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This is the thread to add any books about the study of Mathematics, (non fiction and/or historical fiction)

Is Mathematics a science?

There is already discussion about mathematics. I had to ask myself if Mathematics really is a science. Here is article about that question. This thread is also a thread to add any books about the subject of mathematics

Article asking the question: Is Mathematics a Science?

Is mathematics a science?

Author: Stefan Bilaniuk
Department of Mathematics
Trent University

Abstract: Mathematics is not a science, but there are grey areas at the fringes.

Mathematics is certainly a science in the broad sense of "systematic and formulated knowledge", but most people use "science" to refer only to the natural sciences.

Since mathematics provides the language in which the natural sciences aspire to describe and analyse the universe, there is a natural link between mathematics and the natural sciences. Indeed schools, universities, and government agencies usually lump them together. (1)

On the other hand, most mathematicians do not consider themselves to be scientists and vice versa.

So is mathematics a natural science? (2) The natural sciences investigate the physical universe but mathematics does not, so mathematics is not really a natural science. This leaves open the subtler question of whether mathematics is essentially similar in method to the natural sciences in spite of the difference in subject matter. I do not think it is.

A disclaimer is in order. This essay is a "native informant's" opinion: I am a practicing (if mediocre) mathematician, but not a philosopher or student of the practice of science or mathematics. I have a relevant philosophical bias, in that I am a Platonist where mathematical reality is concerned. (3)

The object of the natural sciences is to devise and refine approximate descriptions or models of aspects of the physical universe. The feature distinguishing science from other means of doing so is its characteristic method. Crudely, this consists of asking a question, formulating a hypothesis, testing it, and then, on the basis of the results, rejecting or provisionally accepting the hypothesis. One usually repeats the process after refining the question, the hypothesis, or one's ability to test it. The ultimate arbiter of correctness is the available empirical evidence: a hypothesis which is falsified -- i.e. inconsistent with good data -- is not acceptable. (A hypothesis which could not be falsified by any empirical data is not scientific.) Note that a scientific theory or hypothesis is (at best) only provisionally acceptable at any given time, because a new piece of evidence may force it to be modified or rejected outright.

In mathematics, however, the ultimate arbiter of correctness is proof rather than empirical evidence. This reflects a fundamental diffence in what one is trying to achieve: mathematics is concerned with finding certain kinds of necessary truths. For a mathematical statement to be accepted as a theorem, its conclusion must be known to always be true whenever its hypotheses are satisfied. We accept it only when we have a proof: a chain of reasoning demonstrating that the conclusion must follow from the hypotheses. (4) Empirical evidence does, to be sure, play an important part in doing mathematics. Conjectures are usually formed by observing a common pattern in a number of examples, and are often tested on other examples before a proof is attempted. However, such evidence is not sufficient by itself: consider the assertion that every even integer greater than 4 is the sum of two (not necessarily different) odd prime numbers. (5) We have lots of empirical evidence supporting this assertion: 6 = 3+3, 8 = 5+3, 10 = 7+3 and 10 = 5+5, 12 = 7+5, and so on. However, we cannot be sure it is true unless someone finds a proof. Until then, it is conceivable that someone might find a very big even number which is not the sum of two odd prime numbers. (6)

The essential difference in method between mathematics and science, and the weakness of each, is neatly exploited in the following joke:

Some academics relaxing in a common room are asked whether all odd numbers greater than one are prime.
The physicist proceeds to experiment -- 3 is prime, 5 is prime, 7 is prime, 9 doesn't seem to be prime, but that might be an experimental error, 11 is prime, 13 is prime -- and concludes that the experimental evidence tends to support the hypothesis that all odd numbers are prime.

The engineer, not to be outdone by a physicist, also proceeds by experiment -- 3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime, 13 is prime, 15 is prime -- and concludes that all odd numbers must be prime.

