In 1610, Galileo published his *Sidereus Nuncius,* the first publication to make known the new astronomical discoveries made with the recently invented telescope.

Although, one should also emphasise that although Galileo was the first to publish, he was not the first to use the telescope as an astronomical instrument, and during that early phase of telescopic astronomy, roughly 1609-1613, several others independently made the same discoveries. There was, as to be expected, a lot of scepticism within the astronomical community concerning the claimed discoveries. The telescopes available at the time were generally of miserable quality and Galileo’s discoveries proved difficult to replicate. It was the Jesuit mathematicians and astronomers in the mathematics department at the Collegio Romano, who would, after initial difficulties, provide the scientific confirmation that Galileo desperately needed. The man, who led the endeavours to confirm or refute Galileo’s claims was the acting head of the mathematics faculty Christoph Grienberger (the professor, Christoph Clavius, was old and infirm). Grienberger is one of those historical figures, who fades into the background because they made no major discoveries or wrote no important books, but he deserves to be better known, and so this brief sketch of the man and his contributions.

As is all too oft the case with Jesuit scholars in the Early Modern Period, we know almost nothing about Grienberger before he joined the Jesuit Order. There are no know portraits of him. The problems start with his name variously given as Bamberga, Bamberger, Banbergiera, Gamberger, Ghambergier, Granberger, Panberger and a total of nineteen variations, history has settled on Grienberger. He was born 2 July 1561 in Hall a small town in the Tyrol in the west of Austria. That’s all we know till he entered the Jesuit Order in 1580. He studied rhetoric and philosophy in Prague from 1583 to 1584. From 1587 he was a mathematics teacher at the Jesuit university in Olmütz. He began his theology studies, standard for a Jesuit, in Vienna in 1589, also teaching mathematics. His earliest surviving letter to Christoph Clavius, who he had never met but who he describes as his teacher, he had studied the mathematical sciences using Clavius’ books, is dated from 1590. In 1591 he moved to the Collegio Romano, where he became Clavius’ deputy.

In 1595, Clavius went to Naples, the purpose of his journey is not clear, but he was away from Rome for somewhat more than a year. During his absence Grienberger took over direction of the mathematics department at the Collegio Romana. From the correspondence between the two mathematicians, during this period, it becomes very obvious that Grienberger does not enjoy being in the limelight. He complains to Clavius about having to give a commencement speech and also about having to give private tuition to the sons of aristocrats. Upon Clavius’ return he fades once more into the background, only emerging again with the commotion caused by the publication of Galileo’s *Sidereus Nuncius*.

Rumours of Galileo’s discoveries were already making the rounds before publication and, in fact on the day the *Sidereus Nuncius* appeared, the wealthy German, Humanist Markus Welser (1558–1614) from Augsburg wrote to Clavius asking him his opinion on Galileo’s claims.

We know from letters that the Jesuit mathematicians in the Collegio Romano already had a simple telescope and were making astronomical observations before the publication of the *Sidereus Nuncius*. They immediately took up the challenge of confirming or refuting Galileo’s discoveries. However, their telescope was not powerful enough to detect the four newly discovered moons of Jupiter. Grienberger was away in Sicily attending to problems at the Jesuit college there, so it was left to Giovanni Paolo Lembo (c. 1570–1618) to try and construct a telescope good enough to complete the task. We know that Lembo was skilled in this direction because between 1615 and 1617 he taught lens grinding and telescope construction to the Jesuits being trained as missionaries to East Asia at the University of Coimbra.

Lembo’s initial attempts to construct a suitable instrument failed and it was only after Grienberger returned from Sicily that the two of them were able to make progress. At this point Galileo was corresponding with Clavius and urging the Jesuit astronomer on provide the confirmation of his discoveries that he so desperately needed, the general scepsis was very high, but he was not prepared to divulge any details on how to construct good quality telescopes. Eventually, Grienberger and Lembo succeeded in constructing a telescope with which they could observe the moons of Jupiter but only under very good observational conditions. They first observed three of the moons on 14 November 1610 and all four on 16 November.

