This is the 100th post of this blog. As a very senior (translated as old) blogger here, I take the liberty of posting the 100th post. The honor should have gone to other people, most notably KKK, who wrote almost half of the blogs here. Anyone write, comment and read on this blog actually make significant contributions to the blog and we all hope that you can continue your contributions.

I am going to share an article written by Fields medalist John Milnor and I’d like to share an inspiring quote by him.

*…..Many times major results are obtained by those who are not at all well known, or by people we may know but underestimate, so that we are completely surprised to find that they have accomplished so much. It is wonderful that no one has the power to turn such people off!*

In below is the longer version.

John Milnor

Growing up in the old Fine Hall, Prospects in Mathematics: Invited Talks on the Occasion of the 250th Anniversary of Princeton University . p8-p.9.

……. This talk is about the past, but perhaps I should close by saying something with a bearing on the future, something about my philosophy of mathematics. What I love most about the study of mathematics is its anarchy! *There is no mathematical czar who tells us what direction we must work in, what we must be doing. There are thousands of mathematicians all over the world each going in his or her own direction. Many are exploring the most popular or fashionable directions, but others work in strange or unfashionable directions. *Perhaps many are going the wrong way, but cumulatively the many different directions, the many different approaches, mean that new and often unexpected things will be discovered. I like to picture the frontier of mathematics as a great ragged wall, with the unknown, the unsolved problems, to one side, and with thousands of mathematicians on the other side, each trying to nibble away at different parts of the problem using different approaches. Perhaps most of them don’t get very far, but every now and then one of them breaks through and opens a new area of understanding. Then perhaps another one makes another breakthrough and opens another new area. Sometimes these breakthroughs come together, so that we have different parts of mathematics merging, giving us wide new perspectives. *Often the people who make these breakthroughs are those who are well known, those we expect to obtain good results; but not always. Many times major results are obtained by those who are not at all well known, or by people we may know but underestimate, so that we are completely surprised to find that they have accomplished so much. It is wonderful that no one has the power to turn such people off! Of course they can be discouraged, and often have to fight for recognition, but there are many universities, many places where one can do mathematical research, and no astronomical budget is required.* Thus there is always hope that even people who have unpopular ideas will have a real chance to succeed.

Thank you for your warm encouragement, especially I want to say Milnor is my “hero” in mathematics.

My aim of making this blog is to encourage more people in our department to share whatever math they think are interesting (but not necessary advanced), and sometimes I fail to do this myself. Nearly two years has passed already. Looking back, clearly there are lots of things which we may had done better, and there is still a long way to achieve the goal (hopefully it will as ). As I and many of these bloggers are not in CUHK anymore (and my lack of personal appeal), it seems even harder for us to attract people writing on this blog now. What’s in my mind is that, if there are five to six (or even more) active writers for this blog, each writing about one post per month on the average, is much much better for two or three of us who are writing weekly/bi-weekly (even if the total number of posts are the same in these two cases). For one thing, it is then easier to maintain this blog (and keep it active) if there are more users, and at the same time preventing too much “subject concentration” (which perhaps is happening in this blog).

Therefore I hope Charles and others (perhaps, you?) who are still in CUHK can promote this blog to the fellow schoolmates and at least make them aware of this blog. In my mind, mathematics is all about sharing ideas. It would not be beautiful if no one appreciate it right? Let me end by the quote of another Fields medalist Bill Thurston (which in some sense echoes those of Milnor):

“Mathematics is a process of staring hard enough with enough perseverenceat at the fog of muddle and confusion to eventually break through to improved clarity. I’m happy when I can admit, at least to myself, that my thinking is muddled, and I try to overcome the embarassment that I might reveal ignorance or confusion. Over the years, this has helped me develop clarity in some things, but I remain muddled in many others. I enjoy questions that seem honest, even when they admit or reveal confusion, in preference to questions that appear designed to project sophistication. “