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Science and Method
"Still a joy to read." — Mathematical Gazette This classic by the famous mathematician defines the basic methodology and psychology of scientific discovery, particularly regarding mathematics and mathematical physics. Drawing on examples from many fields, it explains how scientists analyze and choose their working facts, and it explores the nature of experimentation, theory, and the mind. 1914 edition.
304 pages, Paperback
First published January 1, 1908
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1012 people want to read
About the author
Henri Poincaré
462 books175 followersJules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.
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Displaying 1 - 14 of 14 reviews
March 2, 2025
This might be the best thing I’ve ever read about mathematics. The book is relatively short but packed with dense and thought-provoking content. Poincaré takes us from the idea that selecting the right facts is the most crucial task of a scientist to the role of intuition in making those selections. The later chapters become even more interesting, especially when Poincaré delivers his (at times humorous) critique of mathematical formalization. He ultimately provides a deep explanation of how mathematics truly works and why intuition is such a vital part of it.
The final chapters, which discuss mechanics and astronomy, feel somewhat outdated given the advancements in these fields since the book was written.
More I wrote about here
https://hilbert-cantor.medium.com/mat...
The final chapters, which discuss mechanics and astronomy, feel somewhat outdated given the advancements in these fields since the book was written.
More I wrote about here
https://hilbert-cantor.medium.com/mat...
May 11, 2020
Really interesting reflections on what constitutes scientific discovery, how that discovery happens in our minds, and what the place of facts is in that process. I came in with a much stronger background in philosophy of math than physics, so the last section went a bit over my head, but it's still really interesting to see how Poincare ties together these various sciences into a general framework.
Two other things really make this a worthwhile read. First, Poincare is surprisingly sassy. I snorted on numerous occasions while reading, which I certainly didn't expect. Second, it's enthralling to see what the frontiers of science and math were in the early 1900s. Many descriptions that Poincare uses suddenly make more sense to me when I realize that there are certain things we take as fact now that they hadn't yet discovered. Plus, the range of scientists that are working and contributing to the modern understanding we have of math and physics is greater than the classroom-hold names we typically have. It's a good reminder that scientific discovery is the work of many put together, with many names deserving of respect lost to the seas of time.
If you're interested in the philosophy or history of math and science, I would highly recommend a careful read of this text.
Two other things really make this a worthwhile read. First, Poincare is surprisingly sassy. I snorted on numerous occasions while reading, which I certainly didn't expect. Second, it's enthralling to see what the frontiers of science and math were in the early 1900s. Many descriptions that Poincare uses suddenly make more sense to me when I realize that there are certain things we take as fact now that they hadn't yet discovered. Plus, the range of scientists that are working and contributing to the modern understanding we have of math and physics is greater than the classroom-hold names we typically have. It's a good reminder that scientific discovery is the work of many put together, with many names deserving of respect lost to the seas of time.
If you're interested in the philosophy or history of math and science, I would highly recommend a careful read of this text.
December 2, 2014
My interest was in reading the section on creativity. It was interesting to re-read that section after 30+ years of teaching. Poincare was well known for his constructivsm views even though it was early in that approach. It is worth it for you to read.
September 1, 2015
This is an exquisite presentation of the principles of the
scientific method in action. Furthermore, it was written
by one of the masters of the field. You will find this
book extremely readable and understandable.
scientific method in action. Furthermore, it was written
by one of the masters of the field. You will find this
book extremely readable and understandable.
October 15, 2015
The first two chapters seem the most valuable of all.
April 28, 2026
[I've only read Part II, Ch. II: Mathematical Definitions and Education]. I'd heard a quote from the book that spoke to me at a time when I'm being asked to prepare a teaching statement as a novice in math education. I read the whole chapter and picked out a number of quotes (ok in hindsight the number is 5) that I'll be returning to reflect on as I continue to develop my personal teaching philosophy!
The chief aim of mathematics teaching is to develop certain faculties of the mind, and among these intuition is by no means the least precious.
What good is it to admire the mason’s work in the edifices erected by great architects, if we cannot understand the general plan of the master? Now pure logic cannot give us this view of the whole; it is to intuition we must look for it.
Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end.
Whenever it is possible, the justification will precede the statement and prepare it.
The aim of each part of the statement of a definition is to distinguish the object to be defined from a class of other neighbouring objects. The definition will not be understood until you have shown not only the object defined, but the neighbouring objects from which it has to be distinguished, until you have made it possible to grasp the difference, and have added explicitly your reason for saying this or that in stating the definition.
October 12, 2025
Poincaré’s Science and Method is simply brilliant—beautifully written, clear, and full of insight. It reads so smoothly that I’d genuinely recommend it to every researcher. I just finished the first part and felt truly stirred. Here are my two main takeaways:
1. Research taste is important.
Not only in mathematics or physics—every discipline requires a sense of aesthetic judgment in research. Knowing how to select facts or problems that have the potential to lead to interesting results is a crucial part of a researcher’s intuition and capability. Poincaré said, “Inventer, c'est discerner, c'est choisir.” I feel that many studies, for various reasons, start by addressing questions that are unclear or unnecessary. Without intuition for selecting meaningful data, they end up going further down unproductive or tedious paths.
2. Simplicity guides theoretical choice.
Science is often seen as advancing through the interplay between theory and empirical study. Poincaré believed that we tend to choose simpler theories to interpret reality—not because reality itself is simple, but because, pragmatically, the human mind prefers such choices. We gravitate toward theories that are easier to understand and reproduce, ones that help us build order out of chaos (though nature itself may possess a deeper order). Poincaré thought that it is precisely this human tendency toward simplicity and intelligibility that allows science to progress.
