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Blueprints: How mathematics shapes creativity
'WHAT TO READ IN 2025' FINANCIAL TIMES
Many artists are unaware of the mathematics that bubble beneath their craft, while some consciously use it for inspiration. Our instincts might tell us that these two subjects are incompatible forces with nothing in common, but what if we’re wrong?
Marcus du Sautoy, acclaimed mathematician and Simonyi Professor for the Public Understanding of Science at the University of Oxford, looks to art, music, design and literature to uncover the key mathematical structures that underpin both human creativity and the natural world.
Blueprints takes us from the earliest stone circles to the modernist architecture of Le Corbusier, from Bach’s circular compositions to Radiohead’s disruptive soundscapes, and from Shakespeare’s hidden numerical clues to the Dada artists who embraced randomness. Instead of polar opposites we find a complementary relationship that spans a vast historical and geographic landscape.
Whether we are searching for meaning in an abstract painting or deciphering poetry, there are blueprints prime numbers, symmetry, fractals and the weirder worlds of Hamiltonian cycles and hyperbolic geometry. Nature similarly exploits these structures to achieve the wonders of our universe.
In this innovative and delightfully bold exploration of creativity, Marcus explains how we make art, why a creative mindset is vital for discovering new mathematics and how a fundamental connection to the natural world intrinsically links these two subjects.
‘Blueprints is an extraordinary book which shows us how mathematics and art are connected through structures. Du Sautoy shows us how to bridge the divide of science and the humanities and proves that we can only face and solve the big challenges of the twenty-first century if we go beyond the fear of pooling knowledge’ Hans Ulrich Obrist, Artistic Director, Serpentine Galleries
Many artists are unaware of the mathematics that bubble beneath their craft, while some consciously use it for inspiration. Our instincts might tell us that these two subjects are incompatible forces with nothing in common, but what if we’re wrong?
Marcus du Sautoy, acclaimed mathematician and Simonyi Professor for the Public Understanding of Science at the University of Oxford, looks to art, music, design and literature to uncover the key mathematical structures that underpin both human creativity and the natural world.
Blueprints takes us from the earliest stone circles to the modernist architecture of Le Corbusier, from Bach’s circular compositions to Radiohead’s disruptive soundscapes, and from Shakespeare’s hidden numerical clues to the Dada artists who embraced randomness. Instead of polar opposites we find a complementary relationship that spans a vast historical and geographic landscape.
Whether we are searching for meaning in an abstract painting or deciphering poetry, there are blueprints prime numbers, symmetry, fractals and the weirder worlds of Hamiltonian cycles and hyperbolic geometry. Nature similarly exploits these structures to achieve the wonders of our universe.
In this innovative and delightfully bold exploration of creativity, Marcus explains how we make art, why a creative mindset is vital for discovering new mathematics and how a fundamental connection to the natural world intrinsically links these two subjects.
‘Blueprints is an extraordinary book which shows us how mathematics and art are connected through structures. Du Sautoy shows us how to bridge the divide of science and the humanities and proves that we can only face and solve the big challenges of the twenty-first century if we go beyond the fear of pooling knowledge’ Hans Ulrich Obrist, Artistic Director, Serpentine Galleries
451 pages, Kindle Edition
First published May 8, 2025
60 people are currently reading
509 people want to read
About the author
Marcus du Sautoy
35 books502 followersMarcus Peter Francis du Sautoy, OBE is the Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.
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Displaying 1 - 7 of 7 reviews
August 17, 2025
As a mathematician by education, I am drawn to anything that revels in the beauty of mathematics, but whilst an admirable effort to link mathematics to the arts, this book often ends up drawing flimsy or niche links rather than showing genuine remarkable parallels or manifestations of mathematics.
Most of the links tend to be some classical composer or musician being “inspired” by some field of maths rather than it organically occurring, and even then you’re unfortunately left feeling a bit ‘meh’ about the outcome. You get the feeling of a lot of the examples being stretched in how mathematically inspired they really are, or feeling that the artist’s enthusiasm, inspiration, or interest in maths is very over-stated.
