Decoded

Honestly speaking I have planned not to read the book and pass a book review at all.  Its Christmas break and I have been planning to spend it sleeping, watching movies and reading fantasy books and not reading another boring math book. I was having a success with my plan when the good side of me reminded me how important a book review is. And so I hesitantly went to my room and read the book. I thought it will be like reading the first book. Yes, I did learned a lot in that book but I had a hard time reading and understanding it. Like I said in the review, I had to read it twice. So it was shocking and amazing how the second book, Mathematics of Life, is easy to read and so interesting that the reader will be hooked from the very first page.  

Ian Stewart started his exploration of mathematics of life with the five revolutions that changes biology or simply life. These are the invention of microscope, the systematic classification, the theory of evolution, genetics and the structure of the DNA.  He then said that it didn’t merely end in the fifth revolution because there is a sixth revolution and its coming on its way.

He first discussed the first evolution. He interestingly told how a simple invention led humans to the first biological revolution, how it opened the eyes of the people in the wonderful and complex life and opened new ideas and knowledge that was never thought before. He gave an excellent history of the long list that gave order and organization to the diverse organisms living in our world which is the classification. He started it with the tale of Noah’s Ark to how Carl Linnaeus classified organisms and how mathematics is applied. His explanation of the plants patterns connection with the Fibonacci sequence gave me idea that through math, we can discover and explain clues and secrets about the patterns we can see in living organisms like plants just like a detective decoding clues in a case.

He continued his discussion on how mathematics tries to decode the concepts and ideas that forms and creates life. He started with the third revolution which is evolution. In this revolution, Stewart told Darwin’s quest in discovering evolution. In the fourth revolution which is Genetics, he introduced and discussed Gregor Mendel’s experiment and how he discovered genes. I find it amazing that I don’t need to review those painful algebra equations but through simple arithmetic some ideas of evolution and Mendel’s heredity can be explained.

With the growing understanding of genes, people searched for more knowledge about it. This gave rise to the fifth revolution, the structure of DNA. In this chapter he explored the discovery and journey of DNA and how Watson and Crick discovered the double-helix structure of DNA. He also discussed the most ambitious Human Genome Project which is the sequencing of the human genome or creating a book of like. He also captivatingly discuss how math can answer one of the greatest question asked, does life exist on other planets?

In the last chapter, Stewart discussed the sixth revolution which is mathematics. He started with Galileo’s great prophecy of the universe being written in the language of mathematics. We need it to understand the world and without it, we are like wandering a dark labyrinth. He then said that mathematics played a central role for physical science. It is the driving force for dramatic advances. Mathematics becomes inseparable with science. Until recently, mathematics played a smaller role. He discussed the reason behind this. He also said that mathematics played a significant role since of Mendel’s heredity and people just didn’t see it. Moreover, he said that before it was thought biology was the science you took to avoid mathematics. Now this is changing. Mathematics is becoming more essential to biology and this interrelation will be the hottest area today and in the future.

Mathematics of Life is an excellent book. I praised the author’s work of translating the complex concepts of biology to be understandable for the readers and for being an engaging writer. It’s also an interesting book of the history of biology with simple mathematics explaining it.  Biology majors, mathematics majors and majors of different fields will surely enjoy reading this. I agree with his book that mathematics is essential and needed by biology. 

The book reminded me of a quote I come across with while searching the internet. Charles Colton said that "the study of mathematics, like the Nile, begin in minuteness but ends with magnificence." Before all these book reviews and documentaries, the study of math is a bit insignificant for me. There were a lot of lessons that I feel is not important and necessary to my existence here on earth. After reading the first book and now Ian Stewart's book, I feel my eyes and mind were opened in a new understanding and value of mathematics. It is not only about helping us count our money, solving math problems but it is now greater than that. Mathematics is essential to biology or the study of life. Biology didn't exist to stand alone but it needs mathematics to discover secrets, patterns and truths of life and decode it. Reading the book put me to the middle of the river of math. I can now see some of the magnificence and   greatness that mathematics has to offer. 

What's that got to do with Math?

Mathematics has been dealing with almost all sciences. It has manipulated all the laws and theories of physics, stoicheometry to the subatomic numbers of chemistry, and the like. Yet math was at the least importance to Biology. We cannot describe the morphological changes of a butterfly or the evolution of a species through math. We may study minute organisms, but what’s that got to do with math?

            Somehow, that was a traditional interaction of Biology and Mathematics. As our world innovates, our mathematical thinking slowly intertwines with the science of Life. As a Biology student, I have noticed that there is not one Biology thesis without ANOVA tables or a chi-square test or any statistics involved. I have realized massive statistics while doing an activity in Genetics. Statistics is most common and used in Biology nowadays. To tell you, we were never noticing how math is involved in making instruments to see the micros, in classifying all living domains, in showing the patterns of evolution, in gene distributions especially in our central dogma. The preceding shows the five great revolutions of Biology. The revolutions of Biology provided its greatness and importance. And the small subjects that had contributed are what made it happen.

            Traditional knowledge and history is the network starting point. The origin of all species became a worldly inquiry since the early times. The Creation was widely accepted way before some people began their doubts and scientific inquiries. Later, a variation of species from one another and between them was a big question. “Creation of species, one by one, seemed absurd. So much neater to create just one and then let it change”(Stewart,2011). Then evolution came to Darwin’s mind. The process of adaptation and natural selection clearly does sip in to the inquiring minds of some. Yes, evolution clearly provided us significant proofs. Creation does not state any evidences as evolution shows, yet it serves possible in a different perspective. Now here is the apparent use of Mathematics in Biology history. In a Monastery garden, Mendel noticed a pattern on how a plant passes on its genes. The pattern was based on the distribution of the dominant and the recessive alleles. The ratio of certain types of genotypes and phenotypes are independent of the type of organism. This time, it requires a lot of numbers and distributions to predict the genotype or the phenotype of the next generation.

            Designing an instrument requires precision and accuracy. Something goes wrong when a measurement gets even a bit out. That’s why the accuracy of mathematics is needed. To see small things, specific ranges of magnifications should be considered otherwise, the picture would be a blur. You need to adjust the focal points to acquire a clear view of the specimen. The microscope is a proud innovation of Antoine van Leewenhoek. Taking it next level, the DNA-the molecule of life. The DNA sequence grants access to our information and the information provides knowledge on cures of certain diseases or how we can prevent any formation of abnormalities. There is also the Human Genome project which is a very big project that takes 15 years to complete. I don’t know how math is used in DNA sequencing but I’m sure it counts.