Clavius wrote to the merchant and mathematician Antonio Santini (1577–1662) in Venice, who had been to first to confirm the existence of the Jupiter moons in 1610, with a telescope that he constructed himself, detailing observation from 22, 23, 26, and 27 November but stating that they were still not certain as to the nature of the moons. Santini relayed this information to Galileo. On 17 December, Clavius wrote to Galileo:

…and so we have seen [the Medici Stars] here in Rome many times. At the end of the letter I will put some observations, from which it follows very clearly that they are not fixed but wandering stars, because they change position with respect to each other and Jupiter.

Much of what we know about the efforts of the Jesuit astronomers under the leadership of Grienberger to build an adequate telescope to confirm Galileo’s discoveries come from a letter that Grienberger wrote to Galileo in February 1611. One interesting aspect of Grienberger’s letter is that the Jesuit astronomers had also been observing Venus and there is good evidence that they discovered the phases of Venus independently at least contemporaneously if not earlier than Galileo. This was proof that Venus, and by analogy probably also Mercury, orbit the Sun and not the Earth. This was the death nell for a pure Ptolemaic geocentric system and the acceptance at a minimum of a Capellan system where the two inner planets orbit the Sun, which orbits the Earth, if not a full blown Tychonic system or even a heliocentric one. This was in 1611 troubling for the conservative leadership of the Jesuit Order, but would eventually lead to them adopting a Tychonic system at the beginning of the 1620s.

Clavius died 6 February 1612 and Grienberger became his official successor as the professor for mathematics at the Collegio Romano, a position he retained until 1633, when he was succeeded in turn by Athanasius Kircher (1602–1680). The was a series of Rules of Modesty in Ignatius of Loyola’s rules for the Jesuit Order and individual Jesuits were expected to self-abnegate. The most extreme aspect of this was that many scientific works were published anonymously as a product of the Order and not the individual. Different Jesuit scholars reacted differently to this principle. On the one hand, Christoph Scheiner (1573–1650), Galileo’s rival in the sunspot dispute and author of the *Rosa Ursina sive Sol*(1626–1630) presented himself as a great astronomer, which did not endear him to his fellow Jesuits.

On the other hand, Grienberger put his name on almost none of his own work preferring it to remain anonymous. There is only a star catalogue and a set of trigonometrical tables that bear his name.

However, as head of the mathematics department at the Collegio Romano he was responsible for controlling and editing all of the publications in the mathematical disciplines that went out from the Jesuit Order and it is know that he made substantial improvements to the works that he edited both in the theoretical parts and in the design of instruments. A good example is the heliotropic telescope, which enables the observer to track the movement of the Sun whilst observing sunspots, illustrated in Scheiner’s *Rosa Ursina*.

This instrument is known to have been designed and constructed by Grienberger, who, however, explicitly declined Scheiner’s offer to add a text under his own name describing its operation. Grienberger also devised a system of gearing theoretical capable of lifting the Earth

Grienberger, admired Galileo and took his side, if only in the background, in Galileo’s dispute with the Aristotelians over floating bodies. He was, however, disappointed by Galileo’s unprovoked and vicious attacks on the Jesuit astronomer Orazio Grassi on the nature of comets and explicitly said that it had cost Galileo the support of the Jesuits in his later troubles. He also clearly stated that if Galileo had been content to propose heliocentricity as a hypothesis, its actual scientific status at the time, he could have avoided his confrontation with the Church.

Élie Diodati (1576–1661) the Calvinist, Genevan lawyer and friend of Galileo, who played a central role in the publication of the *Discorsi*, quoted Grienberger in a letter to Galileo from 25 July 1634, as having said, “If Galileo had recognised the need to maintain the favour of the Fathers of this College, then he would live gloriously in the world, and none of his misfortune would have occurred, and he could have written about any subject, as he thought fit, I say even about the movement of the Earth…”

Several popular secondary sources claim the Grienberger supported the Copernican system. However, there is only hearsay evidence for this claim and not actual proof. He might have but we will never know.

