Name: Street-fighting mathematics
ISBN: 9780262514293

Street-fighting mathematics

In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology.

What Hacker News says

poppingtonicJul 2026

Street Fighting Mathematics! Loved taking this Sanjoy Mahajan's course on OCW in high school

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ggr2342May 2023

How to estimate things. That is the best thing in Math I have learnt. It is known as Street Fighting math or Fermi estimation and many other names. One book that is close to my heart is:

Street Fighting Mathematics by Sanjoy Mahajan.

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taericFeb 2023

Ha! Seeing the headline, I was going to say that this is basically the intro to Street Fighting Mathematics. Reading it, I thought I was just having deja vu with how similar the treatment was. Fun book.

I always think of dimensional reduction when I see these headlines, which is sadly very unrelated.

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sriram_malharFeb 2023

The book this blog post is based on -- Sanjoy Mahajan's "Street-fighting Mathematics" -- is a fantastic read. It is a bit like watching cirque du soleil; I don't come away having internalised much because I have no practice thinking that way, but I come away hugely entertained!

https://ocw.mit.edu/courses/18-098-street-fighting-mathemati...

The reading list has a link to both the printed version and a free pdf of the book.

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newsoulFeb 2023

For me it was:

1. Writing out input output relations for a function with quite a few examples before actually starting to write the function. Basically writing tests. It makes you realise what the function is actually supposed to do. I learnt this from How to Design Programs (htdp) book. It was a game changer.

2. Working on Fermi Problems aka Street Fighting Mathematics. I learnt from the books of Sanjoy Mahajan. They made me much better at estimating how the output to some input may be like.

What about you?

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jordibcJan 2023

For sure I got significantly(?) better with classics like Spivak, Apostol, Rudin.

"Real and Complex Analysis" by Rudin, and the two books both named "Calculus" from Spivak and Apostol. But also from Apostol his more concise and far-reaching "Mathematical Analysis". And from Spivak his small gem "Calculus On Manifolds" made quite a dent on me.

Other than more "classic math" books, I also wanted to mention two outliers that I found eye-opening and generally awesome:

* Street-Fighting Mathematics, by Mahajan (http://streetfightingmath.com/). Intuitive, useful and fun.

* Geometric Algebra for Physicists, by Doran and Lasenby. I found the power and elegance of geometric algebra mesmerizing, and even if this book is also about physics and there may be more appropriate math-only books about geometric algebra, this is the one that made it for me.

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