He’s tried to make a good fist of it, but unless you’re a big fan of some of the more high brow, upper class entertainments and enjoy reading about their origins in often niche (or pretentious) art forms, this book might be best swerved. Naively i had assumed this book would be driven by the maths with the art following, but alas its more of a book about art with some links to maths (directly, often indirectly, and quite often tenuous). Next time I’ll try to make sure my purchase is very on the nose in its mathematical contents rather than being an aside for a less interesting subject.
Most of the links tend to be some classical composer or musician being “inspired” by some field of maths rather than it organically occurring, and even then you’re unfortunately left feeling a bit ‘meh’ about the outcome. You get the feeling of a lot of the examples being stretched in how mathematically inspired they really are, or feeling that the artist’s enthusiasm, inspiration, or interest in maths is very over-stated.
He’s tried to make a good fist of it, but unless you’re a big fan of some of the more high brow, upper class entertainments and enjoy reading about their origins in often niche (or pretentious) art forms, this book might be best swerved. Naively i had assumed this book would be driven by the maths with the art following, but alas its more of a book about art with some links to maths (directly, often indirectly, and quite often tenuous). Next time I’ll try to make sure my purchase is very on the nose in its mathematical contents rather than being an aside for a less interesting subject.
June 29, 2025
Truly impressed by the scope of interests, breadth of knowledge and incredible personality of Marcus du Sautoy. The author artfully connects the mathematical ideas with real world examples and explains them in a very approachable manner, without any pomposity, making it easy to appreciate the scientific discoveries and contemplate their impact. The book wonderfully challenges one’s mathematical thinking but also serves as an enriching guide explaining the ideas behind modern art (previously quite obscure to me) and modern math (similarly hazy despite my degree in Math).
I liked the definition of math as a study of structures, much like architecture and music. A mathematician, a painter and a composer are makers of patterns where the structures / blueprints are physicalised as sound, or paint etc. Art and math are two languages though which we try to understand physical universe we live in.
Umberto Eco noted that the way artistic forms are structured reflects the way, in which science or contemporary culture views reality. For example, XIX century scientific beliefs were grounded on patterns and eternity, while reality of the XX century posited that chaos was the most fundamental force.
However, the difference between art and math is that the former tolerates ambiguity while the latter demands certainty. Mistakenly, some people think the true difference is that math lacks emotional aspect so pronounced in art. In reality, very few artists talk about putting emotions into work seeing them as a consequence of their primary work, for example, music.
What makes math different from other sciences is that it doesn’t have limiting factor that theory has to match the reality of the world. The mathematical world is open for imagination - the invention of complex numbers would be a great example of such.
Overall, a brilliant book offering refreshingly challenging mathematical ideas, insights into the great works of art and secrets of nature, at the same time encouraging deep thinking and mental creativity!
***
Below is the list the artists whose work resonated with me:
Sculptors: Kapoor, Wallinger
Architects: Hadid, Kahn, Buckminster Fuller, Le Corbusier
Painters: Jean Arp, Escher, Pollock, Richter (mosaics for Cologne Cathedral)
Composers: Cage, Xenakis, Philip Glass
Writers: Catton (The Luminaries), Queneau, Borges
Physicist: Paul Dirac (discovery of antimatter)
One new mathematical idea I particularly liked is the difference between random chance, where unpredictability comes from inherent uncertainty (e.g. radioactive particles), and deterministic chaos, which unpredictable nature arises from extreme sensitivity to initial conditions in a system governed by precise rules (e.g. weather systems).
One artistic idea I liked in particular is the fractal like muquarnas, honeycomb type structures in Islamic architecture.
I liked the definition of math as a study of structures, much like architecture and music. A mathematician, a painter and a composer are makers of patterns where the structures / blueprints are physicalised as sound, or paint etc. Art and math are two languages though which we try to understand physical universe we live in.
Umberto Eco noted that the way artistic forms are structured reflects the way, in which science or contemporary culture views reality. For example, XIX century scientific beliefs were grounded on patterns and eternity, while reality of the XX century posited that chaos was the most fundamental force.
