The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?

— Stephen Hawking

## Stunning Mathematical Models quotations

Lottery: A tax on people who are bad at math.

### All models are wrong, but some are useful.

I'm very good at integral and differential calculus, I know the scientific names of beings animalculous; In short, in matters vegetable, animal, and mineral, I am the very model of a modern Major-General.

What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of "model," is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors.

I took a break from acting for four years to get a degree in mathematics at UCLA, and during that time I had the rare opportunity to actually do research as an undergraduate. And myself and two other people co-authored a new theorem: Percolation and Gibbs States Multiplicity for Ferromagnetic Ashkin-Teller Models on Two Dimensions, or Z2.

### Do not trust financial market risk models.

Despite the predilection of some analysts to model the financial markets using sophisticated mathematics, the markets are governed by behavioral science, not physical science.

The difference is that we have the hardest and most painful evidence that there was a Holocaust. But, for the global warming scenario that is causing such hysteria, we have only a movie made by a politician and mathematical models whose results change drastically when you change a few of the arbitrarily selected variables.

### The core of science is not a mathematical modeling--it is intellectual honesty.

It is a willingness to have our certainties about the world constrained by good evidence and good argument.

If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.

I recognize that I have a unique position to be a role model to young girls because I am doing something that they consider glamorous, which is acting, and yet I took a time to really get my education and study mathematics, and I think math is the cat's meow.

A theory is just a mathematical model to describe the observations.

The good news is that, at least in economics, I've seen movement away from its overemphasis on mathematical models of purely rational behavior to a more eclectic and commonsense approach: research that is, among other things, more respectful of insights from psychology.

### Why does the universe go to all the bother of existing?

For far too long economists have sought to define themselves in terms of their supposedly scientific methods. In fact, those methods rely on an immoderate use of mathematical models, which are frequently no more than an excuse for occupying the terrain and masking the vacuity of the content.

The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us.

The magic of the mechanisms inside each genetic structure saying exactly where that nerve cell should go - the complexity of these mathematical models is beyond human comprehension.

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work.

Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?

In teaching, I wanted to offer a general pharmacology course based on chemical principles, biochemical classification and mathematical modelling. In the event I achieved neither of my ambitions.

Is war an inevitable outcome of competing interests in a complex society? In other words, would war be the same even if human nature were very different? There are mathematical models of large groups working together that lead to conflict on a reliable basis. So there's a whole other view of war that is not psychological at all.

If you go through the list of things that are not possible you're left with a very finite amount of possibilities. The fancy name for this is constraint theory. It's a nonquantitative model, but it's a field of mathematics.

I think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.

It is clear that the building of models is not a purely mechanical process but requires skill of a high order - not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour equations which are reasonable, tentative hypotheses in explaining the behaviour of actual economies.

The once-surprising existence of non-Euclidean models of Euclid's first four axioms can be seen as a sort of mathematical joke.

The standard model gives us an accuracy of ten decimal digits, this is an amazing success that has never been achieved before in science.

Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?): geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness - and not merely conveyed to his mind through the eyes.

We chose to do this work mathematically, which has the advantage of precision but is not always appreciated by readers. It is perhaps for this reason that anthropologists have not shown much interest in these models, unlike economists, for example, for whom the use of mathematics poses no problem. However, one could reach the same conclusions by using just a bit of common sense.

In the popular mind, if Hoyle is remembered it is as the prime mover of the discredited Steady State theory of the universe. "Everybody knows" that the rival Big Bang theory won the battle of the cosmologies, but few (not even astronomers) appreciate that the mathematical formalism of the now-favoured version of Big Bang, called inflation, is identical to Hoyle's version of the Steady State model.

### The space that we're looking through is nine-dimensional.

If you build a mathematical model, the amount of searching that we've done in 50 years is equivalent to scooping one 8-ounce glass out of the Earth's ocean, looking and seeing if you caught a fish. No, no fish in that glass? Well, I don't think you're going to conclude that there are no fish in the ocean. You just haven't searched very well yet. That's where we are.

### One might say the computer is being used to program the child.

In my vision, the child programs the computer, and in doing so, both acquires a sense of mastery over a piece of the most modern and powerful technology and establishes an intense contact with some of the deepest ideas from science, from mathematics, and from the art of intellectual model building.

### The pursuit of learning is not a piece of content that can be taught.

It is a value that teachers model. Only teachers who are avid, internally motivated learners can truly teach their students the joy of learning.

Nothing has done more to render modern economic theory a sterile and irrelevant exercise in autoeroticism than its practitioners’ obsession with mathematical, general-equilibrium models.

When I entered graduate school I had carried out the instructions given to me by my father and had knocked on both Murray Gell-Mann's and Feynman's doors and asked them what they were currently doing. Murray wrote down the partition function for the three-dimensional Ising model and said it would be nice if I could solve it (at least that is how I remember the conversation). Feynman's answer was 'nothing'.

Modern economics is a set of formal models and equations purporting to fully determine human behaviour, at least in the economic realm. And there is no way that uncertainty can be compressed into determinate mathematical models.

There is a history of mathematical models of oligopolistic competition dating from Cournot to the theory of games. There is also a literature generated by institutional economists, lawyers, and administrators interested in formulating and implementing public policy. It has been the tendency of these groups to work almost as though the other did not exist.