How to Free Your Inner Mathematician

Susan D'Agostino is a mathematician and writer whose essays have been published in Quanta Magazine, Scientific American, Financial Times, Nature, Undark, Times Higher Education, Chronicle of Higher Education, Math Horizons, Mathematics Teacher, and others. 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. Her website is www.susandagostino.com and her Twitter handle is @susan_dagostino.

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