Grienberger made no major discoveries and propagated no influential new theories, which would launch him into the forefront of the big names, big events style of the history of science. However, he played a pivotal role in the very necessary confirmation of Galileo’s telescopic discoveries. He also successfully helmed the mathematical department of the Collegio Romano for twenty years, which produced many excellent mathematicians and astronomers, who in turn went out to all corners of the world to teach others their disciplines. By the time Athanasius Kircher inherited Grienberger’s post there was a world-wide network of Jesuit astronomers, communicating data on important celestial events. One such was Johann Adam Schall von Bell (1591–1666), who studied under Grienberger and went on to lead the Jesuit mission in China.

Science is a collective endeavour and figures such as Grienberger, who serve inconspicuously in the background are as important to the progress of that endeavour as the shrill public figures, such as Galileo, hogging the limelight in the foreground.

Great post, this is the part of the story we never get to hear. The contribution of Grienberger and his colleagues deserves to be much better known. It strikes me that, quite apart from the dominance of the popular Galileo vs the Church narrative, there are two other themes here that arise again and again in science:

(i) While science bestows great honour on the first to discover things (or, more accurately, the first to publicly report the observation or to be credited with the finding etc), we pay very little attention to those involved in the subsequent observations that support the finding – the so-called context of justification. We rely heavily on the latter for verification, yet those scientists are reduced to a supporting role and never receive any attention at all. No wonder priority disputes are so bitter!

(ii) The fact many of the observations by the Jesuits did not receive the attention they deserved because were not published under a particular person’s name has resonance today. I have often heard physicists in industry complain that they did not receive due credit for a discovery because it was published internally

cormac,

Point ii) Yes, it happened to me twice in my career as an applied physicist working in industry. On the first occasion, I was actually paid the fee by my then employer that i would normally have received for publishing. I suspect that there is a considerable amount of IP in ‘trade secrets’ that are never published for commercial reasons. Although patents should allow someone ‘skilled in the art’ to reproduce the invention, in my own experience there are often little ‘tricks of the trade’ that may only be known to employees of the company patenting the invention that make all the difference to how easy it is to reproduce.

The problems start with his name variously given as Bamberga, Bamberger, Banbergiera, Gamberger, Ghambergier, Granberger, Panberger and a total of nineteen variations,….Leading to the supposition that he was a budding con man who took refuge in the college?

I think you have a typo in a date: Markus Welser (1588–1614). The 1588 seems suspicious.

You’re right 🙄

Bamberg was the seat of the royal house of Austria before the show was moved to Vienna. Bamberger means “someone from Bamberg.” Also, Babenburg. German initial B- can easily be heard as P- To me, most of the names look like non-Germans trying to spell the same German name. How Italians might go from B- to Gh- parallels the well-known shift of W (V) to Gh- (e.g., Welf–>Guelph)

In the Early Modern Period before orthography became fixed by dictionaries, one gets all sorts of variant spellings of peoples names. There are something like fifty versions of Copernicus’ family name and a dozen variant spellings of Copernicus

Really enjoyed this one Thony. Keep up the great work.

I think you win the prize for the most stupid comment of the year

😂🤣😂🤣😂

Oh dear! This hurts – poor Thonyc: Now you, Thonyc, try (and maybe are) the most correct historian, and now this!

Galilei:

Galilei was in astronomy a publishing observer. He did not observe most of the astronomical features as the first and he was not a real astronomer. The origin of the dispute with the Jesuits was that Galilei kept the comets for meteorological phenomena as Aristoteles (but Tycho Brahe, the best astronomer before the telescope, had proven that comets are beyond the moon!). Galilei kept Brahe for a fool (and he said it).

Galilei thought also that he had a proof for both the annual as the daily revolution of the earth – but this was nonsense and is nowadays almost forgotten.

He was still confined in antique thinking. He was a genial Renaissance physicist, but not a modern scientist. At the end he was more a disaster in the history of science than a help. The unfortunate comment above proves it. I know this is completely against 19th century novels where Galilei “knows the truth” and which still today determine the public opinion.