            Aside from having numbers flying around through computations of the magnifications, genetics, years an organism dated back, we must see math as a broader subject in biology. Its fun thinking that math involves shapes, sequences, and patterns. It’s like having our kindergarten activity books again. In plants, we see patterns in leaf or node arrangement, number of petals and the weird spirals we see in a sunflower. It is odd that the same number and patterns appear elsewhere in plants. The Fibonacci principle explains all. The series of numbers are quite exact as it provided the correct form of a plant. The Golden angle  (137.5)was new to me. Astonishing it is that it distributed the seeds of the sunflower spirally (clockwise and counterclockwise) without spaces and initiated stem growth.

            Not only do plants have patterns, animals do too. The stripes on a tiger are biochemically formed. On its embryonic stage, there is a pre-pattern formed by a pattern of protein pigments. And this laid the distinct pattern of these animals. I never knew that and I never thought of knowing why patterns on animals occur too. Again, it was astonishing. That is math in action.

            I also had some things I did not quite completely understand. Stewart considered viruses as fourth dimensional. Based on a script from the book “The Time Machine”, the first dimensions are the 3 dimensions of space (x, y, z) and the fourth would be time. So, as I have understood, there is a form of the virus capsid in space and it is relative through time. Another absurd fact is the Icosahedral shape of the virus capsid. In math, icosahedral is said to solve mathematical equations to a higher degree. Biology states icosahedral as the shape of the capsid due to a extraordinary arrangement of proteins. Nature also occurs beautifully through the patterns and forms it creates.

            It is nice to see how Biology is intertwined with Mathematics. Mathematics does explain almost all biological phenomena. Biology now isn’t a science of observing and theorizing life. It is also a subject of analysis, computations, patterns, and the like. So, if a highschool graduate says he’s going to take up Biology in college to get away from Math, well, he should’ve thought again. It is the sixth revolution, Mathematics has invaded Biology.

The Algorithms of Life

-Book review on The Mathematics of Life by Ian Stewart


“Philosophy is written in...the language of mathematics,... without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth.” 
-Galileo Galilei , The Assayer           

                                

        There was one random day when I was browsing in the Web. I came across the University of Hawaii’s website and, as any student would do, looked up the available courses being offered.  I saw some interesting and some rather not so interesting course programs until I stumbled upon one that made me stop dead on my tracks-mathematical biology. Damn that M word.

        Biology is the study of life. The question is: how do we study it? One mathematician and author, Ian Stewart, pointed out the revolutions that exploded out of humankind’s ingenuity as we had painstakingly unravelled the mysteries of life over the course of time: microscopy, taxonomy or classification, evolution, genetics, and DNA structure, and his latest, mathematics. But why math? In his book, The Mathematics of Life,  Stewart expertly points out the innumerable ideas and concepts derived from mathematics that help us understand what living organisms are. Better yet, how and why they are what they are today.

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         It’s hard indeed, to imagine that life would exist in the head of a pin . Thanks to technology, and when I say technology I include the pioneer versions way back in the past, we can now have visible proof of its existence. I wanted to know how biology-a field that I had come to admire during high school-had to be associated with math-my worst nightmare yet-just to explain how these microscopic critters exist. From what Stewart wrote about the development on lenses, it was obvious that mathematics was involved. The magnifications that each lens provides need calculations in its making so that the desired result would be obtained. But that’s just the beginning of mathematics’ integration to the study of life. Viruses were being debated about whether they qualify to have the title of a living organism or not. Typical problem for a biologist. But as to how they form and organize their structures, especially their capsids,  it would give quite a headache. So it’s geometry to the rescue. I was not surprised by this, since shapes and symmetry are its main problem. Instead, the way geometry was utilized to give a purely logical and scientific explanation somehow amazed me, even though I had difficulty understanding the details in the book. 

        Speaking of microscopic stuff, mathematics had  helped explain how biological molecules make up our bodies. Rather, helped us in a way that explains the behaviour of how these molecules occurs. Mentioned on the book was the Knot Theory, which was about......knots. It was hard to digest the technical information, but one can sense the mathematics involved. Through this theory it was explained how DNA forms into loops and how proteins like hemoglobin behave during their folding and formation. It’s interesting to know that such complex process can be fully understood with the use of math concepts. Yep, it’s hard to be a biologist. Much more in being a mathematical biologist.

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        Gregor Mendel surely didn’t have much of a problem with solving the basic problems in genetics. I mean,  he was once a mathematician. He had what other geneticists lack-the familiarity on mathematics.  Having this advantage, he determined the factors that controlled heredity and traits. Though not every problem about the rules of genetics were solved or fully understood, Mendel was able find his way around this biological field. Armed only with the knowledge of mathematics.

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        It’s quite comical to imagine Darwin holding a Leithold book and a calculator. Sorry, just bored here. But in Stewarts\’s a point of view, mathematics does matter when it comes to evolution. No, not the numbers nor the shapes. But a certain concept that had me interested since it was involved with behaviour. It’s the Game theory, another one of math’s tricks up its sleeve. It’s just like the rock-paper-scissors game. This kind of concept may be used to determine how a population or species adapt to the factors that are present in its environment. How they deal with courtships and fights over mates. Amazingly the explanations are logical and quite accurate. Even Linnaeus’s concept of the binomial nomenclature classification somehow utilized logic to develop a system that worked smoothly and without fail. Somehow mathematics was able to seep into the tiny cracks of evolution and strengthened it as a science. Even more surprising to my part was that it was able to translate behaviour patterns into something understandable.

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I still have many things left unsaid in this review, so pardon my lack of ability to wholly explain in full detail. I would like instead to explain the interplay between mathematics and biology as a whole.

        What is life indeed? I mean, can’t we explain it with just a simple sentence from a dictionary and spare the hassle? Sadly, no. Just like some other abstract aspects, it’s hard to define life as a whole. Instead, the definition of life can be seen by understanding the concepts and behaviour of its elements. That way we see a pattern, an algorithm that guides these processes. Like the watch-glass in Spiderwick Chronicles, we can see the algorithms of life working in sync through our very own device: the sixth revolution, mathematics.

Biomaths According to Mr. Stewart

To be honest, (growing up) I was told this: 1. There are two kinds of people according to skill (words or numbers); 2. I am a ‘word’ person and; 3. ‘Word’ people usually do not excel in numbers.