However, the difference between art and math is that the former tolerates ambiguity while the latter demands certainty. Mistakenly, some people think the true difference is that math lacks emotional aspect so pronounced in art. In reality, very few artists talk about putting emotions into work seeing them as a consequence of their primary work, for example, music.
What makes math different from other sciences is that it doesn’t have limiting factor that theory has to match the reality of the world. The mathematical world is open for imagination - the invention of complex numbers would be a great example of such.
Overall, a brilliant book offering refreshingly challenging mathematical ideas, insights into the great works of art and secrets of nature, at the same time encouraging deep thinking and mental creativity!
***
Below is the list the artists whose work resonated with me:
Sculptors: Kapoor, Wallinger
Architects: Hadid, Kahn, Buckminster Fuller, Le Corbusier
Painters: Jean Arp, Escher, Pollock, Richter (mosaics for Cologne Cathedral)
Composers: Cage, Xenakis, Philip Glass
Writers: Catton (The Luminaries), Queneau, Borges
Physicist: Paul Dirac (discovery of antimatter)
One new mathematical idea I particularly liked is the difference between random chance, where unpredictability comes from inherent uncertainty (e.g. radioactive particles), and deterministic chaos, which unpredictable nature arises from extreme sensitivity to initial conditions in a system governed by precise rules (e.g. weather systems).
One artistic idea I liked in particular is the fractal like muquarnas, honeycomb type structures in Islamic architecture.
September 5, 2025
Marcus du Sautoy's latest book is about the strong and sometimes unexpected links between mathematics, creativity (art in particular) and nature. I found this a very slow read, not due to any criticism of the book, the subject or the writing but because I was frequently stopping to look interesting facts and pictures up on Google! Platonic solids, the focal point of the Last Supper, the Le Corbusier buildings, the golden ratio, etc.
Sometimes I felt that too little was given on the basics of a topic - a level of mathematical understanding was assumed which occasionally went beyond me (armed only with my 45 year old GCE 'O' level in Maths), and although some diagrams and pictures were included there weren't nearly enough to satisfy my curiosity, or understanding. I didn't get many of the musical references so skimmed over some of these. I did try listening to a couple of the pieces referenced (briefly) but... oh well.
The sections on fractals, Salvador Dali, Fibonacci numbers and Shakespeare were all fascinating. As was anything to do with nature because being a biologist I was on much safer ground. I will confess to messaging a poet friend at 1am to ask if she'd heard of Fibonacci poetry (she hadn't).
In summary I found the book to be interesting but something of a mixed bag - I didn't enjoy the music bits but others will no doubt disagree. And I think those Le Corbusier structures look like 1980s Communist Party HQ buildings. Don't shoot me!
Sometimes I felt that too little was given on the basics of a topic - a level of mathematical understanding was assumed which occasionally went beyond me (armed only with my 45 year old GCE 'O' level in Maths), and although some diagrams and pictures were included there weren't nearly enough to satisfy my curiosity, or understanding. I didn't get many of the musical references so skimmed over some of these. I did try listening to a couple of the pieces referenced (briefly) but... oh well.
The sections on fractals, Salvador Dali, Fibonacci numbers and Shakespeare were all fascinating. As was anything to do with nature because being a biologist I was on much safer ground. I will confess to messaging a poet friend at 1am to ask if she'd heard of Fibonacci poetry (she hadn't).
In summary I found the book to be interesting but something of a mixed bag - I didn't enjoy the music bits but others will no doubt disagree. And I think those Le Corbusier structures look like 1980s Communist Party HQ buildings. Don't shoot me!
July 9, 2025
The premise of this book sounded amazing and it certainly delivered.
Generally mathematics is looked at by the general population as this isolated, incredibly difficult field of study that has some applications to every day life but mostly feels like a bunch of nonsense letters and numbers. Marcus Du Sautoy cleverly rectifies this point of view throughout this book by highlighting how integrated maths is in a variety of fields, from art and music to nature.