Darwin:

The comment about Darwin hurts even more. Darwin is one of the greatest scientists ever. He proved the evolution (instead of a naive creation of all species together a short time ago) in a scientifically exact although elementary way on the Galapagos islands. This was a deep paradigm change long before science could explain what is happening, and against the resistance of the society. With this, he opened the field of modern biology. Today evolution is the main pillar of biology.

In science, it is possible in the hindsight to understand better what happened.

Kehlmann’s presentation of Gauss is factual so inaccurate, it hurts. I#ve never done a statistical analysis but I think you’ll find that Gauss did not in fact publish most of his results.

Gauss is indeed one of the greatest mathematicians of all time but I never use the word genius.

On the Shoulders of Dwarves: title of your next book.

I really do think there should be more books about the little guys and less about the so-called geniuses

I strongly agree. One role of the so-called little guys that is under appreciated lies in the validation, interpretation, and application of novel results. The literary critics have what they call reception theory. Something similar is necessary to understand how the sciences work and sometimes don’t work. Thus developing countries need an an infrastructure of highly educated scientists in order to process work done in other countries. In the U.S. we’d simply say that pitchers need catchers. I don’t know the cricket equivalent.

By “so-called”, do you mean to cast doubt on the existence of actual geniuses? Or is this intended as a restrictive adjective?

In any case, the “genius quotient” seems not to matter all that much for the biography count. Surprisingly few bios of Gauss in English, considering how large he looms in the history of mathematics.

The problem with Gauss is that he’s fundamentally boring. No scandals, no disputes, no murders, no duels, mo mental illness, he just sits in his office churning out one brilliant result after the other and when he’s finished putting them away in a drawer.

Maybe Gauss just avoided dangerous stuff, but boring? Didn’t he spend a lot of time with prostitutes? Perhaps not everyone’s cup of tea, but certainly not boring.

The problem with Gauss is that he’s fundamentally boring.Exactly. And Galileo is the opposite. Plus, never-ending fodder for controversy.

However, Daniel Kehlmann did fantasize a highly readable novel

Die Vermessung der Welt(Measuring the World). He did throw in Humboldt as another protagonist, which helped. But the Gauss segments did not suffer by comparison.churning out one brilliant result after the other and when he’s finished putting them away in a drawerA good line, but in fact Gauss did publish most of his discoveries. Of course, what he

didn’tpublish would have made the undying reputation of two or three mathematicians.Which brings us back to the genius matter. Gauss, I claim, qualifies as a genius, no “so-called” about it. Perhaps you agree?

@thonyc: That’s why I said “fantasize”. I still found it a fun read.

When you see a sci-fi movie or TV show, do you spend all the time complaining that the science isn’t accurate?

”A good line, but in fact Gauss did publish most of his discoveries. Of course, what he didn’t publish would have made the undying reputation of two or three mathematicians.“Gauss is the real deal. Kehlmann’s book is interesting because in the original (in contrast to at least in some translations), all conversation is via indirect quotations.

Kehlmann’s book, as far as he presentation of Gauss is concerned is 100% historical bullshit

I was commenting on the presentation, not the content. 🙂

And of course highly educated scientists are needed in business to interact with research scientists, a need in wealthy countries such as Australia as well as elsewhere.

A literal translation of baseball’s ‘pitchers need catchers’ to cricket would be ‘bowlers need wicketkeepers’, But the analogy doesn’t work very well because catchers shape pitchers’ tactics far more than wicketkeepers shape bowlers’ tactics.

Trolling.

I’m not sure which is worse your ignorance or your arrogance

You know absolutely nothing about me but keep making wildly inaccurate comments about, what I have or haven’t studied, what I know or don’t know, what I have read or not read, my linguistic abilities and then cancelling me off with the term Caucasian, which, despite your ignorant denials, is a term from a discredited 19th century theory of race that is no longer used. All of this is far more insulting that any profanity that I might use.

There is a fundamental rule on the Internet: Don’t feed the trolls! And that is exactly what you are an ignorant, arrogant, conceited, boastful toll. Occasionally I enjoy taking the piss out of people like you but now it has stopped being entertaining, so we have reached the end of the road.

Bye, bye troll!

