Book review of international book "What is Mathematics Really" which is wriiten by Rubean Hersh(born1927) is an American mathematician and academic,best known for his writing on the nature ,practice and social phenomena of mathematics.This book fully describes humanism philosophy which see mathematics as human creation,human activities,human product and culture.

1. Prepared by
Puja Tiwari
7328419
Lesson Plan – 3 Slide
Presentation
Date : 2076 – 5 -15
What is Mathematics Really ?

3.  Title : What is Mathematics Really ?
 Author : Reuben Hersh
 Genre : Programmetic (Philosiphical,Logical) and
Historical
 Divided into two parts : Part I and Part II (Part
I,Chapter 1 through 5 is Programmetic and
PartII,chapter 6 through 12 is Historical )
 Publisher's Name : Oxford University Press, New
York
 Year of Publication : 1997
 contains : 368 pages
 ISBN Number : 0 – 19 – 511368 -3
 Reviewer's Name : Puja Tiwari ( M.ed. fourth
semester student of Tribhuvan University )

4. Contents :
Chapter Chapter Name Page
no.
1. Survey and Praposals 3 –
23
2. Criteria for Philosophy of Mathematics 24 -
34
3. Myths,Mistakes and Misunderstanding 35 -
47
4. Intution,Proof and Certainity 48 -
71
5. Five Classical Puzzles 72 -
90
6. Mainstream before the Crisis 91 -
118
7. Mainstream Philosophy of its peaks 119
- 136
8. Mainstream Since the crisis 136
- 164
9. Foundationism dies Mainstream lives 165

5. Conti …..
Chapter Chapter's Name
Page no.
12. Contemporary Humanities and Mavricks
220 -234
13. Mathematics is a form of Life
235 - 248
 Mathematical Notes and Comments
249 –316
 Bibilography ( Refrences )
317 – 334
 Index

6. Introduction of The Book
Purpose of the book :
• To provide knowledge about Survey and Proposals.
• To make readers familiar with criteria for Philosophy of
Mathematics .
• To provide knowledge about Myths Mistakes
Misunderstanding.
• To provide knowledge about intitution,proof and certainity.
• To make readers familiar with five classical Puzzles.
• To provide brief knowledge about Mainstream of
Mathematics.
• To make readers familiar with different forms of humanities
and mavricks.
• To acquint the readers how mathematics is form of life.
• To make readers familiar with some mathematical notes and
comments.

7. Authors Background
Source : Online
Reuben Hersh (born1927)is an American
mathematician and academic ,best known for
his writing on the nature ,practice and social
phenomena of mathematics .This work
challenges and complements mainstream
philosophy of mathematics. Reuben Hersh
taught at several distinguished collages and
universities around the country .Now retired ,
he resides in Santa Fe , New Mexico.

8. Summary of the book
 Focus on Humanist Philosophy.
 Focus on how to take survey and write
Praposals.
 Focus on Philosophy of Mathematics.
 Focus on mainstream of Mathematics.
 Focus on Mainstream philosophy of
Mathematics.
 Focus on modern Humanities and Mavricks of
old.
 Focus on how Mathematics is form of life.
 Focus on history of Mathematics.
 Focus on different Mathematical Notes.

9. Analysis and Examing of the
book
 This book fully describes humanism philosophy. The
Philosophy which see Mathematics as a human creation,
human activity, a product, and a characteristics of human
culture and society is known as humanism philosophy.
 The idea of mathematics is human creation has been
advocated many times by Aristotle, by the empiricists John
Locke, David Hume, and John staurt Mill, and many others.
 This book presents genuine philosophy of Mathematics
such as absolutist,falliblist and platonist .
 This book prominently describes mainstream of
mathematics which includes analysis, algebra, number
theory and geometry.
 Gottlab Fredge is grandpa of mainstream in mathematics.
 Fredge introduce quantifier ,philosophy of arithmetic and
philosophy of geometry.He is first full timer philosopher of
mathematics.

10. This book :
 describes about set theory which is developed by
george cantor, empty set, operation of set,logicist,
tutology.
 report briefly on structuralism and functionalism.
 desribes brifly symbolic logic and symbolic language.
 sway analytic philosophy.
 includes most important mathematical notes and
comments such as
- Fourier series,
derivative,calculas,quaternion,infinite series, Gibb's
vector , concept of real and complex number, two
Bizzarres curves,The four colour theorem and Non-
Euclidean Geometry, rotation group, and how Real
numbers are uncountable e.t.c.

11. Overview and evaluation of the
book
This book is useful for philosophical ideas,
mainstream of mathematics, symbolic logic
,survey, proposals and puzzles but doesn't
describe historical hummanist approach. This
book doesn't attack effectively the great
problem philosophy of Mathematics. In this
book, Hersh doesn't tell more about
mechanism by which human can interact the
world.

12. Conclusion
I think this book is very valuable for its sketch of a
number philosophical ideas relating to Mathematics
and its introduction to Hersh's humanist philosophy
of Mathematics. As a constructivist, I disappointed
that Hersh says so little about intution and proof. As
major criticism, Hersh makes use of Platonism. He
point out that it posits an idea world independent of
human thought or activities. This book contains
some carelessness that the preface claims there is a
discussion of teaching in chapter 1 but I couldn't
find it .The stunning paoint of this book is symbolic
logic which is vitally useful in designing and
programming digital computers.This presents
genuine trends of philosophy such as absolutist,
fallibilist,platonist,philosophy of arithmetic and
geometry. The key part of this book is humanist
philosophy and mainstream of mathematics.

13. Overall, I conclude this book is a graet book in
the field of mathematics education and also
most essential for Mathematician,
Mathematics educators, Mathematics learners
and all who loves mathematics to know "how
mathematics is form of life?,what is
mathematics really? and what is the history of
Mathematics?". So, I highly recommended it
to read rigorously to enjoy the beauty of
Mathematics Education.

14. THANK
YOU