How to Free Your Inner Mathematician: Notes on Mathematics and Life

ISBN : 9780198843597

Susan D'Agostino
352 Pages
129 x 196 mm
Pub date
Mar 2020
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How to Free Your Inner Mathematician: Notes on Mathematics and Life offers readers guidance in managing the fear, freedom, frustration, and joy that often accompany calls to think mathematically. With practical insight and years of award-winning mathematics teaching experience, D'Agostino offers more than 300 hand-drawn sketches alongside accessible descriptions of fractals, symmetry, fuzzy logic, knot theory, Penrose patterns, infinity, the Twin Prime Conjecture, Arrow's Impossibility Theorem, Fermat's Last Theorem, and other intriguing mathematical topics.

Readers are encouraged to embrace change, proceed at their own pace, mix up their routines, resist comparison, have faith, fail more often, look for beauty, exercise their imaginations, and define success for themselves.

Mathematics students and enthusiasts will learn advice for fostering courage on their journey regardless of age or mathematical background. How to Free Your Inner Mathematician delivers not only engaging mathematical content but provides reassurance that mathematical success has more to do with curiosity and drive than innate aptitude.


1 Mix up your routine, as cicadas with prime number cycles

2 Grow in accessible directions, like Voronoi diagrams

3 Rely on your reasoning abilities, because folded paper may reach the moon

4 Define success for yourself, given Arrow's Impossibility Theorem

5 Reach for the stars, just like Katherine Johnson

6 Find the right match, as with binary numbers and computers

7 Act natural, because of Benford's Law

8 Resist comparison, because of chaos theory

9 Look all around, as Archimedes did in life

10 Walk through the problem, as on the Konigsborg bridges

11 Untangle problems, with knot theory

12 Consider all options, as the shortest path between two points is not always straight

13 Look for beauty, because of Fibonacci numbers

14 Divide and conquer, just like Riemann sums in calculus

15 Embrace change, considering non-Euclidean geometry

16 Pursue an easier approach, considering the Pigeonhole Principle

17 Make an educated guess, like Kepler with his Sphere-packing Conjecture

18 Proceed at your own pace, because of terminal velocity

19 Pay attention to details, as Earth is an oblate spheroid

20 Join the community, with Hilbert's 23 problems

21 Search for like-minded math friends, because of the Twin Prime Conjecture

22 Abandon perfectionism, because of the Hairy Ball Theorem

23 Enjoy the pursuit, as Andrew Wiles did with Fermat's Last Theorem

24 Design your own pattern, because of the Penrose Patterns

25 Keep it simple whenever possible, since

26 Change your perspective, with Viviani's Theorem

27 Explore, on a Mobius strip

28 Be contradictory, because of the infinitude of primes

29 Cooperate when possible, because of game theory

30 Consider the less-travelled path, because of the Jordan Curve Theorem

31 Investigate, because of the golden rectangle

32 Be okay with small steps, as the harmonic series grows without bound

33 Work efficiently, like bacteriophages with icosahedral symmetry

34 Find the right balance, as in coding theory

35 Draw a picture, as in proofs without words

36 Incorporate nuance, because of fuzzy logic

37 Be grateful when solutions exist, because of Brouwer's Fixed Point Theorem

38 Update your understanding, with Bayesian statistics

39 Keep an open mind, because imaginary numbers exist

40 Appreciate the process, by taking a random walk

41 Fail more often, just like Albert Einstein did with

42 Get disoriented, on a Klein bottle

43 Go outside your realm of experience, on a hypercube

44 Follow your curiosity, along a space-filling curve

45 Exercise your imagination, with fractional dimensions

46 Proceed with care, because some infinities are larger than others

About the author: 

Susan D'Agostino is a mathematician and writer whose essays have been published in Scientific American, Financial Times, Undark, Ms. magazine, Times Higher Education, Chronicle of Higher Education, Math Horizons, Mathematics Teacher, and other venues. She earned her PhD in Mathematics from Dartmouth College, Master of Arts in Teaching Mathematics from Smith College, and BA in Anthropology from Bard College. She is a Council for the Advancement of Science Writing Taylor/Blakeslee Fellow at Johns Hopkins University and has served as Editor-in-Chief of A Celebration of the EDGE Program's Impact on the Mathematics Community and Beyond

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