            I believed what I was told. I deluded myself in that belief.

This has always consoled me whenever I had to slave myself in order to obtain good grades in math exams when I would only put minimal efforts in language ones and still manage to sail on.

Then, lightning struck, college came and my bubble shattered like glass. Every now and then I would find myself picking up after my lost esteem each time I have to enter math class.

If only I had known what I was getting into, choosing Biology over others, thinking I would escape its (Math’s) wrath. Alas! I could’ve never been more wrong.

Far from my previous sentiments, the book acknowledges how mathematics takes the spotlight in the study of life (Biology) by playing a big role in gaining and explaining knowledge in the science.

Here the author addresses the five revolutions of Biology wherein names that are familiar to us are once again introduced: Leeuwenhoek (Microscopy), Linnaeus (Classification), Darwin (Evolution), Mendel (Genetics), and Crick and Watson (DNA). In the said revolutions, math can be encountered from the number of microorganisms which we can now observe with the discovery of the microscope to the sequencing of base pairs in the DNA.

Much like how we learned mathematics, Mr. Stewart approaches his readers rather simply at first, and then becoming more complex as he delves deeper into the relationship between math and bio.

An analogous thought which can be formulated from these is that just like the microscope, although math can be painful due to the complexity it brings, this complexity is also beneficial such that without the discovery of the microscope, leaps in medicine would not be possible today.

However, just like the question “Is anybody out there?” there is still a lot we have yet to learn about mathematics. Much like our fear of the unknown in the world outside of ours including the otherworldly terrestrial beings (excuse my unwanted humor haha), the root of hatred towards mathematics is most probably ignorance of what’s in it (guilty party in here). My guess is that there is an inverse relationship between the lack of knowledge and the bliss we find in math. Sorry Paramore! (unwanted humor (?) mehe)

Like Dany Goky once said, “Replace fear of the unknown with curiosity”.

Who knows? We might make it to the list and create a new revolution.

Oh Math, LIFE Would Suck Without Youuu

To start things off, I was thrilled to read this book because finally, I would have read a book that certainly related Mathematics to the branch of science that I have long been interested in which is of course Biology. At least with this book, I could have definitely connected with because I do love Biology and this paves the way in wiping out some of the blurs in understanding how gravely important Math is in, well, pretty much everything.

The book opened up stating that Math could pass as being practically invisible relative to the life sciences. It was like at most a supporting actor but it never garnered the best actor award. It has not instigated the unraveling of what the other branches of knowledge could offer.  However, as time passed by, the tables have turned because inquiries have sprouted which could not be answered by science alone. This fortunately allowed Mathematics to finally shine. This made scientists and mathematicians to team up in order to solve the great mysteries of the world and beyond and even including the emergence of life itself. 

The author, Ian Stewart, mentioned "five revolutions" in biology which were the invention of the microscope which allowed humans to further observe what cannot be seen by the naked eye. Eventually, the developments made in the microscope lead to the discovery and deeper analysis of the cells.  The next one was about the systematic cataloging and organization of the organisms by the famous Carolus Linnaeus, the father of taxonomy. Then there was evolution in which Charles Darwin became the star who also wrote the book entitled "The Origin of Species". It was defined to be the gradual change, even though slow, over time in the appearances and behaviors of organisms. The fourth was genetics which was revolutionized by Gregor Mendel who experimented with peas and practically discovered that genes existed in the bodies of organisms. Then, the last revolution was the discovery of the structure of the DNA through x-ray diffraction with Rosalind Franklin and Maurice Wilkins to be recognized for because technically, they have initially discovered it and the tag team of James Watson and Francis Crick have mounted the existing data to build the double helix structure DNA.

Stewart pointed out that with each of these revolutions, Mathematics was inevitable, and this was his goal: to reveal the true power of mathematics in the context of life itself. Math is always important because not only did it become a tool for biological concepts but it was also an integral key in the deeper understanding for said concepts. With these claims, he induced the sixth revolution which was of course, Mathematics. It seemed to fill in the gaps that cannot be answered by merely science itself. As stated in the book, there are lots and lots of mathematical applications in Biology which would allow scientists to discover missing links in some topics and to further improve the knowledge that is already present. Math has definitely strengthened the foundation that supports the powerful concepts and insights in Biology.      

          Personally, I appreciate the author’s way of writing this book. This would be one of the non-fictional books that I have enjoyed reading. Well, I could say this with a bit of bias since I am really inclined to Biology and this book provided new points concerning the correlation between the two disciplines. It has definitely opened up the readers into a whole new appreciation for Math. I have already known that the varied fields of knowledge are interrelated, for example, Mathematics and Biology. Math has supplied Biology with concepts that have helped solve problems like the probabilities of how many of the progeny are to express the given phenotypes in genetics or determining cell count and size by solving in the context of microscopy and it is very obvious that even plants and animals naturally exemplify certain mathematical patterns. But even with this present knowledge that I have, I still have not entirely grasped upon how and why they are entirely connected and that is why this book was a great way in widening my scope of understanding on this. But I also could not say that the whole book was satisfying because it lingered more on biological concepts instead of explaining more about the excellent contributions of mathematics to the life sciences so it left me hanging. However, this makes me more excited in future readings that would further strengthen the bond between Math and the study of life.

Nevertheless, I could still say that the author did a wonderful job in writing this book. It was very well written and he has relayed his insights to his readers quite successfully. I really liked the part where calculations were made to stand that life may very well be present in some other, although far planet. I even felt for quite a moment that I was reading a Biology book because it was jampacked with biological concepts which were already very familiar.

And so, to end this review, I would just like to leave these words: Mathematics may be neglected by a lot but its scope is vast and is applied everywhere and therefore should receive the recognition that it deserves. 

