A Quote by Paul Halmos

The heart of mathematics is its problems.

Paul Halmos

Quote Topics

Heart Mathematics Problems

Quote Author

Paul Halmos
American - Mathematician
March 3, 1916 - October 2, 2006

It is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps... Every new discovery in mathematics, results from an attempt to solve some problem.

Howard Whitley Eves

Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.

Ivars Peterson

The broader the chess player you are, the easier it is to be competitive, and the same seems to be true of mathematics - if you can find links between different branches of mathematics, it can help you resolve problems. In both mathematics and chess, you study existing theory and use that to go forward.

Viswanathan Anand

We in science are spoiled by the success of mathematics. Mathematics is the study of problems so simple that they have good solutions

Whitfield Diffie

We in science are spoiled by the success of mathematics. Mathematics is the study of problems so simple that they have good solutions.

Whitfield Diffie

Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.

Keith Devlin

Mathematics and logic have been proved to be one; a fact from which it seems to follow that mathematics may successfully deal with non-quantitative problems in a much broader sense than was suspected to be possible.

Alfred Korzybski

A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.

G. H. Hardy

If you come from mathematics, as I do, you realize that there are many problems, even classical problems, which cannot be solved by computation alone.

Roger Penrose

I love speculating about solutions to problems in mathematics. I have no interest whatever in sudoku. But I do look at chess and bridge problems in newspapers. I find that relaxing.

Vikram Seth

The heart is a gate-less gate to divinity. Move to the heart. We are all hung up, stuck in the head - that is our problem. The only problem is that we think too much. There is only one solution - get down from the head to the heart. All your problems will disappear. Problems are created by the head. The heart is innocent. The heart is a fountain of love.

Vasant Lad

The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases.

Paul Halmos

Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.

Richard Askey

Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.

Paul Lockhart

May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.