This was such a joy to read, highlighting some of my favourite aspects of maths in music and nature whilst opening me up to how maths plays a role in so many more ways, I could hardly put this book down. If you're at all curious about seeing how maths is such a fundamental part of life both biologically and socially, you absolutely need to pick up this book! Marcus explains various mathematical proofs in accessible ways making them easier for the non-mathematician to understand so don't worry about not being able to understand what the book is talking about and give it a go!
Generally mathematics is looked at by the general population as this isolated, incredibly difficult field of study that has some applications to every day life but mostly feels like a bunch of nonsense letters and numbers. Marcus Du Sautoy cleverly rectifies this point of view throughout this book by highlighting how integrated maths is in a variety of fields, from art and music to nature.
This was such a joy to read, highlighting some of my favourite aspects of maths in music and nature whilst opening me up to how maths plays a role in so many more ways, I could hardly put this book down. If you're at all curious about seeing how maths is such a fundamental part of life both biologically and socially, you absolutely need to pick up this book! Marcus explains various mathematical proofs in accessible ways making them easier for the non-mathematician to understand so don't worry about not being able to understand what the book is talking about and give it a go!
March 11, 2025
This is a book about mathematics. It's a book about art. It's a book about nature. And it's a book about the connections between all three. It may seem like art and mathematics in particular are very different in terms of inspiration, practice, and outlook, but Marcus du Sautoy argues that they're not different all--in fact, they come from the same place. Maths provides the structures, which he calls 'blueprints' and art provides the expression of those structures. This book sets out to explain his ideas. He states, "In this book, I want to explore some of the most fundamental mathematical structures that underpin human creativity." (p2) He goes on to say that these same structures can be found in nature: "It's as if human creativity and mathematical discovery are two languages with which to navigate and understand the physical universe we live in." (p2) He likens art, maths, and nature to three points on a triangle and sets out to describe the connections he sees between these three points. He refutes the idea that art alone deals with emotion, arguing that emotion is very evident in mathematics and that mathematicians are actually storytellers whose characters are numbers and geometries. The stories he's telling in this book are structured on his blueprints, which are: prime numbers, circles, Fibonacci numbers, golden ratio, fractals, Platonic solids, symmetry, hyperbolic geometry, and randomness. In the end, du Sautoy muses that perhaps art and mathematics has an edge over nature because they can go "beyond what nature allows." Nature is "real," art doesn't have to be, and mathematics is abstract and can "live in the mind." (p 330)
The book was fascinating and provided much to consider. I do think I might have gotten more out of it if I was someone with a background in mathematics, musical composition, or both. The author is a mathematician, a musician and a writer, and has worked in collaboration with various others from these fields. I am neither of the first two and I did get bogged down at times with the equations and long discussions about how music is composed. Much of this was meaningless to me, to be honest. This didn't prevent me from enjoying the book or from learning new things; it's simply that I would have understood more and in a different way if I had more knowledge about those disciplines and practices. However, in his discussions of art practice, he doesn't limit himself to composition alone, so whether you're a maths nerd or not and whether you are into the way music is composed or not, there's much here to think about and enjoy.
Thanks to NetGalley, the publisher, and the author for a DRC.
The book was fascinating and provided much to consider. I do think I might have gotten more out of it if I was someone with a background in mathematics, musical composition, or both. The author is a mathematician, a musician and a writer, and has worked in collaboration with various others from these fields. I am neither of the first two and I did get bogged down at times with the equations and long discussions about how music is composed. Much of this was meaningless to me, to be honest. This didn't prevent me from enjoying the book or from learning new things; it's simply that I would have understood more and in a different way if I had more knowledge about those disciplines and practices. However, in his discussions of art practice, he doesn't limit himself to composition alone, so whether you're a maths nerd or not and whether you are into the way music is composed or not, there's much here to think about and enjoy.
Thanks to NetGalley, the publisher, and the author for a DRC.
November 12, 2025
Blueprints is a tour de force linking mathematics to the creativity of music, art, architecture and writing. The author is able to make connections between Euclidean and non Euclidean math to the creativity of so many musicians, artists, writers and architects. I found his chapter on Zaha Hadid and her creative process particularly special.
June 19, 2025
Mathematics Neil deGrasse Tyson strikes again
Displaying 1 - 7 of 7 reviews