The statistician checks a randomly chosen sample of odd numbers -- 17 is prime, 29 is prime, 41 is prime, 101 is prime, 269 is prime -- and concludes that it is probably true that all odd numbers are prime.

The physicist observes that other experiments have confirmed his conclusion, but the mathematician sneers at "mere examples" and posts the following: 3 is prime. By an easy argument which is left to the reader, it follows that all odd numbers greater than one are prime. (7)

The mathematician is wrong by the standards of her field because a valid proof of the assertion that all odd numbers are prime has not been given. (8) (Leaving the hard -- or impossible! -- parts to the reader is a bad habit regrettably widespread in mathematics. (2)) In view of the available evidence, on the other hand, the physicist is quite correct by the standards of his field to accept the assertion. (9)

It must be admitted that the difference noted above between science and mathematics is not completely sharp, even aside from the fact that the practice of mathematics does have empirical content. Some of the areas in which mathematics is applied to modelling aspects of the physical universe are very grey indeed. The basic problem is that one can be confident of a fact derived by mathematical methods only to the extent that the mathematical object being considered is an accurate model of the relevant parts of the universe. One can be completely confident this is so in mathematics (where the mathematical object in question is the relevant part of the universe) and quite confident in, for example, computer science (where the physical objects being analysed are made to conform to a mathematically precise pattern) and parts of theoretical physics (where some theories have survived very extensive testing). However, one cannot usually be very confident in, say, long-term economic projections. The moral is that in applying mathematics to problems from the "real" world, one must judiciously temper the use of mathematical knowledge and techniques with empirical knowledge and testing.

With increasing interaction between mathematics and the natural sciences, plus the practical problems involved in finding and checking really long proofs, it is arguable that the grey areas are expanding. It has even been argued that proof and certainty in mathematics are nearly obsolete [4], though most of those who agree that "empirical" mathematics has a place still believe that proofs have an important role (e.g. [2] and [7]). It is my belief that proofs will remain central for a good while yet.

(1) Which is convenient for mathematicians when grant money is distributed, so don't show this essay to any funding agency!

(2) The problem of showing that mathematics is not a social science is left as an exercise for the reader. One could argue that mathematics ought to be classified with the arts and humanities [3], but it doesn't function like one [6]. There is also the argument that mathematics is "not really accessible enough to be an art and not immediately useful enough to be a science" [1], but this assumes that art is accessible and science is useful.

(3) As for non-mathematical reality, who cares?

(4) Of course, this begs the question of just what constitutes such a chain of reasoning. Philosophers really worry about this, but most mathematicians settle for giving arguments acceptable to most other mathematicians. History suggests that it is a mistake to be too rigid about correctness in mathematics: it took over two centuries, for example, to work out rigorous foundations for calculus.

(5) This assertion is called Goldbach's Conjecture. A prime number is an integer greater than one which is not a product of two smaller positive integers.

(6) If you do either, please publish!

(7) What of the others present in the common room?
The chemist [5] observes that the periodic table gives the answer: 3 is lithium, 5 is boron, 7 is nitrogen, 9 is fluorine, 11 is sodium, ... Since elements are indivisible -- nuclear fission being uncommon in chemistry labs --- these are all prime. (The same is true for even numbers!).

The economist notes that 3 is prime, 5 is prime, 7 is prime, but 9 isn't prime, and exclaims, "Look! The prime rate is dropping!"

The computer scientist goes off to write a program to check all the odd numbers. Its output reads: 3 is prime. 3 is prime. 3 is prime. ...

The sociologist argues that one shouldn't refer to numbers as odd because they might be offended or as prime because the term implies favouritism, and the theologian concurs since all numbers must be equal before God.


(8) If you're still wondering whether it's true, you haven't paid careful attention. (7)

(9) Until subsequent investigation confirms that 9 = 3*3, anyway.