A Book Review on the Book: The Mathematics of Life

A Book Review on the Book: The Mathematics of Life

The very goal of the author is to establish that Mathematics' contribution in Biology is very essential and with that he wanted Mathematics to not just be on the background but rather to be part of the picture where one can see its use immediately. For the author’s first paragraphs, he made mention of five revolutions that has happened over the years that made biology what it is today. With that five, he was hoping to add the sixth revolution and that is his goal to genuinely integrate Biology with Mathematics. In the first chapter of the book, he enumerated the five revolutions. The five revolutions were the following: the invention of the microscope, the development of system of classifications, Darwin’s Origin of Species, the founding of Genetics by Gregor Mendel, and the discovery of the structure of DNA. Though still in the very first chapter, he has already made mention one of the major contributions of Mathematics in Biology which is Bioinformatics. In the following chapter, he made it to the point to start from the basic unit of life, cell. There, he talked about how the first revolution paved the way for the discovery of cell. He has named some personalities whom I am hundred percent sure you all know, the likes of Jansenn, Leuwenhoek and Hooke. In the third chapter, something has caught my attention and that was a sentence saying that the first edition of Encyclopedia Britannica is an entry of how many creatures are there in Noah’s ark. The second revolution was also discussed here. Still in this chapter, it is said that what’s important in classifying is not the characteristics that easily attracts attention. I also found what JBS Haldane said about why there are many species of beetles funny. He said that God has fondness for the said animal.

            In the fourth chapter, it is said that Mathematics was able to squeeze itself to Biology through geometry. The number of petals in a flower and the seed heads all use geometry. Though Mathematics applies in numerology and geometry of plants it still has a range of validity. In the fifth chapter, Darwin’s work, Origin of Species, was discussed. Here I was surprised that his work did not make an impact when presented in the annual gathering of the Linnaean Society. Also, it was also said that even before Darwin proposed about Natural Selection, Aristotle has already an idea about it but doesn’t just use the term natural selection or survival. In the sixth chapter, the fourth revolution was discussed and the star in this chapter is Gregor Mendel and his garden peas. Though irrelevant, I just wanted to point out that before reading this chapter, I didn’t know that Mendel was actually born in Germany and his real name is Johann. Well, Mendel’s ideas on Genetics were not widely accepted because before they believe in blending theory and pangenesis. In chapter seven, I was so ignorant not to know that ancestors of modern man had once made sex with a Neanderthal. I was so shocked.  There is also another Mathematical inference her which is the X-ray diffraction. In Chapter 8, the Human Genome Project was discussed along with its rival which that of Celera. Both have the goal of completing the gene codes in a human but I different approach. HGP make use of “use of clever chemistry to simplify maths” while celera make use of “use the clever math to simplify chemistry.

            In the ninth chapter, mathematics once again proved to have use in Biology through a diagram and mathematics tree, a cladogram. There was also a mention of horizontal and vertical gene. In chapter 10, geometry comes in again with its application in knowing how viruses look. In Chapter 11, it talked more on nerve cells and how the people before take no importance of the brain thinking that it does not have any function. There was also a mention of FitzHugh–Nagumo equations and Hodgkin–Huxley equations that were mathematical models applied to nerve cells and axons. Topology was the highlight in chapter 12 and the use of Mathematical models to explain how an embryo develops was the highlight in Chapter 13.Still in chapter 13, Alan Turing was mentioned as one who developed ideas on spots and stripes based on biological theory on pattern formation after becoming interested on the markings on animals. In chapter 14, there was a discussion of survival and evolution having the lizard mating as an example. In chapter 14, it talks about how each species contain networks within itself and how this network may benefit another species. An example given was that of a slime mould in a railway project. Chapter 16 was mainly on ecosystem and the interrelationship of organisms and its interaction with the environment while the focus of chapter 17 is the definition of life. Chapter 18 talks about the possibility of having life forms outside Earth and in the last chapter it talked about the goal of the author or the sixth revolution which is the “could be marriage” of Mathematics and Biology.

            The book generally talks about the instances on how Math can be of great help to Biology. Though he had mention some equations and he said that there are Mathematical models that can be of great help in explaining biological systems and processes, he did not really expound on the explanations and I find it hanging at the end. On a positive note, I commend the author for having explained the facts he had presented orderly knowing the fact that it is Biology and he is a mathematician. Even if there are things that I still need to fully understand, I agree that Biology needs Mathematics. Sciences are like humans that cannot stand alone. One science cannot expand without the help of other sciences.

The Wrong Mentality

            Biology is the study of life. When you let a child define ‘life’, he or she will always refer to living organisms such as plants and animals. For biologists it is much deeper than that. As a biology student, Biology was my field of choice because it is interesting; how life becomes ‘life’ and how life is lived variously. Of course, there are always other reasons like – biology does not require that much of Mathematics which was contradicted by Ian Stewart. He said that Biology without Mathematics is a wrong mentality. He also added that there have been five revolutions which changed how biologists viewed life.

            The first revolution was the discovery of microscope 300 years ago. This discovery unraveled the mystery of the basic unit of life – cell. It was then known that an organism may be made up of one, millions, or trillions of cells. The second revolution was known as the Linnaean system by a botanist Carolus Linnaeus. He established the system of binomial nomenclature. This revolution, in my opinion, is one of the greatest events that happened in biology. Due to the numerous languages, dialects, and other means of communications the world has in it, it was hard to know which species of cat you are referring to. That is the main reason why we have the so called ‘scientific names’. The third revolution was when Charles Darwin proposed his theory of evolution in his book The Origin of Species by Natural Selection in 1859. He proposed that humans evolved from monkeys and this was due to the environment with all the biotic and abiotic factors in it. The fourth revolution is the discovery of genes by a monk named Gregor Mendel who is also known as The Father of Genetics. He studied about peas and how traits were passed on or inherited from parents to offspring.  The fifth revolution happened due to a new invention called the X-ray diffraction – the discovery of the structure of DNA or Deoxyribonucleic acid which is said to be the main reason why a monkey is a monkey and a human is a human. The discovery of the structure was by Watson and Crick.

Stewart then mentioned that due to these five revolutions, biology was never the same. It was not limited to plants and animals but it has now a wider scope. It requires and touches other fields of sciences and of course, Mathematics. What is common in all these revolutions is Mathematics. He said that it is Mathematics that united all these revolutions. As you start to read the book, you can’t help but think twice if this book is really this easy to read and to understand. As you read the first twenty pages, it was all about Biology and how Mathematics was used as a tool to analyze and understand data obtained from experiments until there became Biomathematics. I, myself, was afraid of such term (but note my tense ‘was’). It was a marriage of biological sciences and Mathematics. Yet, Stewart explained that there is nothing to worry or to be afraid of. It does not necessarily mean to create new mathematical concepts but to also try to use and apply ‘old’ concepts which you think would be necessary in your study. This is, according to Ian Stewart, the sixth revolution.

