AMMOC is an international mathematical circle devoted to the identification, cultivation, and sustained advancement of early scientific and mathematical talent. Its programme is systematic and rigorous, and the reading of classics stands within it beside olympiad mathematics (IMO) and undergraduate mathematics as an essential component rather than an ornament. The vision of AMMOC is to form mathematicians in the manner of the circles of the USSR and of the other nations of Eastern Europe. Its mission follows from that vision: to teach elementary mathematics from the advanced standpoint — the standpoint central to the IMO — together with undergraduate subjects such as abstract algebra, geometry and topology, and mathematical analysis, to a select group of pre-college pupils.

These commitments are set out below under five heads.

• A-Attraction and Preparation of Pre-College Pupils.

  AMMOC seeks out pupils in grades VII–X and grounds them in proof-theoretic mathematics and the discipline of problem solving, with the object of refining their proof-writing and bringing them to scientific maturity — while preserving throughout the pleasure that ought to attend such work.

  The rationale is historical. When one considers the scientific contributions of the mathematicians and scientists trained in the Eastern European circles of the twentieth century, what is most striking is the mathematical maturity these figures had already attained before they entered a university. AMMOC aims at an education of the same order: one that extends a pupil’s command of several branches of mathematics and of their application in problem solving. In this we share the conviction of our heroes, Vladimir Arnold and Jerrold E. Marsden, that instruction of this kind, offered early, initiates a lifelong attachment to the joy of discovery and to critical thought. AMMOC is one instance of how so noble a cultivation of future scientists and academicians may be undertaken.

• M-Mathematics as Both Sprint and Marathon.

  At AMMOC, mathematics is pursued at once as a sprint, through the IMO curriculum, and as a marathon, through the early study of the undergraduate curriculum.

  Within this scheme, preparing and mentoring our circlers — as participants are known — for the principal competitions serves as a dependable barometer of their growing command of the arts and crafts of mathematical thinking: the Princeton University Mathematics Competition, the Caltech Math Meet, the Berkeley Math Tournament, the Stanford Math Tournament, the IMO, EGMO, AMC/AIME/USAMO, COMC, and the contests of the CEMC.

  Distinction in these contests carries a second value. In the most formative of academic years, it confirms for a pupil that sustained effort is answered, and so multiplies the faith upon which further effort depends. Our own emphasis remains upon education as an intellectual art and a cognitive necessity; yet even for a pursuit so conceived, contests furnish a stage upon which talent may be shown and an identity earned. The cultivation of these early scholarly habits and academic ambitions has allowed us to prepare and, in time, to form young protégés and aspiring mathematicians: Tisya Chandrashekhar Rawat, Konstantinos Charalampous, Adelina Patlatii, and Sarthak Dattatray Dhobale.

  These four fellows of the inaugural class of 2020–23, together with the instructor of our programme, Yaashaa P. Golovanov, remain a standing example to the present participants of the scholarly trajectory that is possible. The same record has assisted pupils of AMMOC in gaining admission to Cornell, UC Berkeley, Carnegie Mellon, Georgia Tech, Purdue, UIUC, Wisconsin–Madison, Waterloo, Reed College, Imperial College London, Columbia, Stony Brook, and the City University of New York.

• M-Mentorship Toward a Life in Research.

  We mentor our protégés toward careers as research mathematicians through guided early-career research and directed reading programmes.

  Each year the senior pupils write expository theses drawn from readings in the core and elective courses in pure mathematics offered to undergraduate and master’s students at the major research institutions of North America, Europe, and the former USSR. At the close of a pupil’s education at AMMOC — the final year of high school — a committee of three professional mathematicians is constituted to examine, systematically, the candidate’s understanding of the research conducted under the guidance of Yaashaa Golovanov. In this way AMMOC bridges the distance between professional study in mathematics, where theoretical abstraction is central, and the IMO curriculum, where rigorous ingenuity within pre-college mathematics is the dominant theme.

  This element of guided early-career research has been integral to the college applications of our protégés — Sarthak, Tisya, Konstantinos, Adelina, and Nihad — each of whom was offered admission with a full scholarship to read for an undergraduate degree in mathematics at Princeton, Caltech, UChicago, KAIST, and Toronto.

  The work has drawn notice beyond the admissions process. The committee at Caltech sent Tisya a “letter of exceptional appreciation” for her project, “Proofs of Some Classical Theorems of Number Theory Using Group Theory” — among the most ambitious scientific undertakings completed under the supervision of her mentor, Yaashaa Golovanov. The Office of Admissions at the University of Chicago likewise wrote to the founder of AMMOC in appreciation of his tireless work as an educator, observing that his students are fortunate in a teacher who works hard and cares for their academic advancement.

• O-Online Functioning as a Deliberate Design of Serious Scientific Education.

  The wholly online functioning of AMMOC gives it a distinctive standing among programmes of its kind, for its very conception grew out of a reflection upon the mathematical maturity of high school students matriculating into mathematics at the leading universities.

  University mathematicians are frequently critical of the preparation of the present generation of entering undergraduates. Their criticism is commonly read as a call for more material in the syllabus; in truth the concern is subtler than that reading allows. AMMOC is committed to mathematizing its protégés to the standard that mathematicians at the foremost universities actually look for in incoming students. That the protégés of the inaugural class have academically impressed several mathematicians who have delivered invited lectures at the International Congress of Mathematicians is some evidence that the standard can be met — an invitation to address the ICM being widely regarded as the discipline’s equivalent of entry into a hall of fame, and the highest honour open to a professional mathematician.

  Two consequences follow:

  • The standard of rigour in the writing of proofs, and the academic impetus, vision, and feel that the instructor Yaashaa Golovanov conveys to our small and select body of pupils, drawn from more than seventeen countries across six continents, in seminars conducted entirely online, is equal to that of the best offline circles run by professional mathematicians in North America and in the nations of Eastern Europe.
  • Our senior mentees study theoretical mathematics covering the first three years of an undergraduate course, together with its concrete applications to problems set in international competitions at both the school and university level. The lectures carry theoretical content and problems of uncommon difficulty—such as would tax the ingenuity of any research mathematician.

• C-Creation of Mathematical Ability and Its Continual Advancement.

  Every theorem, problem, and definition at AMMOC begins with an attempt made by the pupil. By leading participants through the guided rediscovery of the proofs of classical theorems, we seek to permeate and bring to culmination three qualities:

  • mathematization of the thought process;
  • ingenuity and creativity; and
  • cognitive endurance.

  The consolidation of these qualities in the course of study at AMMOC gives pupils both a form of happiness and a first apprehension of the scientific life that lies before them. We therefore do not measure the mathematical ability of our students. We create it, and we continually advance it.

  Protégés of AMMOC — Tisya, Adelina, Konstantinos, Sarthak, and Nihad Hashimov, Prasanna Mahesh Pawar, Raslene Labbedi, Madani Harouach Valensi — received mentorship of lasting value in the process of successful selection of colleges and prestigious fully funded summer program (SuMAC, PROMYS, UWC) and in research projects in such fields as abstract algebraic structures and topological and differential structures. They continue to received subjectual academic support and needed careeristic guidance from their mentor, Yaashaa Golovanov. 

The culmination of these traits in pupils while learning at AMMOC gives them a sense of happiness and an idea of a culture of scientific life ahead of them. Therefore, we don’t measure the mathematical abilities of students. Instead, we create and continually advance these traits.