Olivia Xu

on the atlas — 10

• Division algebra1 savers
• Brunnian link1 savers
• Ten Lessons I Wish I Had Been Taught6 savers
• A New Consciousness of Mathematics - by Apoorva Panidapu4 savers
• Superfoods: Cultural and Scientific Perspectives | Springer Nature Link1 savers
• The courage to think in an age afraid of meaning1 savers
• Editorial Board | Stanford students would rather not think1 savers
• Future of Work for Women Initiative w/ Dr. Suhani Jalota - Google Search1 savers
• demi.1 savers
• You and Your Research77 savers

highlights — 4

• Later work showed that in fact, any finite-dimensional real division algebra must be of dimension 1, 2, 4, or 8. This was independently proved by Michel Kervaire and John Milnor in 1958, again using techniques of algebraic topology, in particular K-theory.

  Division algebra

• There are a variety of reasons, as we’ve discussed. Some do math for an unequivocal truth (regardless of whether the truth is ascertained by humans or AI), and many do it for the love of the game. I do math for the same reason I paint and write: because it is beautiful, it is difficult, it is joyful, it has made me cry more than once, and because I can find individuality in it, with a sense of precision and rigor.

  A New Consciousness of Mathematics - by Apoorva Panidapu

• Mathematics is many things to many people. Like music, it resists definition…Willard Gibbs thought of mathematics as a language. Hilbert thought of it as a game. For Benjamin Pierce it was “the science that draws necessary conclusions.” Hardy joyfully stressed its uselessness; Hogben stressed its practicality. Mill thought it an empirical science, whereas to Sullivan it was an art, and to the wonderful J.J. Sylvester, it was “the music of reason.”

  A New Consciousness of Mathematics - by Apoorva Panidapu

• Part of the challenge, then, is that we cannot motivate students by giving them only one reason to do mathematics. Its usefulness will work for some, its beauty will convince others. Its precision, its cleverness, its community—there is no universal reason, but there is a reason to be found for every person. If we want students to choose the slower path of understanding over quickly generating answers, we have to give them many ways to find meaning in it, to help them find their reason.

  A New Consciousness of Mathematics - by Apoorva Panidapu