As the book progresses, it becomes harder to analyze and requires re-reading especially the part of Fibonacci and Lucas sequences. Actually, I love how the author deal more on the applications of mathematics in the field of science rather than dealing with mathematics per se which will sure cut my interest off the book. It was also good that the author used analogies to explain his ideas in order for it to be easily understood. I particularly like the chapter entitled “Is Anybody Out There?’ and want to reiterate a line, “So either Earth won a jackpot in a cosmic lottery, or we are not alone”. In this chapter he says that the re is probability that there are other lifeforms outside Earth as well as the probability that there isn't.

The book was able to convey that science is far more complex than what we can imagine but as we know more and discover more does not mean that the basic concepts we once knew were invalid. Also, Science isn’t always about what is directly observed. Most of the time, it is indirect deduction.

A Book Report: The Mathematics of Life

 Ian Stewart’s The Mathematics of Life, informs us that there was more to the history of science that we ought to know. The discovery of theories and principles, inventions of different kinds of both scientific apparatuses we use in this modern age, the breakthroughs that lead us to where we are right now by our forefathers; was with the help of both science and mathematics.

The author did a great job to make us acknowledge the emerging and probably one of which will be the greatest breakthrough to our human age; biomathematics. The author points out that there were five (5) revolutions that changed the scientists’ point of view towards life. These five revolutions are the microscope, classification, evolution, genetics, and lastly, the structure of DNA. But there was one thing the author said in his book and it is about the sixth revolution, and it is mathematics.

            I, too, was shocked when he stated this in his book but the author pretty much changed my way of thinking too. Since mathematics has been with the human race for hundreds of years, Babylonians was even intrigued by theoretical mathematics that they wrote an ample amount of text involving geometry and algebra to uphold their civilization. But more than that, Stewart stated that the first revolution happened 300 years ago. And it was the microscope, which surprisingly enough, was inspired by the works of the great Galileo Galilei’s telescope. This gave way to different breakthroughs in biology, genetics, etc.

The next evolution is the classification, taxonomy, for that matter. And taxonomy was not just some fancy way to classify an animal just by naming one after the other by putting some fancy Latin names, it was a systematic way to classify a domestic cat, a Siamese cat, etc. Part of which is mathematics had a role in classifying units and sets of variables with the use of diagrams and tables. Furthermore, the reason why subdivisions were made is because, over time more and more animals and organisms are discovered and then classified to the groups they are related. The amounts of animals and/or organisms are so plenty that scientists used mathematical equation to get a theoretical sum of a certain species. This operation and many others are now commonly used to get a theoretical amount of a certain species, endangered or not.

The third revolution stated by the author was evolution. When I was a kid, I was fascinated by the theory of evolution. Watching informative yet theoretical television shows gave me such bliss. I often question myself if they were really true. How thousand years ago, certain fishes knew how to walk the earth with their odd fins that acted like feet. But the author said that the third revolution got off of a bad start. Since evolution was not widely acknowledged when it was first introduced solely because scientists, mostly taxonomists, encouraged that newly discovered species were not evolving – just not seen yet. Charles Darwin opposed the idea, he said that evolution was an essential key to survival. In his research he used various arithmetic operations because, theoretically he calculated the population of the evolving species.

Fourth revolution was brought to light due to the help of the microscope. Genetics was triggered by the great mind of Gregor Mendel, who was a gardener when he was young. Biologists those days did not accept Mendel’s theories, mainly because they are conflicted with prevalent belief that characters passed from parent to offspring by ‘blending’. But after his death, two scientists rediscovered his unappreciated and unread papers. Various biologists began experimenting, too. One of which, tested breeding on grasshoppers and found out that a physical factor of heredity, the chromosomes.  Stewart did not fail to miss a single string in this thread, he profoundly explained the origins of the discovery of genetics. He noted every single important details through the subject matter, using mathematics in figuring out the probability of an offspring.

            The fifth revolution, and is widely known as our genetic code that makes us different from everyone else, is the DNA. DNA or deoxyribonucleic acid is a molecule that encodes the genetic instructions used in the development and functioning of all living organisms and viruses. Scientists used a series of mathematical experiments. They substituted these molecules into letter and began to illustrate the DNA, until they got what they were looking for, a double helix DNA structure that fits perfectly to a molecule that sustains life.

And lastly in Stewart’s book, he implied that Mathematics is the sixth revolution. He described that Mathematics has been in accord with the works of physical science for a long time. The author talks about Mathematics’ wide range of help in various discoveries in the field of the burgeoning biomathematics. I was inspired by this book because I learned more about science and how mathematics aided in its research. Many of which are surprisingly enough, I thought had nothing to do with Mathematics. The author pointed out that biomathematics aim is the selection of useful models, it wants us to take biology seriously – not missing out anything crucial, and lastly is to pay attention to the problems biologists want to solve. Ian Stewart stated in his book that his sixth revolution is not that revolutionary, though. Since no one ever used mathematics solely to solve a scientific problem. What is revolutionary about it is the paramount of methods used, and the extent of which they are starting to set the agenda of biology. The author encourages us to be eclectic to the idea that the Mathematics and Biology community has long been interconnected. We should embrace his work, and embrace the new epoch that is to come. The profundities are infinite when you use both of them to seek out neoteric theories, discoveries, and inventions that would help both humans and other organisms alike.

           

Life with Numbers

‘The Mathematics of Life’ is a book that was written by Ian Stewart which talks about the rich connections which already exist between mathematics and biology.  This book included and tackled about the likes of the Human Genome Project, the structure of viruses, the organization of the cell, the interactions of organisms holistically, and many other biological concepts. The author then showed and discussed on how mathematics helped to solve issues concerning many biological breakthroughs by well-known scientists: starting from the basic concepts to the discovery of the DNA which led biologists to focus more on the so-called ‘molecule of life’.

The main points on this book certainly revolve around the great revolutions which led the scientists to change their way of analyzing life. There are five great revolutions: the microscope, the systematic classification, the theory of evolution, the discovery of genes, and the discovery of the structure of the DNA as what he noted in the book and accounted the coming of the sixth one: Mathematics.  Before tackling the sixth great revolution, he first discussed the first five revolutions. 

“If human eyesight had been better, we might never have experienced the first revolution, when we noticed the hidden wonders of life.” as said by Mr. Stewart. It was clearly stated by that statement that the first point of this book is all about instruments with magnifying lenses. This part clearly and concisely discussed on the ideas and principles with regards to the construction of these instruments especially the Microscopes. I agree with his statement, if we human beings have better eyesight we wouldn’t have a need to construct an instrument which magnifies small things, that we can uncover, observe and study the vast richness of the complexity of the world of microorganisms without the aid of any instrument, thus lessening the complex works and costs of studies. This part of the book talks about the discovery and construction of microscopes by Anton van Leeuwenhoek and then eventually led to the discovery of the cell by Robert Hooke. 

