silver+ silver+ silver+ silver+ silver = gold; orange * gold = violet; blue* silver = blue.  The answer is that the colors represent the value of money. If we’ll try to look at it, it’s mind puzzling, but if you’ll know the idea behind it, you’ll get to appreciate it. And it’s indeed amusing, and that what makes up algebra.  

I’ll be not talking about the contents of the algebra subject, I believe you know it already. I just wanted to impose here that nothing to be afraid of when it comes to algebra. Learn to love it and it will love you back unconditionally. Algebra has something to do with our daily living.  It makes our life easier consciously or not.

              

Perfect Combination (Book Review on A Certain Ambiguity)

When I first learned that we were to read a mathematical novel, I was surprised and excited. Being in a course exposed to different literature for four years, a mathematical novel is something new. I remembered thinking, is this a new form of literature? What could be in this novel that couldn’t be found in normal, ordinary novel? Well, of course there’s a given fact that it would be more of the mathematical theorems and the like. When I started reading it, I realized it was actually a novel. A real novel observing all the basic structural basis of a literary novel. But what is more astounding is it’s a novel with several points discussed, several fields looked into, and to top that it was well-written and delivered. A Certain Ambiguity by Gaurav Suri and Hartosh Singh Bal discusses about mathematics, the philosophy behind it and the beauty and utility in practical time that comes with mathematics.
The novel starts with the protagonist’s, Ravi Kapoor’s, experience with his grandfather who gave him a math problem to solve out on his calculator. This conversation between the two of them shows the good relationship between the two of them. In this single scene only, it is apparent how much they love for each other. They are very close with each other. The next day, the grandfather died but later in the novel, it is still evident how much the memories of the grandfather took part in the life of Ravi. With the loss of his grandfather, Ravi grew a little more apathetic with mathematics.
In college, Ravi was accepted in Standford where he enrolled in an economics course. Here, he also found himself loving mathematics once again through a professor named Nico and his class Thinking about Infinity. Because of Nico, too he saw an academic paper written by his grandfather with a footnote that his grandfather was imprisoned to New Jersey before. This was new to him and he had no idea about it. The story continued with the parallelism of Nico discussing about how important and complex the concept of infinity actually is, and Ravi searching for answers about the imprisonment of his grandfather. Later on, he would find out that his grandfather was jailed because of violating a blasphemy law.
There were a great scope and variety of mathematical topics discussed in the novel. More than about the complexity of infinity first discussed in Nico’s class, the novel also dealt with the topics from Zeno’s paradoxes, Infinitude of primes, and also the Consistency of Theorems by Paul Cohen. Big words. Huge concepts. Who would ever think it would be possible to have these mathematical concepts in a literary piece, and what’s more, Suri and Bal were able to pull it off. It was given that they were mathematician and discussions of these terms might be easy for them but in the format of a novel, it would be more challenging.
In one way or another, the authors succeeded, not only in presenting and discussing the mathematical theories, but also they were able to let the readers see math in a different perspective. They presented mathematics as a widely-accepted struggle of human beings, not just those in the mathematical academe; even great scientists have attempts and struggles with mathematics. Through this, we readers are shown a humane face of mathematics – it is something sought after by different kinds of people. The book by itself is very informative and at the same time, enjoyable to read since it is not as objective as all the other mathematical books. In A Certain Ambiguity, we follow a certain story, a certain character’s personal life, at the same time; we also tread the path of mathematics which actually turned out to be a good combination.
In the Epilogue, it is very interesting how Claire and Ravi ended up together. The authors did a very good job when they still kept in their mind the personal life of Ravi even after all his mathematical adventures. Good literary writers do not get lost with their theme, they knew how to play with it. However, I would have appreciated it if Claire and Ravi’s story was also discussed in another mathematical novel. It would be interesting since they are both very much into mathematics and they met in a math class.
But overall, the novel was beautiful and informative. I’ve never imagined myself reading a novel like it before. The two seemingly-contradictory fields – math and literature – were successfully merged together without the other inferior and the other one superior. There was a good balance between the two, and that is two thumbs up for Gaurav Suri and Hartosh Singh Bal.

