Mathematical Simplicity Quotes

A physical law must possess mathematical beauty.

It does not say in the Bible that all laws of nature are expressible linearly!

If mathematics is to be understood widely, we need to emphasise its elegance and its applications. Sometimes it seems that universities want to emphasise how difficult it is!

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.

What is especially striking and remarkable is that in fundamental physics, a beautiful or elegant theory is more likely to be right than a theory that is inelegant. A theory appears to be beautiful or elegant (or simple, if you prefer) when it can be expressed concisely in terms of mathematics we already have. Symmetry exhibits the simplicity. The Foundamental Law is such that the different skins of the onion resemble one another and therefore the math for one skin allows you to express beautifully and simply the phenomenon of the next skin.

So mathematical truth prefers simple words since the language of truth is itself simple.

The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty ... It often happens that the requirements of simplicity and beauty are the same, but where they clash, the latter must take precedence.

Textbook science is beautiful! Textbook science is comprehensible, unlike mere fascinating words that can never be truly beautiful. Elementary science textbooks describe simple theories, and simplicity is the core of scientific beauty. Fascinating words have no power, nor yet any meaning, without the math.

All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.

It is indeed a surprising and fortunate fact that nature can be expressed by relatively low-order mathematical functions.

Math is like water. It has a lot of difficult theories, of course, but its basic logic is very simple. Just as water flows from high to low over the shortest possible distance, figures can only flow in one direction. You just have to keep your eye on them for the route to reveal itself. That’s all it takes. You don’t have to do a thing. Just concentrate your attention and keep your eyes open, and the figures make everything clear to you. In this whole, wide world, the only thing that treats me so kindly is math.

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.

Mathematics is so much easier than words mathematics makes things clear that words merely muddle and confuse and mess up.

My mathematics is simple: one plus one = one.

There's a beauty to math. Math is so simple. It's just one step after the next.

Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as we have succeeded in unraveling fully the natural laws which govern reality, we find them to be expressible by mathematical relations of surprising simplicity and architectonic perfection. It seems to me to be one of the chief objects of mathematical instruction to develop the faculty of perceiving this simplicity and harmony.

If nature leads us to mathematical forms of great simplicity and beauty - by forms I am referring to coherent systems of hypothesis, axioms, etc. - to forms that no one has previously encountered, we cannot help thinking that they are "true," that they reveal a genuine feature of nature... You must have felt this too: The almost frightening simplicity and wholeness of relationships which nature suddenly spreads out before us and for which none of us was in the least prepared.

To a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-footed animal is an animal.

The English language is more complex than calculus because numbers don't have nuances.

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

A circumstance which has always appeared wonderful to me, is that such sublime discoveries should have been made by the sole assistance of a quadrant and a little arithmetic.