In the fourth grade, out of curiosity I went to the library and took out a book on first year algebra. I taught myself first year algebra in a month, and went back for the second year algebra book.

The fraternity participated in all three interfraternity sports competitions - football, basketball, and baseball, as well as the interfraternity sing and the scholastic achievement contest. ... Scarab helped the Bank of Hope during its collection drive.

The most interesting classes were in ancient Greek, where we read the tragedies, the comedies and the great orators (in the original), and my philosophy classes with Brand Blanshard, a wonderful old scholar who had not changed his philosophical ideas since before WWI.

A manifold is a topological space which is locally like a Euclidean space of some dimension. A two-dimensional manifold is called a surface. A manifold that does not go off to infinity but closes back on itself is called compact. We understand all the possible shapes of compact surfaces. The oriented ones are the sphere, the donut, or donuts with several holes.

Our world space is three dimensional (not counting time). But according to Einstein it is not flat but curved, with curvature appearing as gravity. Of course we have limited experience of only a small part of it, and hence no idea of the total shape. Like the earth, it may curve back on itself, or have wormholes connecting one part to a distant part. So topologists naturally asked what are all the possible shapes of compact three-dimensional manifolds?

On the compact surfaces, the sphere is the only one where every curve bounds a disk; on the others, a curve going around a hole does not. Such a manifold is called simply connected. In 1904, Poincaré conjectured the only compact simply connected three-manifold is the sphere. Famously, a proof of this conjecture was given by Dr Perelman in 2002-2003, using the Ricci flow.

A manifold can carry a metric, measuring the distances between points. In differential geometry, the metric is given as a quadratic function on tangent vectors, measuring the square of their lengths. The length of a path is given by an integral of the lengths of tangent vectors.

The heat equation on a surface (or manifold) is a partial differential evolution equation for a function whose solution describes how the initial given heat will spread by diffusion around the surface (or manifold) to approach a constant equal distribution of heat. The Ricci flow is a partial differential evolution equation for a metric which tries to spread the curvature to approach a constant equal distribution. The idea for the Poincaré conjecture is that if the metric converges to constant positive curvature, the manifold must be the sphere.

It is tempting to describe global analysis as a holistic approach to mathematics. In it the whole geometry or topology of the spaces involved play a role, rather than just the equations describing the behaviour or motion in small areas. Non-linearity, especially that caused by curvature, is a prevalent aspect. A prime example is Eells's most famous article, "Harmonic Mappings of Riemannian Manifolds", published in the American Journal of Mathematics in 1964. Written with J H Sampson of Johns Hopkins University, it founded the theory of "harmonic maps" and the "non-linear heat flow".

This was the first example of using a nonlinear parabolic flow to solve an elliptic equation in geometry, and was my inspiration for creating the Ricci flow. ... By the mid seventies I had begun work on the Ricci flow, and published the first result in 1982 on the case of three dimensional manifolds with positive Ricci curvature.

While most of the arguments are quite elementary, using only the classical maximum principle to estimate various quantities, the convergence arguments are quite delicate and ingenious, and are special to the 3-dimensional case. One key observation is that the geometric entities all satisfy various heat equations. As an added bonus, this beautiful paper is nicely written and should be accessible to many geometers who would like to see a good application of analysis to geometry.

That year [1982], Richard Hamilton, a mathematician at Cornell, published a paper on an equation called the Ricci flow, which he suspected could be relevant for solving Thurston's conjecture and thus the Poincaré conjecture. Like a heat equation, which describes how heat distributes itself evenly through a substance - flowing from hotter to cooler parts of a metal sheet, for example - to create a more uniform temperature, the Ricci flow, by smoothing out irregularities, gives manifolds a more uniform geometry.

This paper is a careful exposition of the Nash-Moser inverse function theorem in a setting that allows one to apply the theorem without the need to prove a new version of it for each new kind of application. Along with this comes much useful extra equipment (a priori estimates) fitting perfectly into the setting. Convincing examples show the theorem with its different "outfits" at work.

