Explore the beauty of mathematics

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As a PeakMath member, you get

  • Rich course notes for the RH Saga

  • Collaborative research projects in number theory

  • An interactive model of the mathematical landscape

  • Q&A forum for all things math-related

  • A friendly community with a passion for mathematics

Please note: We are about to sunset the community. You can still join and explore all of the above, but only for a short period of time. We will redesign our approach and hope to keep sharing our love for math in new ways.

Free for the first two weeks, then 15 USD/month.

Our Projects

  • A first sketch of the landscape of mathematics. The aim is to explore mathematical concepts not in isolation, but as nodes in a rich web of connections and interrelationships.

    The PeakMath Landscape

    Using the zbMATH database and many other sources, we are building an interactive digital model of the mathematical landscape. This is the starting point of our vision for a deeper, broader and more holistic math education.

    The beginning of this project consists of an informal tour of the landscape, in which you will get a unique overview or “map” of mathematics as a whole.

    Join now to follow the tour and see the landscape prototype.

    Read more
  • The zeroes of the Riemann zeta function give rise to the prime numbers via these mysterious cosine waves.

    The Quest for F1

    There are many clues spread throughout the literature and mathematical folklore, that point towards a possible new geometry underlying the theory of L-functions. The Quest for F1 is a longterm research project aiming to collect all of these clues and synthesize them into a new theoretical framework.

    The beginning of this project is the RH Saga, an introductory course on L-functions, with videos, course notes and interactive Sage code.

    Join now to see the latest Episodes not yet available on YouTube.

    Read more

A community and a different kind of learning experience

The PeakMath community is centered around the dreams of building a digital model of the entire mathematical landscape, and to search this landscape for clues for a new geometry of L-functions. Each step of the journey will be shared with you in two parallel projects.

The Landscape project offers a roadmap to all of math and a unique perspective on mathematics as a whole.

The F1 project (which includes the RH Saga) will give you an accessible introduction to some of the deepest math problems of all time, and ample opportunity to engage with difficult and interesting problems (including many unsolved research problems in number theory).

  • My approach to research consists in looking to the mathematical landscape […]. If you see a bridge across a river, you try to imagine what lies on the other shore. If you see a mountain pass between two high mountains, you try to imagine what is in the valley you don’t see yet but secretly know must be there.

    Enrico Bombieri

  • My style is mostly original. I loved to attack problems which seemed out of reach. You then have to build everything from scratch. It is like exploring a new continent. A feeling of wilderness.

    Yves Meyer

  • Thurston did not succeed in proving the conjecture, but he did show that if it were true, it would form part of an extraordinary mathematical landscape with all sorts of features no one had ever dreamed possible.

    Cedric Villani

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 FAQs

  • The Landscape project requires no specific background beyond a deep interest in mathematics. The RH Saga is aimed at anyone already familiar with calculus and basic number theory. The wider Quest for F1 is a more advanced research project, but we will help out with Sage code and answer all questions along the way as best we can.

  • Legend of Ishango was our earlier working name for the PeakMath Landscape. So not much has changed, just the name!

  • The theory of L-functions is at the centre of the deepest mysteries of pure mathematics. The Riemann Hypothesis, the Birch and Swinnerton-Dyer Conjecture, and Langlands reciprocity are all expressed in terms of L-functions, and they are intimately connected to many other deep mathematical themes, like the Hodge Conjecture and amplitudes in quantum field theory.

    There are many introductory YouTube videos about the Riemann zeta function, but in the RH Saga you will get a much more thorough introduction to the general theory of L-functions and the computational tools needed to explore the great conjectures on your own. And together we hope to eventually discover something that lies beyond the current frontier of research.

  • Research on mathematical cognition indicates that the human brain almost invariably perceives the world of mathematics as a landscape, i.e. as an arena for exploration, expanding horizons and gathering of new information.

    We believe that landscape exploration is the best metaphor for supporting deep and accelerated math learning, and that the time has come for the creation of a digital realm in which such learning can take place.

  • We are radically committed to equal educational opportunity for all. If for whatever reason it is impossible for you to pay for PeakMath membership, send us a message here and we will set up a longterm free trial.

    (Also, if you want to support this model of online math education, you can donate to PeakMath.)

Andrea Langva, CEO of Motivic Labs, creating PeakMath

Our vision

Mathematics is an art form of “breathtaking depth and heartbreaking beauty” (Paul Lockhart). We want to see a future in which everyone has access to a meaningful, inspiring and comprehensive math education.

PeakMath is built on ideas from cognitive science, learning design, the philosophy of mathematical practice, and a deep love for mathematics itself.