References

Robert Ainsley, Bluff Your Way In Math, Centennial Press, Lincoln, Nebraska, 1990.
Keith Devlin, The Death of Proof?, Notices of the American Mathematical Society 40 (1993), p. 1352.
JoAnne S. Growney, Are Mathematics and Poetry Fundamentally Similar?, American Mathematical Monthly 99 (1992), p. 131.
John Horgan, The Death of Proof, Scientific American 269 (1993), pp. 92-103.
Hans H. Limbach, personal communication (1994).
Kenneth O. May and Poul Anderson, An Interesting Isomorphism, American Mathematical Monthly 70 (1963), pp. 319-322.
Doron Zeilberger, Theorems for a Price: Tomorrow's Semi-Rigorous Mathematical Culture, Notices of the American Mathematical Society 40 (1993), pp. 978-981.
Stefan Bilaniuk's Home Page
Department of Mathematics
Trent University

Definition of Mathematics from Wikipedia:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns,[2][3] formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.[4]

Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics continued to develop, for example in China in 300 BC, in India in AD 100, and in the Muslim world in AD 800, until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.[5]

There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions".[6] Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[7]

Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered.[8]

Source of article:

Wikipedia

This is the one book in my to-read pile that I found in the math section of the bookstore. That is not a section I peruse with any regularity as my math/science comprehension is, well, less well developed than other parts of my brain. It deals with randomness, which is math related. Likely my only contribution to this thread but I am quite interested to see if others have read it or what they have to say about it. And I fully intend to read it, some day.

by Leonard Mlodinow
An intriguing and illuminating look at how randomness, chance, and probability affect our daily lives.

Successes and failures in life are often attributed to clear causes, when actually they are profoundly influenced by randomness and chance. Here, with the sense of narrative and imaginative approach of a storyteller, Leonard Mlodinow vividly demonstrates how wine ratings, corporate success, school grades, and political polls are less reliable than we believe. Showing us the true nature of chance and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow provides the tools we need for more informed decision making. From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's insights will intrigue, awe, and inspire

Thank you Alisa for the add.

I'm trying to think if there are any historical fiction books centered on mathematics. Drawing a blank so far. Maybe I'll have to write one myself. How about a mystery where the detective is a famous mathematician?

Oh, how about a series of books, each with an alliterative name, each based on a different mathematician? Such as Pascal's Puzzle, and Euclid's Enigma, and Plato's Poser. Okay, now I thought of the titles, someone else has to write the mysteries. :)

I think you have stumbled on a great idea Elizabeth S (smile)

Here's one on my to-read list:

by Luetta Reimer

From the goodreads description:

"Volume Two dramatizes the lives of Omar Khayyam, Albert Einstein, Ada Lovelace, and others. Stories in Volume One focus on moments of mathematical discovery experienced by Thales, Pythagoras, Hypatia, Galileo, Pascal, Germain, and still others. 15 illustrated vignettes per book introduce students to great mathematicians from various cultures."

Fermat's last theorem is one of the most famous mathematical puzzles in history. From wikipedia:

In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. This theorem was first conjectured by Pierre de Fermat in 1637, famously in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. No successful proof was published until 1995 despite the efforts of many mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th. It is among the most famous theorems in the history of mathematics and prior to its 1995 proof was in the Guinness Book of World Records for "most difficult math problem".
See:

I've read
by Amir D. Aczel
which did a nice job describing the history of the theorem, from Fermat's conjecture to the 1995 solution. I've been told that non-mathematically minded souls can enjoy the history even if they don't understand the math.

Excellent additions Elizabeth S. Thanks for helping out on this thread.

Here are a couple of history of math type books that are on my to-read list. Just sounds so interesting.