Systematic classification of organisms by Carl Linnaeus is the second great revolution in science according in the book. With his admirable work, living organisms are classified and named in terms of its species, genus, family and other extensive groupings that made this present society easily classify and differentiate one species to another. The author also said that the “Linnaeus’s classification scheme has brought a degree of order into the apparently chaotic world of life on Earth today.”  With this systematic classification, hierarchical structures could also show the evolutionary ancestry of the organisms present today.

Mr. Stewart also made an important distinction between the descriptive and explanatory models that is related with “the strange numerology of the plant kingdom”. He observed some strange patterns and also connected these patterns with the golden ratio, the golden angle, and the Fibonacci sequence. Such matters would indicate the possible occurrence of a mathematical pattern in nature.

The third main point of the book is all about the theory of evolution or the origin of species which was made famous by Charles Darwin. This evolution is said to be recognized by natural selection. With the presence of natural selection, those organisms that can adapt and fit well with the environment will survive and those that are inadequate will not survive. Due to this selective pressure, evolution takes place. 

Genetics is considered as the fourth great revolutionary in science as noted by Mr. Stewart. Here, Gregor Mendel and his discoveries like that of inheritance, that is greatly important to the world of genetics, were tackled. Mendel first observed the various characters that were exhibited by the parent organism (plant), and then cross-fertilized a plant which has a particular version of that character with another plant, having the same version or a different one, and finally sees the corresponding characters present in the next generation.

The fifth one is the discovery of the structure of the molecule of life, DNA. With Crick and Watson provided the double-stranded model of the DNA, many advances in the field of medicine were accomplished in the recent times. This is because when the double-helix structure of the DNA was published, more studies were conducted in order to understand this molecule of life more. These researches include the understanding of amino acids, nitrogenous bases and such. With this new knowledge, the molecule of life is understood well and many genetically inherited diseases could also be understood and then possibly be cured.

This book also discussed and nourishes our understanding about viruses. He observed that viruses consist of a genetic material that is wrapped in a protein coat; with each virus have a definite structure, either icosahedral or helical. These shapes successfully correlate mathematics with biology with the help of the application of geometry to these structures. But shockingly, it is geometry in six dimensions. With the help of Geometry, potential weak points of the assembly process of the virus will be provided.

This is really considerate and good of him to first tackle the first five because those readers whom are not truthfully interested in these kind of matters  will understand more and will be able to relate on how or why he saw mathematics as the sixth great revolution in biology. I somehow enjoyed reading this book given that I am a biology student and that most of the terms used here are not new to me, thus, I can appreciate his work well enough. His discussion on the first five revolutions was good since he provided facts in relation with each revolution. As for the coming of mathematics as the sixth one, his correlation with biology was a little off. Maybe because his main point on this one has yet to emerge. His point here can just be considered as the beginning of a whole new set of great and unforgettable scientific revolutions.

PARTNERS IN CRIME: GUILTY FOR EXCESSIVE DIFFICULTY

                I actually had the same reaction towards the ‘Meet a Mathematician’ talk, both just made the Biology universe much more difficult. I chose Biology mainly based on the fact that it relies on memorization and some analysis of concepts and ideas, no computations and such. Who would’ve thought that even after shifting, math would still haunt me? This book actually summed up what I was starting to realize entering this semester, especially during ecology and genetics. First they were just a few equations and some ratios/patterns. But after reading Stewart’s book and most of my lab manuals, it is clear that the time that math strikes back has come...

                Unlike the previous book, this one proved to be easy to read and very VERY relatable. It is so relatable, that I practically skipped (actually skimmed) the first few chapters. I have read more than a dozen versions each of Chapters 1 to 7 (with a few exceptions). Some were from lectures mostly introductory classes such as the ones we had at the start of the semester. This information can be considered as ‘common sense’ for future biologists. However, I will still add some of my more memorable reactions, since this is supposed to be a “review”.

Well, the first thing that interested me was already in Chapter 3, the one about Noah’s Ark. Before reading this book, Noah’s Ark was just a simple story for religion and enlightenment. And… math just makes it worse, why would I want to know how they fit those animals there? Using math to explain how they fit everything in an ark? The better question is “How did ~8 people gathered that much resources and animals then even build something to carry everything?”. In addition, why would it matter? Most of the scientific revolutions go against traditional religion… it’s like math is conspiring with the enemy.

After this chapter, I began to realize that the book itself jumps from interesting facts to boring basic biology with the occasional math-related interjection. To justify this, chapter 3 goes on about classifications, blah blah blah, been there done that. Most chapters are full of these basic and common biology facts. Overall, I’ll just review those interesting side stories and ideas, since I already have had enough biology from my BIOLOGY subjects.

So the book goes on and on and on about biology, not much about math…until Fibonacci. I have already heard of Fibonacci from high school, but just a little bit, not enough to destroy my brain. Before I would say things like, “look that sunflower’s spiral looks pattern-y”. Now I can’t help but think like a nerd…” blah blah blah Look! That sunflower’s spiral rotates at an angle of blah with the number coinciding with the Fibonacci sequence inclined to an angle of blah blah blah”… I blame it all on “math+biology”, you ruined me. I can’t look at plants the same way ever again… I mean they’re just flowers, why make them constant reminders of MATH… T.T

Then it goes back to boring biology facts, something about patterned rabbit baby-making and plant growth. I think that was part of “Meet a Mathematician” and the plant thing is still about Fibonacci and some other patterns, so I’ll just skip that. As I read further and further, the book delves deeper and deeper into biology eventually leaving me behind. By Chapter 5, it already tackles biology concepts in levels beyond my comprehension. I can still read it, but I can’t maintain the information long enough to fully analyze it. Most of the time, I read the sentences 3 times each to barely grasp their meaning or at least their implication. The Origin of Species, as I know it, is the book of natural selection written by Charles Darwin. Stewart makes it near impossible to completely understand this chapter by repeatedly going from one research to another. In my mind, his discussion should be easy enough to follow but in reality there is just so much information given from different perspectives that I can’t fully synthesize whole meaning (mainly because I don’t recognize many of the names in this Chapter). At least the math in this chapter was minimal, YEY! This “complexity” was carried over for all of the succeeding chapters. Chapters 6 to 10 were still bearable, since I still have stocked knowledge concerning these fields. The succeeding chapters were relatively new, and by extension painful.