To Infinity and Beyond (Story of Maths 4)

The fourth and last episode of BBC Story of Math was entitled To Infinity and Beyond. The video episode started out with mention of “twenty-three then unsolved” mathematical problems formulated by David Hilbert. Throughout the video, it was discussed how different mathematicians through generations tried to solve these problems and how they came up with solutions to these problems raised.
First of which was Georg Cantor who dealt with the concept of infinity. He measured how the infinity of fractions could actually be bigger than the infinity of real numbers. This statement seemed strange for me. I thought how does one measure something infinite? How does one know that one infinite is bigger than the other? Shouldn’t it be immeasurable? The concept of infinity is as huge and broad as infinity itself. I think it is a very complicated thing to discuss and even in the video I wasn’t able to fully grasp and understand the concept of infinity. I think that it is actually the nature of infinity. If people were able to grasp it that easily, if people could understand this in an instant, then it would defeats the purpose of being infinite. For example, scientists and astronomers claimed that the universe is so diverse, no one could ever note the exact width and breadth of the solar system. It is the nearest example of infinity that I could think of. And it is not known to us how complicated the universe is.
However, in Cantor’s search for answers about the concept of infinity, there was one hanging question he couldn’t answer: Is there an infinity sitting between the smaller infinity of all the fractions and the larger infinity of the decimals? The search for this question’s answer ended up with the formulation of the Continuum Theory. This only proves that in mathematics a question may be left unanswered but it will probably open new doors for new possibilities and new concepts, just exactly how philosophy works. Mathematics by itself resembles infinity.
In the 1950’s though, this problem of Continuum Theory was revisited by Paul Cohen. He discovered that “there existed two equally consistent mathematical worlds. In one world the Hypothesis was true and there did not exist such a set. Yet there existed a mutually exclusive but equally consistent mathematical proof that Hypothesis was false and there was such a set. Cohen would subsequently work on Hilbert’s eighth problem, the Riemann hypothesis, although without the success of his earlier work.”

Champorado’t Tuyo (Chocolate Rice Porridge and Dried Fish)

A Book Review on Mathematics of Life by Ian Stewart

“The interaction between mathematics and biology is one of the hottest areas of science. It has already come a long way in a very short time. Only the future will show just how far it can go. But one thing I guarantee: it’s going to be an exciting ride.”

                                                              -Ian Stewart

                                                                       

I have two questions for you. First, did you hear about the student who passes her work a month late? I know her. She has a late syndrome, but she’s charming. ;) Second, have you tried champorado paired with tuyo? Most people would disagree that champorado and tuyo can make such really, really, really, great breakfast or even meryenda. How can salty dried fish compliment sweet chocolate rice porridge? Biology and Mathematics seems like champorado and tuyo. How can deadly Math improve beautiful Biology? Yes, I’m biased. For me, Biology is much, much more enjoyable. In Biology, we study different forms of life while in math, we study death. Ian Somerhalder, Ian Stewart I mean, proved this wrong in one of his book, Mathematics of Life. Mathematics and Biology can be a perfect tandem. Stewart explained the five revolutions of Biology. He also added a sixth one which greatly improved and truly revolutionized Biology, and that is Mathematics. He showed the different connections of Biology and Mathematics that already existed a long time ago.

When I read the contents page and the first few chapters, it seems to be a Biology book. Something was wrong. The first three chapters introduced the five revolutions of Biology: invention of microscopy, systematic classification, theory of evolution, discovery of the gene, and the discovery of the DNA. The typical Biology was showed in these chapters; discusing about cells, Carolus Linnaeus, Origin of the Species by Charles Darwin, Gregor Mendel and pea plants, Crick and Watson, and structure of the DNA. When I started reading the next chapters, it still seems to be a Biology book. I was wrong. The rest of the chapters explained the various hidden roles of Mathematics in biology throughout the five revolutions.

In 17^th century, Mathematics was the force that caused the advancement of physical sciences. Mathematics and Physics were buddies along with Astronomy, Chemistry, Engineering and other related areas. Biology was left out. Mathematics had little role in the development of biological science. However, little did people know that Math was secretly hanging out with Biology. It was doing so long before anyone noticed.

The microscope’s development was only empirical, but when Mathematics of optics came, it transformed the microscope into a really good one. We can’t study and appreciate microorganisms if that didn’t come. The systematic classification was helped out by mathematical trees. Let’s go to Charles Darwin and evolution. Evolution did not require any math expressions. Geology, not Math was vital to it, but Darwin was on the Beagle because the vessel was carrying out a chronometric survey which is a Math technique for finding longitude. Even Gregor Mendel’s discoveries were possible with the help of simple mathematical patterns like in the arrangement of petals or seeds in a flower called Fibonacci. It is also found in the shell of snail. Even the patterns or spots and symmetry of animals have a math to it; so, next time you go to a zoo, appreciate Math. Animals have life. What defines life?