& by Carl B. Boyer

Can't forget:

by Sylvia Nasar

Publisher's Weekly:
Nasar has written a notable biography of mathematical genius John Forbes Nash (b. 1928), a founder of game theory, a RAND Cold War strategist and winner of a 1994 Nobel Prize in economics. She charts his plunge into paranoid schizophrenia beginning at age 30 and his spontaneous recovery in the early 1990s after decades of torment. He attributes his remission to will power; he stopped taking antipsychotic drugs in 1970 but underwent a half-dozen involuntary hospitalizations. Born in West Virginia, the flamboyant mathematical wizard rubbed elbows at Princeton and MIT with Einstein, John von Neumann and Norbert Wiener. He compartmentalized his secret personal life, shows Nasar, hiding his homosexual affairs with colleagues from his mistress, a nurse who bore him a son out of wedlock, while he also courted Alicia Larde, an MIT physics student whom he married in 1957. Their son, John, born in 1959, became a mathematician and suffers from episodic schizophrenia. Alicia divorced Nash in 1963, but they began living together again as a couple around 1970. Today Nash, whose mathematical contributions span cosmology, geometry, computer architecture and international trade, devotes himself to caring for his son. Nasar, an economics correspondent for the New York Times, is equally adept at probing the puzzle of schizophrenia and giving a nontechnical context for Nash's mathematical and scientific ideas.
Copyright 1998 Reed Business Information, Inc

Excellent

Edwin Abbott Abbott

This is such a charming story you hardly know you're being asked to think about the nature of reality. In it you are introduced to a place where the inhabitants only exist in two dimensions and you find out what happens when they encounter beings with three dimensions.

A related book is Dionijs Burger (no photo). I don't remember if I read this, although I do own a copy.

Thank you so much Vicki for the add and personal write-up and recommendation.

Vicki, I also love and recommend Flatland. It is such a short little tale that helps expand the reader's mind for examining the world without some of the assumptions so basic we never think about them. (Assumptions such as 3 spacial dimensions.)

by Edwin Abbott Abbott

Because I liked Flatland so much, I grabbed a copy of a book called Flatterland. I knew it had a different author, but I figured anyone who enjoyed Flatland enough to build on it would probably write a good book. Flatterland is not nearly as good. Rather than focusing on the basics and teaching your mind to ignore assumptions, it focuses on cutting-edge physics. Now, that is cool stuff, but it isn't timeless, which is part of the magic of Flatland. So it is a good book for 2001 physics, but adding the Flatland twist didn't make it a great book.

by Ian Stewart

I'm curious if Sphereland did a better job.

by Dionijs Burger

by Apostolos Doxiadis
is a very interesting look at how mathematicians and logicians/philosophers, principally Bertrand Russell, were looking at the foundations of math in the early 20th century. It's in the form of a comic book which makes it the opposite of dry and boring.

Another good book by Doxiadis is the novel . I'm not sure fiction belongs in this thread, but you do learn things about math from the book.

Thanks so much Vicki...I did not want folks to miss an opportunity to see your comments about Doxiadis's book.

Apostolos Doxiadis

And you added an additional perk to boot. (smile)

Here's a funny little book about math. Introductory Calculus For Infants (no cover photo) by Omi M. Inouye (no photo). It's in the form of an ABC book for kids, although I wouldn't expect anyone who hadn't taken some high school math, at least, to get it. X isn't a popular letter until he teams up with Friendly F, who shows him how they can be many things together. So we get f(x)=|x|, absolute value, for A, down through the alphabet.

Thanks for adding the recommendation. When there is no book cover it's probably best to add just the link with (no cover photo) noted. I think some covers were lost in their recent data converstion.

Thanks again.

Here's a book on mathematics that sounds like it might be up my severely math-challenged alley.

Å·±¦ÓéÀÖ blurb:

"xn + yn = zn, where n represents 3, 4, 5, ...no solution

"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."

With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

by Simon Singh

Sounds like a great book Bea; thank you for adding. Maybe some of the mathematicians out there can think of a few more that we should not miss.

Oooh, math books. Here are some favorites:

by Paul Lockhart which is simply the best book on mathematics education I have read.

by Gregory J. Chaitin which lets you see a rather brilliant mind at play (in conversation with himself).

by takes us into a math classroom where some fascinating things are being discussed.