At this point my brain is at its limit, normally I can’t finish any book I don’t like and I really don’t like this one. I was wrong in thinking that this was better than the first, in fact I think it’s more evil. Instead of being obviously boring, it starts of easy and fun, but when your guard is down it wrecks your brain with math-bio combos. Chapters 11 to 18 show some more specific application of math on biological concepts. I was from an electrical engineering course, and believe me it was HARD… and this book thinks its fine to just add it to biology!?! Brains are complex enough by themselves and now you want to add voltage, wavelength, etc. Even Ecology is being “mathemathized”. I didn’t even understand how lizards are like rock-paper-scissors. So what if there are three types, they aren’t playing a game, they can’t even choose. And good ol’ Stewey (Stewart) didn’t even bother to finish explaining this nonsense.

The last few chapters were a blur, my mind couldn’t process anymore, it was just too difficult. But I at least remembered the alien thing. I liked that part, didn’t understand it but still liked it. I don’t really believe in aliens but I do agree that we need broader mindsets. We really shouldn’t limit our “imagination”. I mean, maybe life could have emerged from conditions different to ours.

Now that I think about it, the book itself seems to be declining in quality. At first I liked it, it was simple, straightforward, relatable and cohesive. But as it progressed, the information seemed to become more and more disorganized and convoluted. There were just too many things going on. For each topic there were too many insights that weren’t completely explained, which made it harder to see the relationship between ideas. Maybe he got tired like me, hahaha.

To conclude, I think that the math and bio combo overall is beneficial to mankind. But I still it should be limited to those who enjoy math and pain. By themselves, they are already headaches, why would you want to combine them? Maybe inside a lab or within a computer or written in papers, this combinations could flourish, but definitely not in day-to-day life. The world will look so boring and nerdy, everything in numbers and patters, really? I OBJECT!!!

Connections: The Link Between Biology and Mathematics

        Connection. This word might mean a lot of things. This may make life easier. This may enlighten theoretical problems. This may lead to new discoveries and wonders.

            Reading through the book “The Mathematics of Life” by Ian Stewart boggled many questions and at the same time answered mysteries that may possibly arise in the near future. Tricky it is that the author tried to make interconnections of two fields that make impact in today’s world, however, the coherence and flow of the reading made the whole work successful.

            The book started vaguely as the author tried to pursue linkage between Biology and Mathematics. As a Biology major in the university, I am conscious enough that mathematics has a vital role in biological studies. However, being well-informed in the theories of mechanisms and complexities in living systems sometimes limits my idea of the existence of biomathematics. The early part of the book introduced the five revolutions in biology: the microscope, classification, evolution, genetics and the DNA structure. The author tried to address that biology started with observations and queries which had led to new revolutions as time goes. He then introduced mathematics as the sixth. The main thing that I have reflected with the explanation of the sixth revolution was that mathematics learned basically at school is just a tiny view of what it really is. Indeed, it is hard for us to understand how it could explain the complexity in creatures but as we see today, it is widely used in research through the computer. Statistics and other fields are becoming helpful in answering hypotheses in biology. This approach constructed by the author could effectively lead my track as I read the next chapters.

            This is an important feature in all bodies of knowledge. The author scrutinized complexities of living creatures through crediting the development of instruments used in scientific research. Through the invention of the microscope, protists, cells and other biological forms were studied and new knowledge were generated. Classification of living forms, on the other hand, put the starting hint in me on the inclusion of mathematics to biology. How plants and animals are classified is an essential way to study life. Characteristics such as shapes and patterns that could be observed are significant. And as I could recall, mathematics is the science of patterns.

             “Florally Finding Fibonacci” was interesting at first sight. Mathematics and Biology in one phrase, perfect. It was really amusing for me to get to learn Fibonacci in this book. As basic as possible, I see it as a body of knowledge that deals with sequence of numbers. And surprisingly, it was seen on patterns of some traits of living forms such as number of petals of different flowers of angiosperms, phyllotaxis, patterns of the spots in pineapples and a lot more. Now it made me clear how the first two revolutions got connected with math. Indeed, numerical patterns in living creatures can be seen in detail.

            We all wonder how it all started. The issues revolving existence and philosophy. The evolution of species might be a key to answering several questions on mutations as well as the phenomena that are frequently happening today. As what I could infer from the book, characterizing evolution has figured out patterns. These patterns have led also to the next revolution in biology which is genetics. I struggle in our genetics class. However, I find it quite interesting when mathematics comes in especially in solving frequencies and also discovering patterns. The application of mathematics in this field was briefly explained in the 6^th chapter. The fifth revolution is the DNA structure known as the molecule of life. This is where genetics and evolutions revolve. As it is composed of nitrogenous bases, percentage of such were computed in each species. Its discovery was indeed remarkable and evolutionary.

            Now that the author has established basic information about the 5 revolutions in biology, I am quite excited on his approach on explaining the vital role of mathematics in this field of study. The discovery of the DNA structure opened the way to more research problems and more opportunities for development of knowledge. On the chapter tackling about taxonomy, I was very interested to have learned how big the contribution of math in Biology is. In taxonomy, phyologenetic trees are essential. Forming cladograms are metaphorically similar to mathematical trees as said in the book. Also, the probabilities of the number of forms trees could have is important to taxonomical research. I was pretty much astonished on how people in the old days interconnected these knowledge. Moreover, I thought that maybe the discovery of its interconnections is spontaneous.

            As I see in today’s world, viral infections and diseases are rapidly increasing. I never thought that in a broad science of math, it can be applied to the features of these viruses such as its shape (e.g. icosahedral) and a lot more in its genetic material. Such mathematical studies are important in the study of molecular biology as well as searching for new breakthroughs in medicine. Also, math became more attached to biology on studying nerves and complexities in the human brain. Studying the brain using our brain is indeed fun. The axons and the dendrites and the neurons and all the nerves follow numerical details which amazed me as a reader. It gets more peculiar and unique as I learned that even through the simplest detail in an animal’s body pattern, math should be employed such as in spots and in the stripes, its symmetries and the like. The application of mathematics to animal morphology is what I vaguely saw before. In ecology, a broad topic on species interaction and diversity, more numbers and statistics are used. Studying populations is undeniably vital in predicting the global status environmentally and ecologically since we encounter more and more problems everyday.

