Science and Method

by Henri Poincaré, Amit Hagar (Introduction)

"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.

Genres: Science, Philosophy, Nonfiction, Mathematics, Classics, Physics, France

304 pages, Paperback

First published January 1, 1908

About the author

Jules 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.

Reviews

[rohola zandie · Rating 5 out of 5]

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The final chapters, which discuss mechanics and astronomy, feel somewhat outdated given the advancements in these fields since the book was written.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...

[Kevin Hu · Rating 4 out of 5]

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.

[Steve · Rating 4 out of 5]

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.

[Marco Bitetto · Rating 5 out of 5]

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.

[Kim · Rating 4 out of 5]

The first two chapters seem the most valuable of all.

[louis · Rating 5 out of 5]

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.

[NoWillNoWord · Rating 5 out of 5]

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

[Hind · Rating 4 out of 5]

First bit is great, last bit is good, middle part is confusing.

[Alex · Rating 5 out of 5]

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...

[THN · Rating 5 out of 5]

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.

[Jayant · Rating 3 out of 5]

I will have to re-read this to appreciate it fully. Good work.