innovation

Milestones in Mathematics History


20,000 BC Carved notches in wood represent numbers. 3500 BC Numbers based on place value (base 60) used in Sumeria. The Sumerians had no symbol for zero. They used an empty space to represent a zero in the middle of a number but had no way to represent zero on the end of a number. Thus…

light

Fields Medal: Fundamental Lemma Proof – Prof. Ngo Bao Chau


Links to the original proof: – In French: Fundamental Lemma Proof – Ngo Bao Chau – In English: bodecoban-ngobaochau A talk by David Ben-Zvi on the Fundamental Lemma for a broad graduate audience at The University of Texas at Austin: The Fundamental Lemma, abstract: I will give a gentle overview of the ideas surrounding the Fundamental Lemma and…

300px-BPTI_seq_ribbon_sticks

Unsolved Problems in Chemistry


Organic chemistry problems Solvolysis of the norbornyl cation: Why is the norbornyl cation so stable? Is it symmetrical? If so, why? This problem has been largely settled for the unsubstituted norbornyl cation, but not for the substituted cation. See Non-classical ion. On water reactions: Why are some organic reactions accelerated at the water-organic interface?[2] What is the…

300px-Mass_Properties

Unsolved Problems in Physics


  Theoretical problems The following problems are either fundamental theoretical problems, or theoretical ideas which lack experimental evidence and are in search of one, or both, as most of them are. Some of these problems are strongly interrelated. For example, extra dimensions or supersymmetry may solve the hierarchy problem. It is thought that a full theory of quantum gravity…