Not clear

howyou’d do a statistical analysis. A page count?!?Let’s see what he published. Lots of number theory, including not just the Disquistiones, but also the Gaussian integers and Gauss sums. The Gaussian integral. Plenty of celestial mechanics. The foundations of differential geometry, including the “theorema egregium” which introduced intrinsic curvature, and Gauss’s lemma on geodesic coordinate systems. Two seminal results in topology, namely the integral for the linking number (spinoff of his celestial mechanics!) and the Gauss-Bonnet theorem. Gauss’s lemma on the product of primitive polynomials, a foundation stone of commutative algebra. The hypergeometric function. The least-squares method in statistics. In physics, the principle of least constraint, and the divergence theorem. In complex analysis, the fundamental of algebra (with proofs anticipating both topological aspects, and some of Galois theory) and the geometric interpretation. Etc. etc.

Two big unpublished items spring to mind: his work on elliptic functions, and (according to E.T.Bell) Cauchy’s integral theorem. I’m sure there are others—did he ever publish his result on the AGM? But the idea that most of his major results went unpublished is, I believe, just myth.

Certainly your right, but I get the impression that you think no one should use that word.

Oh yes, add noneuclidean geometry to the unpublished list. (Doh!) But frankly, his published work on surfaces mattered more for the development of differential geometry.

One question about the publications of Gauss. I read that one of his proofs of the FTA is based on the Jordan’s curve theorem that was still not proven and also that Gauss published his results only if he was completely satisfied of the rigor of the proof. How these two things conciliates? He didn’t publish it or he was anaware of this gap in the proof?

To quote Hermann Weyl sort-of quoting the Bible: “Sufficient unto the day is the rigor thereof.”

Gauss’s first proof used a topological fact quite similar to the Jordan curve theorem. At the time, this would have been regarded as so obvious as not to need proof. By the late nineteenth century, standards had risen. Gauss used the fact without further remark. So by modern standards, his proof wasn’t fully rigorous.

Not that Gauss or anyone else worried about it at the time (afaik), but a special case of the Jordan-like theorem would have been sufficient, one where the curves in question are continuously differentiable and not merely continuous. The Jordan curve theorem and its ilk are not hard to prove rigorously with this additional hypothesis.

So, when people talks about the rigor of Gauss exagerates a bit, right?

Gauss’s proofs met the highest standards of rigor

for its time. That’s the point of the Weyl quote.His first proof used a topological fact similar to the Jordan curve theorem; later he gave other proofs whose topological underpinnings were more modest, from a modern perspective. One used a big dose of algebra plus these two facts: (a) positive real numbers have real square roots; (b) the intermediate value theorem.

What does it take to give a proof of (a) and (b) that is rigorous by modern standards? Something like Cantor’s or Dedekind’s construction of the real numbers. Neither Gauss nor any of his contemporaries had anything like that available to them. OTOH, I think the Jordan curve theorem and facts (a) and (b) are about equally intuitive.

Ok then, I thought from some expositions that Gauss’ standards of rigor were as high as the modern ones, but now i got it.

Btw, I tried several times to understand exactly when and from who exactly were introduced rigorously the real numers, i usually read that the first was Dedekind in 1872, but by a rapid check on the Wikipedia page I have read that Cantor published his work on the topic in 1871. Can you help me to clarify this?

There is a widespread myth that the concept of mathematical proof is some sort of absolute that has remained constant of the millennia; this is very much not the case. Two very good historical/philosophical works that tackle this problem are Judith V. Grabiner’s paper

Is Mathematical Truth Time Dependent(The American Mathematical Monthly, Vol. 81, No. 4. (April, 1974), pp. 354–365) and Imre Lakatos’ bookProofs and Refutations: The Logic of Mathematical Discovery, eds. John Worrall and Elie Zahar, CUP, 1976.A good example of the historical evolution of the standards of mathematical proof is given by

The Elements of Euclid. It was regarded for two thousand years of the epitome of strict logical proof. However, in the 19th century the German mathematicians, Moritz Pasch (1843–1930) and David Hilbert (1862–1943) both exposed and corrected the logical errors in the axioms and proofs ofThe Elements.The same problem exists in the other mathematical disciplines. For example, there is quite a lot of literature that demonstrates that Newton’s experiments in optics didn’t necessarily prove what he claimed they did.