            Now we see that the world is indeed full of complications, but thinking that the Earth is just a piece of dust in the universe, it’s immeasurable. Upon finishing the book, I could not explain how enlightened I am to the fact that in the world of science, everything is related. It makes me even think that mathematics is bigger than the universe since it goes beyond limits. As a biology student, it is very astonishing to think that to become a great biologist, you should be well-balanced in all fields.

Revolutionizing Life

The Mathematics of life; a book that commences new intellectual idea and knowledge in the field of Biology with accordance to the principles of Mathematics. Biology is basically known as a branch of science that studies life and everything that encompasses it. Because of its broad scope and for it to easily understand the principles behind the phenomenon of life, Biology is interrelated with other branch of sciences. Mathematics on the other hand is the discipline being associated with other branch of sciences because of the principles it has that enables other sciences to solve certain problems underlying it. Mathematics therefore is the core of all sciences. However, Biology and Mathematics are not related since Biology doesn’t directly uses Mathematics but instead, Biology is allied with other branch of sciences that uses the principles of Mathematics. This idea was opposed by an English mathematician, Ian Nicholas Stewart. In his book entitled The Mathematics of life he pointed out how Mathematics had changed the views of different scientists regarding the phenomenon of life, in accordance to that; Biology.

The book written by Ian Stewart revolves in the idea that there were five great revolutions that had changed the way biologist and other scientists think of life. The five great revolutions are; the microscope, classification, evolution, genetics and the structure of DNA respectively. Stewart added a sixth revolution, Mathematics. In his book he tries to prove how Mathematics had become fundamental in unlocking the mysteries of life through giving an overview of the five great revolutions of Biology by incorporating every revolution with Mathematics. He also did not stop with the idea that Biology uses Mathematics but proves that life itself had been using mathematics in each of its phenomenon involuntarily.

He started his book with the introduction of what life is and what is Biology. He mentioned in his introduction that there were five great revolutions that had changed the way scientists think about life and a sixth revolution that is on its way to be revealed. In every chapter he provides information on how Biology had revolutionized through the years and how Mathematics had been clandestinely helping the field.

In the first chapter of his book he had a quick review on the five revolutions that had a great impact on the field of Biology and how it has expound the minds of the different scientists to new possibilities and reasons to explain the phenomenon of life. In the second chapter he explained how microscopes had evolved through time and what great importance it was to the field of biology and other sciences. He explained that through microscopes living organisms were much more understood. Through the birth of the microscope there were also new discoveries that were revealed; as an example, the cell. At the start of the third chapter he made a quick summary through stating; “This is a short chapter of a long list.” Indeed the chapter talks about a long list of classification with the following hierarchy; Kingdom, Domain, Class, Order, Family, Genus and Species. He explained that these hierarchies are used to easily categorize and identify specific organism without interchanging it with other organisms. As an example in assigning an organism in the different hierarchy he used the idea of counting plant organs. In this part he mentioned that most plants have patterns of numbers and shaped observed on their leaves and flowers which are used in assigning them to a specific classification. In the next chapter, he mentioned the first mathematics that had used the idea of patterns in living organisms. This number sequence or pattern was called as the Fibonacci numbers. He explained that most plant organism follow this pattern. Not only do they follow the Fibonacci numbers but also the golden ratio. He states here that life could have probably been using math on its own.

The fifth chapter talks about the third revolution; evolution. This chapter focused on the idea of Charles Darwin. He explained how the theories of Charles Darwin had open up new ideas in the field of Biology and other related sciences. Darwin had caused lots of issue but also may had explained some points regarding the evolution and the variation of different species based on different factors that had been subjected to them. In the sixth, seventh and eighth chapter he mainly discussed about DNA, Genetics and how Genetics had evolved through time. Theses chapters revolved in the idea that through Genetics new ideas and learning about life had helped the scientists in unlocking mysteries. It had explained the different processes that underlie the phenomenon of life and how different organisms contain different genetic materials that had caused each organism to be unique from one another.

 In ninth chapter he explained how taxonomist arranged different organisms based on their direct and common ancestors through a classification scheme. This scheme uses a tree to represent the ancestors and the new generation of species. In the diagram the branches shows how organisms or species are connected by changes in their DNA.

Microorganisms, especially viruses are invisible to the naked eye and it could only be seen with the use of the microscope. The tenth chapter talked about the viruses and the idea of fourth dimension. Viruses follow geometric shapes and patterns which had led to a theory that the geometry of viruses had took place in four dimensions and not three.

Chapter elven to sixteen, talks about important facts, knowledge and ideas concerning the different functioning parts of organisms and how they function themselves. In these chapters mathematics is applied in understanding the different phenomenon and processes that organisms undergo. The final three chapters wraps up the whole book, starting with chapter seventeen which talks about life and what are the standard outlines to consider that a specific entity possesses life or is a living organism. The eighteenth chapter talks about the possibilities of other living organisms living outside our planet and how scientists through the years are trying to figure out missing puzzle pieces regarding this wonder.

The last chapter, chapter nineteen Stewart ended his book with a striking conclusion. He concluded that Mathematics may not have directly revolutionized the way scientists think about Biology but it had given Biology a big favor. Mathematics had helped Biology answer some phenomena that are not answerable by the principles of Biology alone. He finally concluded that each branch of science is related and is essential in answering different phenomenon each of them tries to solve.

            Ian Stewart had written his book in a typically clear and entertaining manner. In my own opinion as a Biology student, he had explained Biology in a manner that I could easily understand ---the knowledge he was trying to impart. However, for people who don’t have a vast background about Biology, they might have a hard time in understanding his book and would easily get bored. This might be the challenge about writing this book but still he had pulled it off because he knows how to get the attention of the readers easily. It was however odd when he added the idea of aliens in his book. It may be considered as other life form however, it was not significant for his main topic. Overall his book was entertaining and interesting which could give readers new insights and intellectual idea.

            I agree with Ian Stewart’s idea of Mathematics as the sixth revolution that would take scientists to a deeper understanding of Biology. Indeed Biology could not stand alone without the other field of science and those other fields could not stand on their own without Mathematics. Through this book, it was imparted that even before Mathematics had been fundamental in answering problems and analyzing answers regarding the different phenomena affects and encompasses life. Indeed Mathematics had changed the way scientists think about life and it would continue to revolutionize the field of Biology in the years to come.