Biology is defined by life, and life is defined by the DNA. Math has a role in this definition of life. Some clues of the structure of DNA was Chargaff’s Rule. Topology, a branch of Math, was used to understand the DNA’s shape.  Math was very useful in studying the DNA further. It simplified the complex DNA.

The topics covered by the book were wide. How symmetry and abstract concept of dimensions plays a role in virus structure, split of a single species into two, and even in animal coat patterns. Why game theory, discussed this using lizards, can help find out which evolutionary strategies were best. What problems in genetics can be understood using probability?

“Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth,”

Galileo, The Assayer (1623)

This was the opening in the last chapter, chapter 19: The Sixth Revolution. Stewart said that Mathematics was not the real revolution because no one ever used Mathematics to solve a biological problem before. What was truly revolutionary was the breadth of the methods used. Biology and Mathematics wouldn’t be as close as Physics and Math. Math has a little chance to dominate Biology, but its role would be essential. Beautiful biology + deadly math = drop dead gorgeous Biomathematics. Even if this two seems very different from each other, they can be a great team like champorado and tuyo.

Today, Biology makes use of Math in ways no one would have dreamed of at the start of the 20^th century. Maybe in 22^nd century, Math and Biology will change each other out of all recognition like what Math did with Physics during the 19^th ad 20^th century. Before, science was an individual job. Now, Science is changing from just individual scientists to clusters of scientists from different fields. Communities can achieve things that are impossible for their individual members. "Welcome to the global ecosystem of tomorrow’s science."

The book is a testament of the versatility of math and how it is shaping our understanding of the world. Stewart’s Mathematics of Life was easier to understand compared to other Math books. His writing is direct to the point and has lightness to it. It started out simple then slowly gets deeper. Stewart laid out the foundations of Biology then slowly builds it up with the connections of Math. Research is a big deal here. His work is just an overview of the bigger picture of math and biology. If he left out questions unanswered and hanging, maybe, just maybe, he wants you to answer it. He wants you to try Biomathematics. It’s nice to read for starters like me. It is not a hardcore math or hardcore biology. Just open your mind.

I like to share a joke from the book. It is originally from Computer Power and Human Reason by Joseph Weizenbaum. There was a drunk searching under a lamp post for his keys.

Random dude:  “Did you drop them here?”

Drunk: “No, but this is the only place where there’s enough light to look.”

Moral of the story? If you’re planning to get drunk, do it at your home and keep your things. Wag burara. (Don’t be messy.) Besides that, the point was that in Science, you have to look under a lamp post in order to find the “keys”. Mathematics, on the otherhand, is a flashlight or a torch. Even if the keys are somewhere else, you’ll find them.

Anyway, back to my real sentiments. Did you hear about the girl who has the late syndrome and have you tried champorado partnered with tuyo?

une certaine ambiguïté

The authors did an excellent job in creating this book. They have set to reconcile the mathematics and the religious faith in this book that is wrapped in a thin plot.

I can say that any book that tried to dig this deep philosophical matter is a direct suspect for an ending that is a crap or a kind of garbage, but “A Certain Ambiguity” managed to end the story leaving the reader thoughtful, and because of this, the authors really did a very good job.

The main character in this novel is Ravi, an Indian student in Stanford University who enrolls in a math class called “Thinking about infinity”. Ravi engages on a quasi-philosophical together with their class lecturer and a small group of friends, guided by court records of his grandfather’s discussions with a judge in the early 20s.

This book contains a lot of interesting facts about math, and the philosophical connections are well developed and very believable even though most of it is on the basic level. This book can be a non-fiction work because its main theme is quite real and it deals with the epistemological questions that the real philosophers have struggled with, throughout the centuries. It is unlikely to change your view of life, but it will induce some of the interesting thinking on the important topics.

I was surprised to find out that this book did a good job in explaining the faith to the people with rational or mathematical view of life. However, it only rationalized the core faith which is Judge Taylor’s “creation axiom” can’t really be disproven. But as Judge Taylor told Vijay, his deductive method was solid and only his axioms were the one that were at question. In any way, the faith that Judge Taylor rationalized as an axiom can’t connect to the modern monotheistic religions, not to mention the polytheistic ones, because it broke down immediately as soon as the first deductions were made from it about the actual human lives. The axiom “everything must be created by something” is an axiom that cannot be proven at the moment, but any attempt to prove that Jesus was born to a virgin and walked on water from it would have to go beyond the limit of its deductive methods.

All in all, I can say that you have to read this book, or should I say I really recommend this book for you to read. Actually, this made me think hard about the philosophical implications of the basic mathematical axioms, and this also encouraged me to read more on the subject mathematics.