@Giulio: While Cantor and Dedekind corresponded regularly, their constructions look rather different; neither was copying the other. As for the

needfor a more solid logical foundation for the real numbers, this was widely felt by the late nineteeth century. (Weierstrass also had his version, though as I recall he never published it.) Dauben’s bio of Cantor has a lot more on this. I wouldn’t lay any weight on a slight difference in publication dates. Incidentally, although the Cantor and Dedekind constructions lead to mathematically equivalent structures, both techniques remain important; they have different generalizations.Historians like T.E.Heath later pointed out that Dedekind’s construction was

technicallyclosely related to Eudoxus’s theory of proportion, as expounded in Euclid Book V. However, the viewpoint was quite different.Michael, I certainly interpreted Thony’s comment about ‘so-called’ geniuses as referring to an over-use of the term to describe anyone out of the ordinary. For me a ‘genius’ has to be someone who, if they don’t discover or prove something, it would have remained undiscovered or unproven for several generations.

So, Galileo fails; Newton passes but only for Gravitation, not for Calculus. I can make a case for Gauss passing purely on the quantity of what he proved and published; if he had not existed it would have probably taken other mathematicians the rest of the 19th Century to catch up.

I agree with your viewpoint, but didn’t Thony just say that “Gauss is indeed one of the greatest mathematicians of all time but I would never use the word genius”?

Your comment didn’t fully register with me the first time. Universal gravitation and the inverse square law were “in the air”, witness Hooke and others. Halley’s famous visit to Newton showed that people were already asking for a derivation of the elliptical orbits from the ISL. There are lots of different ways to do this, none really easy, but none all *that* bad once you have calculus (both John Baez and Greg Egan have interesting posts on the topic). Given all the really bright folk around, I think killing off Newton would not have delayed the discovery all that long. Maybe a decade or two.

The problem with your criterion for “genius” is it asks us to roadmap alternative histories. This is a fun but always iffy activity. For example, Einstein famously claimed that without him, general relativity would not have been discovered for a very long time. There is, however, a quantum field theory route to the GR field equations (outlined in exercises in Misner, Thorne, & Wheeler’s “Gravitation”), and lots of people were trying to reconcile gravitation with special relativity (the real motivation for Einstein’s work on this topic). Tens years? Fifty years? A century? Hard to say. (Also, let’s not neglect the role of experimental data in driving theory.)

I don’t have an operational definition of “genius”. I’m still quite comfortable with applying it to Gauss, Newton, Einstein, and a few others.

Before everybody carries on discussing and disputing what I think about the term ‘genius’, I think I should state my view clearly.

If I could, I would banish the word genius entirely out of the history of STEM discourse. It is a rubbish word, which has continually changed its meaning over the centuries, and for which there is no consistent agreed definition today.

Rather than simply saying that X or Y was a genius, one should take the time to describe what the did, what they achieved and the context in which they did it.

“Universal gravitation and the inverse square law were “in the air”…”

More than in the air Kepler’s Third Law is mathematically equivalent to the Law of Universal Gravitation, as Newton clearly demonstrates in his

Principia. BTW without using calculus!Michael, we are largely in agreement. ‘Genius’ is certainly hard to define, but I think that we recognise it when we see it. Peebles says much the same as Misner, Thorne and Wheeler in his new book “Cosmology’s Century” (which I recommend if you haven’t read it), but even QFT for the electromagnetic interaction was only developed in the late 1940s, so a QFT for gravitation during the 1950s or thereabouts. I just checked my copy of MTW and it was published in 1973; Feynman’s lectures on Gravitation at CalTech, which used a QFT approach, were during the 1962-63 academic year.

We probably should stop at this point as I don’t want to annoy Thony by going too far from his period.

Right. Although you need the formula for centrifugal force to show the equivalence. However, Hooke and others proposed the ISL explicitly.

I’d regard Newton’s lemma on ovals as an instance where he was far ahead of his time.

OK you win Gauss did publish an awful lot of his results