This book on harmonic maps between Riemannian manifolds essentially concerns the examination of the case where the manifolds have a boundary. The method of demonstrating the existence of harmonic applications by the convergence, for $t \rightarrow ∞$, of the solutions of the heat equation naturally associated with this problem, is extended in this new case, thus making it possible to obtain the existence of harmonic maps in homotopy classes of boundary varieties, subject to conditions on curvatures. We will also find in this book an introduction to specialised functional spaces for solving this type of problem.

My son Andrew would visit and we could snow ski in winter, and water ski and scuba dive in the summer.

I really wanted to get out of Cornell. It was lovely in the summer, but summer was short. In the fall it rained all the time, and in the winter it snowed all the time, and in the spring it rained all the time. And I have allergies to mould spores, and that was not a healthy place for me to be, so to speak - so motive to leave ...

Yau was especially impressed by Hamilton, as much for his swagger as for his imagination. "I can have fun with Hamilton," Yau told us during the string-theory conference in Beijing. "I can go swimming with him. I go out with him and his girlfriends and all that." Yau was convinced that Hamilton could use the Ricci-flow equation to solve the Poincaré and Thurston conjectures, and he urged him to focus on the problems. "Meeting Yau changed his mathematical life," a friend of both mathematicians said of Hamilton. "This was the first time he had been on to something extremely big. Talking to Yau gave him courage and direction."

In this paper the author surveys some of the basic geometrical properties of the Ricci flow with a view to considering what kind of singularities might form. The Ricci flow was introduced by the author in his celebrated work on deformation of metrics the by Ricci flow on compact 3-manifolds with positive Ricci curvature. It has been found to be a useful tool in the study of Riemannian geometry, both for compact and for open manifolds. ... The paper is well written and delightful to read. Many examples are worked out in detail to illustrate the idea. It gives a rather complete account and up-to-date references on current research on the Ricci flow.

Richard Hamilton is cited for his continuing study of the Ricci flow and related parabolic equations for a Riemannian metric and he is cited in particular for his analysis of the singularities which develop along these flows.

The 2003 Clay Research Award was made to Richard Hamilton for his discovery of the Ricci Flow Equation and its development into one of the most powerful tools of geometric analysis. Hamilton conceived of his work as a way to approach both the Poincaré Conjecture and the Thurston Geometrization Conjecture.

The 2009 Leroy P Steele Prize for Seminal Contribution to Research is awarded to Richard Hamilton for his paper "Three-manifolds with positive Ricci curvature", Journal of Differential Geometry 17 (1982), 255-306.

... for their highly innovative works on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology.

After a more than 20-year effort, one of the greatest mathematicians of this century has landed at the University of Hawaii's flagship campus. Richard Hamilton, a top scholar in the field of geometry, has joined the University of Hawaii Mānoa faculty as an adjunct professor in the Department of Mathematics.

Hamilton's main contributions are focused around geometric analysis and partial differential equations (found in math-centred scientific fields such as physics and engineering). He is most well-known for creating the "Ricci Flow," a ground-breaking partial differential equation in geometry, which is similar to the diffusion of heat and the heat equation. Many other mathematicians have built upon Hamilton's methods to expand our knowledge of the field of geometry.

"Richard Hamilton is one of the most original and influential mathematicians currently working," said Department of Mathematics Professor and Chair Rufus Willett. "We are honoured to have him join our department, and look forward to his having many fruitful interactions with our students and faculty."

Hamilton is also a member of the Academy of Sciences, and received some of the most prestigious mathematics prizes. This includes the $1 million Shaw Prize split equally between Hamilton and Demetrios Christodoulou for their highly innovative works on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology.

'Wonderful' first visit to the islands

Hamilton first came to Hawaii in 1988 after Professor Emeritus Joel Weiner invited him to visit University of Hawaii Mānoa's mathematics department for an academic year.

"I fell in love with the islands the first morning I woke up here," Hamilton said. "The stay was wonderful and the department treated me great. I have in particular developed a strong relationship with Professor George Wilkens (researcher in the field of differential geometry) and more recently with Professor Monique Chyba, with whom I am collaborating on a textbook introducing the basics of differential geometry, as well as how they can be applied to many areas in mathematics, physics and engineering."

Wilkens added, "It took many years to formalise this collaboration and count Dr Hamilton as a member of our faculty. I cannot be more happy and delighted for our department."