1. Research taste is important.
Not only in mathematics or physics—every discipline requires a sense of aesthetic judgment in research. Knowing how to select facts or problems that have the potential to lead to interesting results is a crucial part of a researcher’s intuition and capability. Poincaré said, “Inventer, c'est discerner, c'est choisir.” I feel that many studies, for various reasons, start by addressing questions that are unclear or unnecessary. Without intuition for selecting meaningful data, they end up going further down unproductive or tedious paths.
2. Simplicity guides theoretical choice.
Science is often seen as advancing through the interplay between theory and empirical study. Poincaré believed that we tend to choose simpler theories to interpret reality—not because reality itself is simple, but because, pragmatically, the human mind prefers such choices. We gravitate toward theories that are easier to understand and reproduce, ones that help us build order out of chaos (though nature itself may possess a deeper order). Poincaré thought that it is precisely this human tendency toward simplicity and intelligibility that allows science to progress.
This entire review has been hidden because of spoilers.
July 23, 2021
Human hardware is extremely limited, and we must be aware of this in order to expand our scientific knowledge above our current high levels of complexity.
How do we make mathematical invention and then innovation?
The first mathematics were discovered through pure intuition, that is from our knowledge imprinted in our genes, that has been learned by nature when our ancestors needed to count if there is one or two mammoths.
But now, we must use empiricism to expand our mathematical knowledge, though, it is unlikely that our hardware is able to unlock the chest containing the future of knowledge, and only artificial intelligence can give us the key.
How do we make physical invention and then innovation?
Physical invention seems to have always been using more empiricism than mathematics, somehow.
Can we know the truth?
No, under our very limited hardware, everything lies in the law of probabilities.
Is there such a thing as absolute space, or everything is relative?
It seems that we are pretty sure now that the world is relative.
Can we expand mathematics through pure logic?
Bertrand Russell has tried hard to prove this, without success according to Poincare?
Poincare goes from philosophy, to logic, to mathematic, to physic, to other sciences.
How do we make mathematical invention and then innovation?
The first mathematics were discovered through pure intuition, that is from our knowledge imprinted in our genes, that has been learned by nature when our ancestors needed to count if there is one or two mammoths.
But now, we must use empiricism to expand our mathematical knowledge, though, it is unlikely that our hardware is able to unlock the chest containing the future of knowledge, and only artificial intelligence can give us the key.
How do we make physical invention and then innovation?
Physical invention seems to have always been using more empiricism than mathematics, somehow.
Can we know the truth?
No, under our very limited hardware, everything lies in the law of probabilities.
Is there such a thing as absolute space, or everything is relative?
It seems that we are pretty sure now that the world is relative.
Can we expand mathematics through pure logic?
Bertrand Russell has tried hard to prove this, without success according to Poincare?
Poincare goes from philosophy, to logic, to mathematic, to physic, to other sciences.
January 14, 2021
Nowadays there's no book that I love in book stores.
Carl Sagan , Steven hawking etc were just Science lover. They just believed Science but (I don't know why) they seems like a person who hate God. They had so much angers in religion.
But emotions like that blind their eyes. It was just boring and I could guess what they will say. so I was tired of Science books.
But this book changed my view to Science and Math. He showed how Science works work. Also he showed how Mathematics works work. It was so fascinating!!!
(Spoiler)
He tells about beauty of mathematics. Simplicity and saving energy. Inventions of 9x9 table. It surely saved energy to count all stones.
And he tells human is a animal. Although we use letters, we can't see whole process at one time. If!!! We don't have new term of that.
For example, a graph is getting closer to x. It's hard to understand ...but with practice, we can understand this with a word "convergence"
He emphasized on importance of term. It has more brilliant ideas
Carl Sagan , Steven hawking etc were just Science lover. They just believed Science but (I don't know why) they seems like a person who hate God. They had so much angers in religion.
But emotions like that blind their eyes. It was just boring and I could guess what they will say. so I was tired of Science books.
But this book changed my view to Science and Math. He showed how Science works work. Also he showed how Mathematics works work. It was so fascinating!!!
(Spoiler)
He tells about beauty of mathematics. Simplicity and saving energy. Inventions of 9x9 table. It surely saved energy to count all stones.
And he tells human is a animal. Although we use letters, we can't see whole process at one time. If!!! We don't have new term of that.
For example, a graph is getting closer to x. It's hard to understand ...but with practice, we can understand this with a word "convergence"
He emphasized on importance of term. It has more brilliant ideas
February 1, 2026
Es un libro viejo pero de verdad valioso. Creo que la aproximación más intuitiva que Poincaré tiene sobre las matemáticas es más que necesaria en las ciencias exactas porque es la que de verdad nos hace apreciar su dimensión estética. Con este y varios otros, toca temas que me llaman sobre filosofía de las ciencias y enseñanza de las mismas. El apartado de física se ve desactualizado, claramente, pero aún así es lindo ver cómo se percibía el nacimiento de la física moderna, también cómo se interpretaban los choques que existían entre los viejos modelos del mundo y los nuevos fenómenos que veían. Es, de nuevo, bonito leerlos ahora y compararlos con lo que sabemos, sea mucha o poca la diferencia entre las respuestas.
March 12, 2019
First bit is great, last bit is good, middle part is confusing.
March 21, 2024
If you are interested in hearing a discussion of this book on my podcast, you can check it out here:
https://www.buzzsprout.com/2132180/14...
https://www.buzzsprout.com/2132180/14...
July 28, 2019
As some other said, the first part is great - great insights on the thinking process; the middle is confusing - kind of too attached to contemporary arguments; the last part is good - you can feel the heat of one of the greatest revolutionary eras in natural science and mathematics. However, the language is somewhat old and cryptic, you need time to get used to it. 5 star for the first part alone.
November 30, 2016
I will have to re-read this to appreciate it fully. Good work.
Displaying 1 - 14 of 14 reviews