I vote for Kronecker.
L.E.J. Brouwer, Hermann Weyl
Kurt Gödel, Georg Cantor, Richard Dedekind
Johann von Neumann,
Karl Friedrich Gauß
Leonhard Euler
Karl Weierstraß
David Hilbert
Mengenlehre, Set theory
My problem is functions of functions.
Numbers are objects. Enumerated functions do not become objects, 
they remain functions.
Infinity is a function; it is not an object.
What are the consequences of treating functions as objects?

Is the apparently stationary earth on which I stand a function? (no) 
Is the rotating earth on which I stand a function? (no) 
Is the rotation of the earth around its polar axis a function? (yes)

Is ascribing function to an object idolatry? (no)
Is motion a function? (yes)
The archetype of function is change.
Change entails the passage of time.
Change may be in situ, as change in quality or intensity, or
Change may be in space, as motion, bounded or unbounded.
Is the change that affects objects a function? (yes)
Does change which an object undergoes transform it into a function? (no) 

Integration is a finite process.
The Integral as the product of integration, is an object. 

Definition of integral:
a function of which a given function is the derivative, 
i.e. which yields that function when differentiated, 
and which may express the area under the curve of a graph of the function.

My problem: that an integral is both an object and a function.

What does it mean to designate an object as a function? 
What does it mean to have faith that a changing object is a function? 

Hebrews 11:
1. Now faith is the substance of things hoped for, the evidence of things not seen.

1. Ἔστιν δὲ πίστις ἐλπιζομένων ὑπόστασις, πραγμάτων ἔλεγχος οὐ βλεπομένων: 

1. est autem fides sperandorum substantia rerum argumentum non parentum

1. Es ist aber der Glaube eine gewisse Zuversicht des, das man hoffet, und nicht zweifeln an dem, das man nicht siehet. 

1. ES ist aber der Glaube / eine gewisse zuuersicht / des / das man hoffet / 
Vnd nicht zweiueln an dem / das man nicht sihet.

In mathematics, transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite. These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used to provide an ordering of infinite sets.[1][2] The term transfinite was coined by Georg Cantor in 1895,[3][4][5][6] who wished to avoid some of the implications of the word infinite in connection with these objects, which were, nevertheless, not finite.[citation needed] Few contemporary writers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as infinite numbers. Nevertheless, the term "transfinite" also remains in use.

I now think I can understand mathematics as a species of symbolic fiction, 
quite analogous to literary fiction, which is composed by mathematicians
who vie with each other in the framework of their tradition to make their 
inventions appear compelling, necessary and incontrovertible; where the 
compulsion and necessity flow from nature only in so far as nature is the 
basis of the internal qualities of the students' minds. It is the nature of 
the students' minds that once they have assimilated the mathematics, the 
function, the formula, the equation, it will become for them an instrument of 
apperception and intuition: they will henceforth perceive (experience, erleben)
the (objective, outside) world as formed, fashioned, configured by the 
mathematics that has molded their minds. Moreover, the mathematical tool is 
arcane and complex to an extent that its continuing application requires 
persistent and continuing recapitulation and exercise which ultimately, as in 
the case of Cantor and Gödel, consumes the mathematicians' spirits. In other
words, mathematics threatens its acolytes with insanity.