One on history of math: by Crosby muses on why the western world made a huge leap forward starting around 1250, and concludes that the reason is quantification. Prior to that time, westerners simply didn't think quantitatively.

Greek mathematician and scientist Archimedes was killed in Sicily in 212BC during the Second Punic War. According to legend Archimedes desired to finish solving a mathematical problem before being taken captive. A Roman warrior then made the decision to kill him with his sword.

Many years later in 75 BC Roman resident Cicero was elected as a Quaestor relegated to Sicily to deal with tax affairs. The folks in Syracuse, Sicily did not know if the grave of Archimedes existed. Cicero was fascinated by the accomplishments of Archimedes and through diligence he located Archimedes grave covered with overgrown brush and thickets.

by Anthony Everitt

Peter,

Please note the proper procedure for posting books by cover, author photo if available and author link.

by Paul Lockhart

by Gregory J. Chaitin

by Imre Lakatos

by Alfred W. Crosby

Here's a couple of math books I've recently read and liked.

by Keith J. Devlin

This was a really interesting book, which cleared up a lot of misconceptions I had about Fibonacci. I had thought his main contribution to math was his series (1, 1, 2, 3, 5, 8, ...), where each new element is the sum of the previous two, and which is found in many places in nature. I had thought he lived in the 17th or 18th century, and that his name was Fibonacci. Actually he lived from around 1170 to 1250, his name was Leonardo Pisano (Leonardo of Pisa) and his real claim to fame was the popularization of the Hindu-Arabic numeral system in medieval Europe. Until his book Liber Abaci (Book of Calculation) became widely circulated, merchants used Roman numerals and abacus-like counting boards to do their calculations. One interesting feature of the book is that the ten chapters are numbered from zero to nine. It's amazing to think how cumbersome simple arithmetic was without zero and using only Roman numerals.

by Paul J. Nahin

I was hoping to really like this book, as it involves my favorite equation, Euler's identity,

e^(i * pi) + 1 = 0.

Such an elegant way to connect the five most important constants in math, along with fundamental mathematical operations. Unfortunately, the understanding of the math involved in the book, which I'm sure I used to have 50 years ago when I got my BA in math, has left me. I had to skip over most of the equations in the book (and there are a lot of them), so I don't even know if I can count this book as "read." But what I was able to read was interesting, especially the early history, where the concept of the square root of minus one helped solve otherwise intractable problems, but the men who figured out the methods were so reluctant to believe in it as a number (hence the designation "imaginary").

If you'd like a much more literary (and somewhat more comprehensible) book on imaginary numbers try by Barry Mazur(no photo)

Thanks, Peter, I'll check it out. You have some really great recommendations.

Following up on Peter's recommendation, here's my review of Imagining Numbers:.

This is an interesting mix of poetry, history, algebra and geometry, leading the reader to appreciate the development of the understanding of i, the square root of minus one. I was particularly struck by the explanation of arithmetical operations (addition, subtraction, multiplication) as manipulations of the real number line. Thus adding 5 to each number shifts the line 5 places to the right (or subtracting shifts it to the left), and multiplying by a positive number causes the number line to expand or contract uniformly, depending on whether the number is larger than one or smaller than one. Next, multiplying by -1 causes the line to flip around 180 degrees. And finally, multiplying by i rotates the line 90 degrees counterclockwise, giving you the complex plane. Once we have this plane, it's easy to visualize addition and multiplication of complex numbers. I've forgotten a lot since studying complex variables 50 years ago, but this book brought a lot of it back.

by Barry Mazur

Journey through Genius: The Great Theorems of Mathematics
by William Dunham
Synopsis
Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve. Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator � from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.

A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

I think history of statistics fits well here. So, here are a few books:

Stephen M. Stigler is a fairly high-level look at mostly 19tj and 20th century statistics. Stigler writes clearly, but this is a book for people with some training in statistics.

James Franklin is about how we thought about chance before we had the math to do it right. Absolutely fascinating and NOT mathematically demanding.

David Salsburg is a book about the ways that statistics changed science in the 20th century. This book is for the general reader and makes no great mathematical demands.

Another book covering similar ground in a different way is Gerd Gigerenzer but this one is intended more for researchers (although it also doesn't make huge mathematical demands.

Yet one more is Theodore M. Porter which covers the period 1820-1900.

Thanks, Peter. The first book needs adjustment:

Stephen M. Stigler

And the last one needs the author link.

Theodore M. Porter

Good additions, thanks Peter.

Thanks Alisa, I fixed them up.

Peter wrote: "Thanks Alisa, I fixed them up."

Much obliged :-)

There's also the golden ratio and zero, which I enjoyed!

Mario Livio

Charles Seife (no photo).

Also read a book on Newton, but I can't recall (It wasn't by James Gleick (sp), didn't read his book on Sir Isaac). gotta dig through my pile of read books!

Excellent, Marc. If you don't have a author photo, don't bother putting it in:

Mario Livio

sorry about that, running on autopilot!

Marc wrote: Also read a book on Newton, but I can't recall (It wasn't by James Gleick (sp), didn't read his book on Sir Isaac). gotta dig through my pile of read books!

Books on Isaac Newton that I've read:

Richard S. Westfall An authoritative and scholarly biography, concentrating on his contributions to physics. Best for those with some math background.

Mordechai Feingold More of a look at how Newton shaped and was shaped by his culture.

Patricia Fara How did Newton, who spent a lot of his life pursuing what would, today, be considered crackpot ideas by nearly all scientists (alchemy, gematria, attempting to find the exact moment of creation through careful reading of Genesis) become the archetype of "genius"?

James Gleick A good "normal" biography, not as mathematically intense as Never at Rest.

and, in fiction (but it's a pretty true rendering of Newton, I think)

and (The Baroque Cycle) all by Neal Stephenson A brilliant but sometimes slow moving and always challenging set of novels that also include other historical characters; most notably for these purposes Leibniz and Hooke, both of whom get too little attention.

Good add and format Kathy.

Euler was the most prolific mathematician of all time. He was so prolific, in fact, that there is a pun on his name about it.

It seems many mathematics graduate students come up with some idea for their dissertation, only to find that Euler already showed that. Thus, Euler's proofs are sometimes known as "Euler's spoilers" (this also shows how to pronounce his name!)

I have read three books that deal with Euler.

by Imre Lakatos uses one of Euler's famous theorems to illustrate the nature of mathematics. It is formatted a discussion among a group of students and a professor in a math class. It is quite accessible.

by William Dunham(no photo) is a much more advanced book, illustrating various of Euler's greatest hits. You better have majored in math to get this one.

by Paul J. Nahin(no photo) is another book about Euler's greatest hits. *Slightly* lower level than Dunham, but you still need some math for it (a year of calculus, perhaps).

Kathy wrote: "April 15th, Leonhard Euler's birthday.
Check out Google's doodle today."

I do not see the link

The link is just Google's home page .

It was the link to the google doodle?

OK if you find the link just add it. Thanks.

Here is a link to the doodle

Terrific doodle thanks.

It does seem interesting. Thanks Kathy.

Kathy wrote: "Love this title!

God Created the Integers

by Stephen Hawking

Bestselling author and physicist Stephen Hawking exp..."

You are right - great title.

Thinking In Numbers: On Life, Love, Meaning, and Math

by Daniel Tammet

Synopsis:

A stunning rumination on math and numbers from the bestselling author of Born on a Blue Day.

THINKING IN NUMBERS is the book that Daniel Tammet, bestselling author and mathematical savant, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives.

Inspired by the complexity of snowflakes, Anne Boleyn's eleven fingers, or his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. THINKING IN NUMBERS will change the way you think about math and fire your imagination to see the world with fresh eyes.